{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":54900,"title":"Find the number of primes less than input","description":"Given an integer n, determine the number of primes less than or equal to n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.5px 8px; transform-origin: 237.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an integer n, determine the number of primes less than or equal to n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(n)\r\n y = n;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 25;\r\ny_correct = 9;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 37;\r\ny_correct = 12;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 5;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":2434635,"edited_by":223089,"edited_at":"2022-10-20T07:05:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":49,"test_suite_updated_at":"2022-10-20T07:05:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-12T15:13:37.000Z","updated_at":"2026-02-15T08:35:09.000Z","published_at":"2022-07-12T15:13:37.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer n, determine the number of primes less than or equal to n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57600,"title":"Extract the prime numbers","description":"Given a list of elements, extract the prime numbers from that array.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 10.4972px; transform-origin: 406.996px 10.5043px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a list of elements, extract the prime numbers from that array.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1,3,4,6,7,9,3,5,11,6432,636451,323423,5454,44363,223,55345,677,5343];\r\ny_correct = [3 7 3 5 11 223 677];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [1,3,4,6,7,9,3,5,11,6432,636,451,3234,23,54,54,443,63,2,23,553,45,677,5,343];\r\ny_correct = [3 7 3 5 11 23 443 2 23 677 5];\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-20T10:59:03.000Z","updated_at":"2026-02-12T19:14:16.000Z","published_at":"2023-01-20T10:59:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of elements, extract the prime numbers from that array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2411,"title":"Largest Prime Number","description":"Given a matrix X, find the largest prime number in X.","description_html":"\u003cp\u003eGiven a matrix X, find the largest prime number in X.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = max(x);\r\nend","test_suite":"%%\r\nx = [1 2 3 9 7];\r\ny_correct = 7;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n\r\n\r\n\r\n%%\r\n\r\nX=[1 2; 7 13;19 23];\r\ny_correct = 23;\r\nassert(isequal(your_fcn_name(X),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":27947,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":151,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-10T16:01:56.000Z","updated_at":"2026-03-04T14:01:30.000Z","published_at":"2014-07-10T16:01:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a matrix X, find the largest prime number in X.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1763,"title":"Primes for Large N: 2^30, System Memory Limit","description":"This Challenge is to further improve the \"primes\" function for speed/memory usage to the Limit of Cody Memory.\r\n\r\nThe Matlab function \"primes\" has a very efficient sieving method but it suffers from memory usage issues, especially on limited memory systems.\r\n\r\nThe \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1761-primes-faster-for-large-n Primes Faster Challenge\u003e gives the first half to maximizing the primes function for optimal memory usage and speed.\r\n\r\nCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\r\n\r\nThe test case of 2^30 pushes the upper limits of Cody memory.\r\n\r\nThe reference solution can process N=2^32 on an 8GB machine in 68sec.\r\n\r\n*Input:* N (max of primes to find)\r\n\r\n*Output:* vector of primes (all primes less than or equal to N)\r\n\r\n*Scoring:* Time to find all primes \u003c 2^30\r\n\r\n*Hints:*\r\n\r\n 1) Doubles use 8 bytes;\r\n 2) The primes method p(((k*k+1)/2):k:q) creates a vector using q/k*8 bytes. This is 8/3 the size of p for k=3 because k is a double. \r\n 3) Segmentation will keep memory usage below limits at the cost of time.\r\n 4) Cody Available Memory appears to be 537.27MB. XP Operating system eats memory.\r\n 5) Usage of profiler and Task Manager combined give performance insights.","description_html":"\u003cp\u003eThis Challenge is to further improve the \"primes\" function for speed/memory usage to the Limit of Cody Memory.\u003c/p\u003e\u003cp\u003eThe Matlab function \"primes\" has a very efficient sieving method but it suffers from memory usage issues, especially on limited memory systems.\u003c/p\u003e\u003cp\u003eThe \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1761-primes-faster-for-large-n\"\u003ePrimes Faster Challenge\u003c/a\u003e gives the first half to maximizing the primes function for optimal memory usage and speed.\u003c/p\u003e\u003cp\u003eCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\u003c/p\u003e\u003cp\u003eThe test case of 2^30 pushes the upper limits of Cody memory.\u003c/p\u003e\u003cp\u003eThe reference solution can process N=2^32 on an 8GB machine in 68sec.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e N (max of primes to find)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e vector of primes (all primes less than or equal to N)\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Time to find all primes \u0026lt; 2^30\u003c/p\u003e\u003cp\u003e\u003cb\u003eHints:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) Doubles use 8 bytes;\r\n2) The primes method p(((k*k+1)/2):k:q) creates a vector using q/k*8 bytes. This is 8/3 the size of p for k=3 because k is a double. \r\n3) Segmentation will keep memory usage below limits at the cost of time.\r\n4) Cody Available Memory appears to be 537.27MB. XP Operating system eats memory.\r\n5) Usage of profiler and Task Manager combined give performance insights.\r\n\u003c/pre\u003e","function_template":"function p = primes_faster_large(n)\r\n% Standard primes will not succeed\r\n p=[];\r\nreturn\r\n\r\n%PRIMES Generate list of prime numbers.\r\n% PRIMES(N) is a row vector of the prime numbers less than or \r\n% equal to N. A prime number is one that has no factors other\r\n% than 1 and itself.\r\n% Class support for input N:\r\n% float: double, single\r\n% See also FACTOR, ISPRIME.\r\n% Copyright 1984-2004 The MathWorks, Inc. \r\n% $Revision: 1.16.4.3 $ $Date: 2010/08/23 23:13:13 $\r\n\r\nif length(n)~=1 \r\n error(message('MATLAB:primes:InputNotScalar')); \r\nend\r\nif n \u003c 2, p = zeros(1,0,class(n)); return, end\r\np = 1:2:n;\r\nq = length(p);\r\np(1) = 2;\r\nfor k = 3:2:sqrt(n)\r\n if p((k+1)/2)\r\n p(((k*k+1)/2):k:q) = 0;\r\n end\r\nend\r\np = p(p\u003e0);\r\n\r\nend","test_suite":"feval(@assignin,'caller','score',55);\r\n%%\r\ntic\r\nassert(isequal(primes_faster_large(1),primes(1)))\r\nassert(isequal(primes_faster_large(2),primes(2)))\r\nfor i=1:10\r\n n=randi(2000,1);\r\n assert(isequal(primes_faster_large(n),primes(n)))\r\nend\r\ntoc\r\n%%\r\ntic\r\nta=clock;\r\n p = primes_faster_large(2^30);\r\nt1=etime(clock,ta); % time in sec\r\nfprintf('P 2^30 %12i %10.3f\\n',length(p),t1)\r\nassert(isequal(length(p),54400028))\r\nassert(all(diff(p)\u003e0))\r\n%assert(isequal(size(unique(p),2),54400028))\r\nptr=randi(7603553,1,10); % small to avoid timeout\r\npchk=double(p(ptr));\r\nassert(all(isprime(pchk)))\r\nfeval( @assignin,'caller','score',floor(min(55,t1)) );\r\ntoc\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2013-08-07T00:23:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-30T19:43:11.000Z","updated_at":"2025-06-07T08:19:24.000Z","published_at":"2013-07-31T04:12:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to further improve the \\\"primes\\\" function for speed/memory usage to the Limit of Cody Memory.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Matlab function \\\"primes\\\" has a very efficient sieving method but it suffers from memory usage issues, especially on limited memory systems.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1761-primes-faster-for-large-n\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrimes Faster Challenge\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e gives the first half to maximizing the primes function for optimal memory usage and speed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody appears to have 2GB of RAM based upon \\\"out of memory\\\" messages observed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test case of 2^30 pushes the upper limits of Cody memory.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution can process N=2^32 on an 8GB machine in 68sec.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e N (max of primes to find)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector of primes (all primes less than or equal to N)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Time to find all primes \u0026lt; 2^30\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1) Doubles use 8 bytes;\\n2) The primes method p(((k*k+1)/2):k:q) creates a vector using q/k*8 bytes. This is 8/3 the size of p for k=3 because k is a double. \\n3) Segmentation will keep memory usage below limits at the cost of time.\\n4) Cody Available Memory appears to be 537.27MB. XP Operating system eats memory.\\n5) Usage of profiler and Task Manager combined give performance insights.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50038,"title":"Number Puzzles - 014","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA number pr is a prime number and it is an average of the squares of four integers m, n, o, and p. Give an example of [m n o p pr]. The answer is not unique and, therefore, your answer will be checked against the requirement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_014()\r\n y = [1 2 3 4 11];\r\nend","test_suite":"%%\r\ny=puzzle_014();\r\nassert(isequal(y(1)^2+y(2)^2+y(3)^2+y(4)^2,4*y(5)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-29T00:53:59.000Z","updated_at":"2026-02-24T10:37:44.000Z","published_at":"2021-01-29T00:53:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA number pr is a prime number and it is an average of the squares of four integers m, n, o, and p. Give an example of [m n o p pr]. The answer is not unique and, therefore, your answer will be checked against the requirement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55170,"title":"Find all prime factors of the input","description":"Given an input x, find its all prime factors. Return the vector with all factors in ascending order.\r\nEfficiency is the key here.\r\nExample 1:\r\nx = 4\r\ny = [2]\r\nExample 2:\r\nx = 6270\r\ny = [2 3 5 11 19]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 106.875px; transform-origin: 407px 106.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an input x, find its all prime factors. Return the vector with all factors in ascending order.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEfficiency is the key here.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ex = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ey = [2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ex = 6270\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ey = [2 3 5 11 19]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = get_prime_factors(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = [2];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [2];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 17;\r\ny_correct = [17];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 6270;\r\ny_correct = [2 3 5 11 19];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 83160;\r\ny_correct = [2 3 5 7 11];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 27;\r\ny_correct = [3];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 999613;\r\ny_correct = [999613];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 99999989;\r\ny_correct = [99999989];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2434370,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-13T19:38:39.000Z","updated_at":"2026-02-19T14:24:12.000Z","published_at":"2022-07-13T19:38:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input x, find its all prime factors. Return the vector with all factors in ascending order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEfficiency is the key here.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = 4\\ny = [2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = 6270\\ny = [2 3 5 11 19]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52298,"title":"Which Prime","description":"Given two prime numbers, specify the relation between them i.e. - \r\n'Twin Prime', 'Cousin Prime', 'Sexy Prime' or 'None'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.5px 8px; transform-origin: 207.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two prime numbers, specify the relation between them i.e. - \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.5px 8px; transform-origin: 1.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Twin_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwin Prime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e', '\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Cousin_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCousin Prime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e', '\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Sexy_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSexy Prime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e' or 'None'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = whichprime(x)\r\n%primes everywhere\r\n%sort accordingly\r\nend","test_suite":"%%\r\nx = [3 5];\r\ny = 'Twin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [17 37];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [3 7];\r\ny = 'Cousin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [5 11];\r\ny = 'Sexy Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [7 11];\r\ny = 'Cousin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [103 3];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [13 11];\r\ny = 'Twin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [101 107];\r\ny = 'Sexy Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [139 137];\r\ny = 'Twin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [397 401];\r\ny = 'Cousin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [3 11];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [313 307];\r\ny = 'Sexy Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [2 5];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [263 269];\r\ny = 'Sexy Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [101 103];\r\ny = 'Twin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [17 7];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [17 13];\r\ny = 'Cousin Prime';\r\nassert(isequal(whichprime(x),y))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2021-07-14T13:56:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-14T13:39:21.000Z","updated_at":"2026-03-03T11:03:32.000Z","published_at":"2021-07-14T13:56:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two prime numbers, specify the relation between them i.e. - \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Twin_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwin Prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e', '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Cousin_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCousin Prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e', '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Sexy_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSexy Prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e' or 'None'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1375,"title":"select the primes of a vector","description":"Find the prime numbers in a vector","description_html":"\u003cp\u003eFind the prime numbers in a vector\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 2 3 4 5 31 67];\r\ny_correct = [2 3 5 31 67];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":12098,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":321,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-22T16:30:19.000Z","updated_at":"2026-02-17T14:58:03.000Z","published_at":"2013-03-22T16:30:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the prime numbers in a vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42483,"title":"Give prime Numbers upto n","description":"You are given a input number x; print all the prime numbers less than equal to x.","description_html":"\u003cp\u003eYou are given a input number x; print all the prime numbers less than equal to x.\u003c/p\u003e","function_template":"function y = prime(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 10;\r\ny_correct = [ 2 3 5 7 ];\r\nassert(isequal(prime(x),y_correct))\r\n\r\n%%\r\nx = 19;\r\ny_correct = [ 2 3 5 7 11 13 17 19 ];\r\nassert(isequal(prime(x),y_correct))\r\n\r\n%%\r\nx = 1;\r\ny_correct = [ ];\r\nassert(isequal(prime(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":47762,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":"2015-08-02T06:07:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-02T06:02:07.000Z","updated_at":"2026-02-19T14:24:46.000Z","published_at":"2015-08-02T06:07:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a input number x; print all the prime numbers less than equal to x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2335,"title":"Find the number that has most primes those less than it","description":"Given an vector x of integer numbers, find the element of x that has the most primes less than it.","description_html":"\u003cp\u003eGiven an vector x of integer numbers, find the element of x that has the most primes less than it.\u003c/p\u003e","function_template":"function y = mostPrimes(x)\r\nend","test_suite":"%%\r\nx = [5 4 7 3 1];\r\ny_correct = 7;\r\nassert(isequal(mostPrimes(x),y_correct));\r\n\r\n%%\r\nx = [5 3 1];\r\ny_correct = 5;\r\nassert(isequal(mostPrimes(x),y_correct));\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":16505,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":71,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-22T04:52:10.000Z","updated_at":"2025-12-18T06:07:24.000Z","published_at":"2014-05-22T04:52:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an vector x of integer numbers, find the element of x that has the most primes less than it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42513,"title":"Is it prime?","description":"Given a number, check whether it is prime or not.\r\n\r\nIf prime output is true, otherwise false.","description_html":"\u003cp\u003eGiven a number, check whether it is prime or not.\u003c/p\u003e\u003cp\u003eIf prime output is true, otherwise false.\u003c/p\u003e","function_template":"function y = prime(x)\r\n y = \r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = 'true';\r\nassert(isequal(prime(x),y_correct))\r\n\r\nx = 4;\r\ny_correct = 'false';\r\nassert(isequal(prime(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":4,"created_by":46868,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":151,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-18T11:21:38.000Z","updated_at":"2026-03-18T23:49:40.000Z","published_at":"2015-08-18T11:21:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a number, check whether it is prime or not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf prime output is true, otherwise false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60948,"title":"Check p² = 24k + 1, p \u003e 3, the 'golden prime squares' equation","description":"Historical context\r\nIn december 2023, I / Nicolas Douillet was working on prime squares properties and I found* the formula :\r\n\r\n \r\n\r\nwhich I named the ‘Christmas eve equation'. From it I then wrote :\r\n\r\n\r\n\r\nand I named it the ‘golden prime squares equation’. These two formulas, which are actually the same one, can easily be proven starting from (note this last formula applies not only to prime numbers). \r\n \r\n* Apparently, I rediscovered it since I found it a posteriori on this excellent French math website : Site de Gérard Villemin\r\n \r\nProblem statement\r\nYour goal here is to check this formula for the first primes less or equal to a given integer m (input). To do so you will simply compute k in a vector. For the two first cases where the formula doesn’t apply -2 and 3- your function should return 0.\r\n \r\nExamples\r\n\r\nIf m = 20 then k = [0, 0, 1, 2, 5, 7, 12, 15], since 5^2 = 24x1 + 1, 7^2 = 24x2 + 1, 11^2 = 24x5 + 1, etc…\r\n\r\nIf m = 40 then k = [0, 0, 1, 2, 5, 7, 12, 15, 22, 35, 40, 57] ; \r\n \r\nFobidden functions\r\n \r\nregexp\r\nstr2num\r\nassignin\r\n \r\nSee also (my file exchange contributions using this equation) :\r\n\r\nIsprime optimus [FAST]\r\nPrime number spiral (my corresponding contribution on my file exchange)\r\nPrime numbers properties II","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1019.47px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 509.733px; transform-origin: 408px 509.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn december 2023, I / \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/profile/authors/8668631?s_tid=user_nav_comm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eNicolas Douillet\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 210.05px 8px; transform-origin: 210.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e was working on prime squares properties and I found* the formula :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"251\" height=\"19\" style=\"width: 251px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.025px 8px; transform-origin: 99.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.7333px 8px; transform-origin: 58.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhich I named the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.4167px 8px; transform-origin: 76.4167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e‘Christmas eve equation'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0417px 8px; transform-origin: 68.0417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. From it I then wrote :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"249\" height=\"19\" style=\"width: 249px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.95px 8px; transform-origin: 57.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand I named it the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.2167px 8px; transform-origin: 99.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e‘golden prime squares equation’\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 215.483px 8px; transform-origin: 215.483px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. These two formulas, which are actually the same one, can easily be proven starting from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"111.5\" height=\"18\" style=\"width: 111.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.033px 8px; transform-origin: 182.033px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (note this last formula applies not only to prime numbers). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 299.367px 8px; transform-origin: 299.367px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e* Apparently, I rediscovered it since I found it a posteriori on this excellent French math website : \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSite de Gérard Villemin\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour goal here is to check this formula for the first primes less or equal to a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.4917px 8px; transform-origin: 45.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003egiven integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.16667px 8px; transform-origin: 8.16667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.8417px 8px; transform-origin: 97.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(input). To do so you will simply compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.575px 8px; transform-origin: 211.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a vector. For the two first cases where the formula doesn’t apply -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e3\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.9083px 8px; transform-origin: 94.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- your function should return 0.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.9833px 8px; transform-origin: 21.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 20\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 82.6333px 8px; transform-origin: 82.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek = [0, 0, 1, 2, 5, 7, 12, 15]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 26.4333px 8px; transform-origin: 26.4333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^2 = 24x\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.075px 8px; transform-origin: 46.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 1, 7^2 = 24x\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.75px 8px; transform-origin: 15.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 1, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 7.4px 8px; transform-origin: 7.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e11\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 26.4333px 8px; transform-origin: 26.4333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^2 = 24x\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 32.0833px 8px; transform-origin: 32.0833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 1, etc…\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.9833px 8px; transform-origin: 21.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 40\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 133.575px 8px; transform-origin: 133.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek = [0, 0, 1, 2, 5, 7, 12, 15, 22, 35, 40, 57] ;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9167px 8px; transform-origin: 64.9167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFobidden functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161.05px 8px; transform-origin: 161.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(my file exchange contributions using this equation) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/171714-isprime-optimus-fast?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-style: italic; \"\u003eIsprime optimus [FAST]\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/171709-prime-numbers-spiral?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime number spiral (my corresponding contribution on my file exchange)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95759\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties II\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = golden_prime_squares(m)\r\n\r\n k = m;\r\n \r\nend","test_suite":"%%\r\nm = 4;\r\nk_correct = [0, 0];\r\nassert(isequal(golden_prime_squares(m),k_correct))\r\n\r\n%%\r\nm = 20;\r\nk_correct = [0, 0, 1, 2, 5, 7, 12, 15];\r\nassert(isequal(golden_prime_squares(m),k_correct))\r\n\r\n%%\r\nm = 40;\r\nk_correct = [0, 0, 1, 2, 5, 7, 12, 15, 22, 35, 40, 57];\r\nassert(isequal(golden_prime_squares(m),k_correct))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('golden_prime_squares.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T06:55:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2025-07-09T05:55:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-06-27T16:53:40.000Z","updated_at":"2026-03-11T11:59:56.000Z","published_at":"2025-06-27T17:08:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn december 2023, I / \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/profile/authors/8668631?s_tid=user_nav_comm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNicolas Douillet\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e was working on prime squares properties and I found* the formula :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall p \\\\in \\\\mathbb{p}, p \\\\geq 5 \\\\Rightarrow \\\\exists k \\\\in \\\\mathbb{N}, \\\\mathbf{p^2 = 24k + 25}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich I named the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e‘Christmas eve equation'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. From it I then wrote :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall p \\\\in \\\\mathbb{p}, p \\\\geq 5 \\\\Rightarrow \\\\exists k \\\\in \\\\mathbb{N}^*, \\\\mathbf{p^2 = 24k + 1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand I named it the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e‘golden prime squares equation’\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. These two formulas, which are actually the same one, can easily be proven starting from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 6n \\\\pm 1, p \\\\geq 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (note this last formula applies not only to prime numbers). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e* Apparently, I rediscovered it since I found it a posteriori on this excellent French math website : \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSite de Gérard Villemin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour goal here is to check this formula for the first primes less or equal to a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egiven integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(input). To do so you will simply compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in a vector. For the two first cases where the formula doesn’t apply -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e- your function should return 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 20\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek = [0, 0, 1, 2, 5, 7, 12, 15]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^2 = 24x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 1, 7^2 = 24x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 1, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e11\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^2 = 24x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 1, etc…\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 40\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek = [0, 0, 1, 2, 5, 7, 12, 15, 22, 35, 40, 57] ;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFobidden functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(my file exchange contributions using this equation) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/171714-isprime-optimus-fast?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIsprime optimus [FAST]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/171709-prime-numbers-spiral?s_tid=prof_contriblnk\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime number spiral (my corresponding contribution on my file exchange)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95759\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties II\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44266,"title":"Sort the prime numbers in each row of a matrix","description":"Considering a 3x3 matrix A, sort the prime numbers of each row in ascending order. For exemple:\r\n\r\n \r\n input A=[5 8 2 4;\r\n 1 11 1 5]\r\n \r\n output B=[2 8 5 4;\r\n 1 5 1 11]\r\n \r\n\r\nYou don't have to sort the other numbers, just the prime numbers.\r\nEnjoy!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 164.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.0833px; transform-origin: 407px 82.0833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 292px 8px; transform-origin: 292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsidering a matrix A, sort the prime numbers of each row in ascending order. For exemple:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 48px 8.5px; transform-origin: 48px 8.5px; \"\u003e input \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 40px 8.5px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 40px 8.5px; \"\u003eA=[5 8 2 4\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 96px 8.5px; transform-origin: 96px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 11 1 5]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 72px 8.5px; transform-origin: 72px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 28px 8.5px; transform-origin: 28px 8.5px; \"\u003eoutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 40px 8.5px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 40px 8.5px; \"\u003eB=[2 8 5 4\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 5 1 11]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 229px 8px; transform-origin: 229px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou don't have to sort the other numbers, just the prime numbers. Enjoy!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function B = SrtPrimesInRows(A)\r\n","test_suite":"%%\r\nA=[5 8 2 4;1 11 1 5] ; \r\nB_correct = [2 8 5 4;1 5 1 11];\r\nassert(isequal(SrtPrimesInRows(A),B_correct))\r\n%%\r\nA=[2 7 5; 1 11 2;2 2 2];\r\nB_correct=[2 5 7;1 2 11;2 2 2];\r\nassert(isequal(SrtPrimesInRows(A),B_correct))\r\n%%\r\nA=[111 12 134;333 654 100000;112227 38 1];\r\nB_correct=A;\r\nassert(isequal(SrtPrimesInRows(A),B_correct))\r\n%%\r\nA=ones(4);\r\nA(2,1:4)=[11 59 7 23];\r\nB_correct=[1 1 1 1;7 11 23 59;1 1 1 1;1 1 1 1];\r\nassert(isequal(SrtPrimesInRows(A),B_correct))\r\n%%\r\nA=reshape(flip(primes(40)),3,4);\r\nB_correct= flipud(reshape(primes(40),3,4));\r\nassert(isequal(SrtPrimesInRows(A),B_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":140751,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2021-04-20T15:13:52.000Z","rescore_all_solutions":false,"group_id":674,"created_at":"2017-07-20T15:29:29.000Z","updated_at":"2026-03-04T15:19:28.000Z","published_at":"2017-07-20T15:29:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsidering a matrix A, sort the prime numbers of each row in ascending order. For exemple:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ input A=[5 8 2 4;\\n 1 11 1 5]\\n\\noutput B=[2 8 5 4;\\n 1 5 1 11]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou don't have to sort the other numbers, just the prime numbers. Enjoy!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45543,"title":"Find the remainder with the factorial of PRIMES?","description":"* Take a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\r\n* calculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\r\n* As mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\r\n* Divide factorial with the remainder (if possible). e.g. 120/5 = 24\r\n\r\nDon't use builtin functions \r\n\r\n primes\r\n\r\n factorial\r\n\r\n mod","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 275.767px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 137.883px; transform-origin: 407px 137.883px; vertical-align: baseline; \"\u003e\u003cul style=\"block-size: 122.6px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 61.3px; transform-origin: 391px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 290px 8px; transform-origin: 290px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTake a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 355px 8px; transform-origin: 355px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecalculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 359px 8px; transform-origin: 359px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 197px 8px; transform-origin: 197px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDivide factorial with the remainder (if possible). e.g. 120/5 = 24\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDon't use builtin functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eprimes\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003efactorial\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emod\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'primes')))\r\nassert(isempty(strfind(filetext, 'factorial')))\r\nassert(isempty(strfind(filetext, 'mod')))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 630;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 49;\r\ny_correct = 3.232790518889602e+58;\r\nassert(abs(your_fcn_name(x)/1e58-y_correct/1e58)\u003c1e-2)\r\n\r\n%%\r\nx = 5;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 17;\r\ny_correct = 6.2270208e+09;\r\nassert(abs(your_fcn_name(x)/1e9-y_correct/1e9)\u003c1e-2)","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":26467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2021-05-20T10:42:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-20T09:50:35.000Z","updated_at":"2025-04-28T21:39:14.000Z","published_at":"2020-05-20T09:54:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTake a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ecalculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDivide factorial with the remainder (if possible). e.g. 120/5 = 24\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDon't use builtin functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[primes\\n\\nfactorial\\n\\nmod]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46848,"title":"Modulo of sum of square of first n primes with 24","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 199.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 99.8px; transform-origin: 407px 99.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the modulo of sum of square of first n primes with 24.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e For n = 1, mod(2^2,24) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e For n = 2, mod(2^2 + 3^2,24) = 13\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e For n = 4, mod(2^2 + 3^2 + 5^2 + 7^2,24) = 15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eNote: n can be very large.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint : refer tag or check the modulo of square of primes(greater than 3) with 24 to observe the pattern\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = modp24(n)\r\n %...rather than a brute force approach, try finding a pattern in primes square and 24 :)\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 4;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 2;\r\ny_correct = 13;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 4;\r\ny_correct = 15;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = 15;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 120;\r\ny_correct = 11;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 1000;\r\ny_correct = 3;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 10^9;\r\ny_correct = 3;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 10^12 + 15;\r\ny_correct = 18;\r\nassert(isequal(modp24(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":442401,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2020-10-17T08:26:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-17T08:22:52.000Z","updated_at":"2026-03-16T11:31:29.000Z","published_at":"2020-10-17T08:26:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the modulo of sum of square of first n primes with 24.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e For n = 1, mod(2^2,24) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e For n = 2, mod(2^2 + 3^2,24) = 13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e For n = 4, mod(2^2 + 3^2 + 5^2 + 7^2,24) = 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: n can be very large.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint : refer tag or check the modulo of square of primes(greater than 3) with 24 to observe the pattern\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44861,"title":"Ratio between sums of prime and non-prime numbers","description":"Write a function that calculates the ratio between the sum of the prime numbers lower or equal than x, and the sum of the non-prime numbers lower than x.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 91.5px; vertical-align: baseline; perspective-origin: 332px 91.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function that calculates the ratio between the sum of the prime numbers less than or equal to x, and the sum of the non-prime numbers up to the greatest prime less than or equal to x.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if x = 7, then:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 20px; perspective-origin: 329px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003esum_prime = sum([2 3 5 7]) = 17\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003esum_non_prime = sum([1 4 6]) = 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, the desired ratio is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eprime_ratio = sum_prime / sum_non_prime = 17 / 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 7;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 28/38;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 20;\r\ny_correct = 77/113;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 31;\r\ny_correct = 160/336;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 32;\r\ny_correct = 160/336;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 42;\r\ny_correct = 238/623;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2020-09-29T13:58:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-03-01T22:30:26.000Z","updated_at":"2026-04-01T10:59:16.000Z","published_at":"2019-03-01T22:30:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that calculates the ratio between the sum of the prime numbers less than or equal to x, and the sum of the non-prime numbers up to the greatest prime less than or equal to x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if x = 7, then:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[sum_prime = sum([2 3 5 7]) = 17\\nsum_non_prime = sum([1 4 6]) = 11]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, the desired ratio is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[prime_ratio = sum_prime / sum_non_prime = 17 / 11]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52397,"title":"Find the nth composite number.","description":"Everyone heard about the nth prime number. Let's try to find out the nth composite. For example , 1 is the first composite, 10 is the 6th composite number. Write a program that takes the value of n and give the nth composite as output,","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEveryone heard about the nth prime number. Let's try to find out the nth composite. For example , 1 is the first composite, 10 is the 6th composite number. Write a program that takes the value of n and give the nth composite as output,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = nthcomposite(n)\r\n y = n;\r\nend","test_suite":"%%\r\nn = 10;\r\ny_correct = 16; \r\nassert(isequal(nthcomposite(n),y_correct))\r\n\r\n%%\r\nn = 2;\r\ny_correct = 4; \r\nassert(isequal(nthcomposite(n),y_correct))\r\n\r\n%%\r\nn = 100;\r\ny_correct = 132; \r\nassert(isequal(nthcomposite(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":1282418,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":"2021-08-01T15:00:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-31T21:09:28.000Z","updated_at":"2026-03-23T11:03:03.000Z","published_at":"2021-07-31T21:09:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEveryone heard about the nth prime number. Let's try to find out the nth composite. For example , 1 is the first composite, 10 is the 6th composite number. Write a program that takes the value of n and give the nth composite as output,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57869,"title":"Identify de Polignac numbers","description":"The numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, , and . The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\r\nWrite a function that determines whether an odd number is a de Polignac number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.55px 8px; transform-origin: 297.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"125 = 109+2^4\" style=\"width: 96px; height: 19px;\" width=\"96\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"329 = 73+2^8\" style=\"width: 88.5px; height: 19px;\" width=\"88.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 320.392px 8px; transform-origin: 320.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.042px 8px; transform-origin: 255.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isdePolignac(n)\r\n tf = isequal(n,p+2^k);\r\nend","test_suite":"%%\r\nassert(isdePolignac(1))\r\n\r\n%%\r\nassert(~isdePolignac(17))\r\n\r\n%%\r\nassert(~isdePolignac(75))\r\n\r\n%%\r\nassert(isdePolignac(127))\r\n\r\n%%\r\nassert(isdePolignac(331))\r\n\r\n%%\r\nassert(~isdePolignac(531))\r\n\r\n%%\r\nassert(isdePolignac(905))\r\n\r\n%%\r\nassert(isdePolignac(1619))\r\n\r\n%%\r\nassert(~isdePolignac(2261))\r\n\r\n%%\r\nassert(isdePolignac(7535))\r\n\r\n%%\r\nassert(~isdePolignac(10413))\r\n\r\n%%\r\nassert(isdePolignac(21453))\r\n\r\n%%\r\nassert(isdePolignac(45233))\r\n\r\n%%\r\nassert(~isdePolignac(70999))\r\n\r\n%%\r\nassert(~isdePolignac(96415))\r\n\r\n%%\r\nassert(~isdePolignac(121399))\r\n\r\n%%\r\nassert(isdePolignac(148243))\r\n\r\n%%\r\nassert(isdePolignac(172841))\r\n\r\n%%\r\nassert(isdePolignac(201599))\r\n\r\n%%\r\nassert(isdePolignac(227107))\r\n\r\n%%\r\nassert(isdePolignac(253151))\r\n\r\n%%\r\nassert(~isdePolignac(267267))\r\n\r\n%%\r\nassert(~isdePolignac(271271))\r\n\r\n%%\r\nassert(isdePolignac(273421))\r\n\r\n%%\r\nassert(isdePolignac(542459))\r\n\r\n%%\r\nassert(isdePolignac(2000039))\r\n\r\n%%\r\nassert(~isdePolignac(123456789))\r\n\r\n%%\r\nassert(isdePolignac(123456791))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,5893:2:5933)')'),288))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,21671:10:21791)')'),4624))\r\n\r\n%%\r\nfiletext = fileread('isdePolignac.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-29T05:27:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-29T05:27:08.000Z","updated_at":"2025-12-25T08:44:06.000Z","published_at":"2023-03-29T05:27:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"125 = 109+2^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125 = 109+2^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"329 = 73+2^8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e329 = 73+2^8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44862,"title":"Ratio between sum of primes and sum of factors","description":"Write a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.","description_html":"\u003cp\u003eWrite a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 8;\r\ny_correct = 17/6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 28/7;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 1060/14;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2019-03-12T22:32:41.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2019-03-01T22:35:36.000Z","updated_at":"2026-03-16T13:27:48.000Z","published_at":"2019-03-01T22:35:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60661,"title":"The Prime Days of Christmas","description":"On the first day of Christmas my true love sent to me partridges in a pear tree.\r\nOn the second day of Christmas my true love sent to me turtle doves, and partridges in a pear tree.\r\nOn the third day of Christmas my true love sent to me French hens, turtle doves, and partridges in a pear tree.\r\nOn the fourth day of Christmas my true love sent to me calling birds, French hens, turtle doves, and partridges in a pear tree.\r\nOn the fifth day of Christmas my true love sent to me golden rings, calling birds, French hens, turtle doves, and partridges in a pear tree.\r\nAnd so on ...\r\n denotes the -th prime. Suppose that there are days of Christmas. How many gifts am I receiving in total?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 276px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 138px; transform-origin: 407px 138px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11.25px; text-align: left; transform-origin: 384px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the first day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11.25px; text-align: left; transform-origin: 384px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the second day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e turtle doves, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.75px; text-align: left; transform-origin: 384px 21.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the third day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e French hens, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e turtle doves, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the fourth day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e calling birds, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e French hens, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e turtle doves, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the fifth day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49\" height=\"20\" style=\"width: 49px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e golden rings, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e calling birds, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e French hens, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e turtle doves, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAnd so on ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11.25px; text-align: left; transform-origin: 384px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"13.5\" height=\"20\" style=\"width: 13.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e denotes the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th prime. Suppose that there are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e days of Christmas. How many gifts am I receiving in total?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function total = prime_days_of_christmas(n)\r\n total = 364;\r\nend","test_suite":"%%\r\nassert(isequal(prime_days_of_christmas(12), 824))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(2), 7))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(6), 103))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(10), 467))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(1), 2))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(25), 8600))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(365), 47830218))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":332395,"edited_by":332395,"edited_at":"2024-07-30T08:36:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-07-30T08:36:00.000Z","updated_at":"2026-04-02T15:11:40.000Z","published_at":"2024-07-30T08:36:54.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the first day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the second day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_2 = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e turtle doves, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the third day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_3 = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e French hens, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_2 = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e turtle doves, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the fourth day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_4 = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e calling birds, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_3 = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e French hens, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_2 = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e turtle doves, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the fifth day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_5 =11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e golden rings, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_4 = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e calling birds, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_3 = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e French hens, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_2 = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e turtle doves, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnd so on ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e denotes the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th prime. Suppose that there are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e days of Christmas. How many gifts am I receiving in total?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3020,"title":"Prime Letters = Removing","description":"Given a string, remove all the letters which in ASCII Code are prime numbers.\r\n\r\nFor Example:\r\n\r\n s1 = 'Determine which array elements are prime'\r\n\r\nBecomes:\r\n\r\n s2 = 'Dtrin which rry lnts r pri'","description_html":"\u003cp\u003eGiven a string, remove all the letters which in ASCII Code are prime numbers.\u003c/p\u003e\u003cp\u003eFor Example:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003es1 = 'Determine which array elements are prime'\r\n\u003c/pre\u003e\u003cp\u003eBecomes:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003es2 = 'Dtrin which rry lnts r pri'\r\n\u003c/pre\u003e","function_template":"function y = primeLetters(x)\r\n y = x;\r\nend","test_suite":"%%\r\ns1 = 'Determine which array elements are prime'\r\ns2 = 'Dtrin which rry lnts r pri'\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'YeS, I SaY, make me SOme egg, aCe'\r\ns2 = ', , , '\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'qwertyuiopasdfghjklzxcvbnmQWERTYUIOPASDFGHJKLZXCVBNM'\r\ns2 = 'wrtyuiopsdfhjlzxcvbnQWERTUPADFHJKLZXVBNM'\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'DISSappearIng'\r\ns2 = 'Dpprn'\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'One, twO, three'\r\ns2 = 'n, tw, thr'\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'GaSSeS GO'\r\ns2 = ' '\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'SageS Must SaY See'\r\ns2 = ' Must '\r\nassert(isequal(primeLetters(s1),s2))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":4690,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":114,"test_suite_updated_at":"2017-09-27T16:27:47.000Z","rescore_all_solutions":false,"group_id":32,"created_at":"2015-02-15T21:22:59.000Z","updated_at":"2026-03-19T20:01:04.000Z","published_at":"2015-02-15T21:24:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string, remove all the letters which in ASCII Code are prime numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor Example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[s1 = 'Determine which array elements are prime']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBecomes:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[s2 = 'Dtrin which rry lnts r pri']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56260,"title":"Leonardo primes","description":"Leonardo numbers are defined by following recurrence relation:\r\n\r\n\r\n\r\nLeonard prime is Leonardo number which is also prime (see https://en.wikipedia.org/wiki/Leonardo_number). \r\n\r\nFor given n, find all Leonardo primes.\r\n\r\nExample:\r\nn=5;\r\nLeoNumbers=[1 1 3 5 9 15];\r\nPrimes=[2 3 5 7 11 13];\r\nLeoPrimes=[3 5];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 392.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 196.375px; transform-origin: 407px 196.375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLeonardo numbers are defined by following recurrence relation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 61px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 30.5px; text-align: left; transform-origin: 384px 30.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-24px\"\u003e\u003cimg 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\" width=\"273.5\" height=\"61\" style=\"width: 273.5px; height: 61px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLeonard prime is Leonardo number which is also prime (see \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Leonardo_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Leonardo_number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find all Leonardo primes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.75px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.875px; transform-origin: 404px 40.875px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=5;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eLeoNumbers=[1 1 3 5 9 15];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ePrimes=[2 3 5 7 11 13];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eLeoPrimes=[3 5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function LeoPrimes = LeonardoPrimes(n)\r\n LeoPrimes=n;\r\nend","test_suite":"%%\r\nn = 5;\r\nLeoPrimes_correct = [3,5];\r\nassert(isequal(LeonardoPrimes(n),LeoPrimes_correct))\r\n\r\n%%\r\nn = 0;\r\n%LeoPrimes_correct = [];\r\nassert(isempty(LeonardoPrimes(n)))\r\n\r\n%%\r\nn = 25;\r\nLeoPrimes_correct = [3,5,41,67,109,1973,5167];\r\nassert(isequal(LeonardoPrimes(n),LeoPrimes_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":2663765,"edited_by":2663765,"edited_at":"2022-10-10T14:54:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":"2022-10-10T13:22:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-10T12:53:17.000Z","updated_at":"2026-01-13T16:14:23.000Z","published_at":"2022-10-10T12:53:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeonardo numbers are defined by following recurrence relation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL(n) = \\n \\\\begin{cases}\\n 1 \u0026amp; \\\\mbox{if }~n = 0 \\\\\\\\\\n 1 \u0026amp; \\\\mbox{if }~n = 1 \\\\\\\\\\n L(n - 1) + L(n - 2) + 1 \u0026amp; \\\\mbox{if }~n \u0026gt; 1 \\\\\\\\\\n \\\\end{cases}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeonard prime is Leonardo number which is also prime (see \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Leonardo_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Leonardo_number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find all Leonardo primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n=5;\\nLeoNumbers=[1 1 3 5 9 15];\\nPrimes=[2 3 5 7 11 13];\\nLeoPrimes=[3 5];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47803,"title":"Check if the input is a strong prime","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 109.995px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.491px 54.9977px; transform-origin: 406.497px 54.9977px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.5882px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10.2941px; text-align: left; transform-origin: 383.496px 10.2941px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMore information about strong primes on \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Strong_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 79.4118px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.493px 39.7059px; transform-origin: 403.498px 39.7059px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisStrongPrime(11) = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisStrongPrime(2) = 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisStrongPrime(9) = 0; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisStrongPrime(227) = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = isStrongPrime(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nstrongPrimeList = [11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499];\r\nfor idx = 1:100\r\n x = randi([2 500]);\r\n y_correct = 0;\r\n if ismember(x, strongPrimeList)\r\n y_correct = 1;\r\n end\r\n assert(isequal(isStrongPrime(x),y_correct))\r\nend\r\n\r\n%%\r\nx = 4673;\r\ny_correct = 1;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 4677;\r\ny_correct = 0;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 46747;\r\ny_correct = 1;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 46748;\r\ny_correct = 0;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 467317;\r\ny_correct = 1;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 467318;\r\ny_correct = 0;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-04T16:46:35.000Z","updated_at":"2026-04-03T03:56:15.000Z","published_at":"2020-12-04T16:46:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore information about strong primes on \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Strong_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[isStrongPrime(11) = 1;\\nisStrongPrime(2) = 0;\\nisStrongPrime(9) = 0; \\nisStrongPrime(227) = 1;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42704,"title":"prime to each other","description":"Given two integers n1, n2 greater than 1, find out if they have common divisors or are prime to each other. Return \"true\" if they have common divisors and \"false\" if they are prime to each other.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two integers n1, n2 greater than 1, find out if they have common divisors or are prime to each other. Return \"true\" if they have common divisors and \"false\" if they are prime to each other.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = prime_to_each_other(n1, n2)\r\n tf = false;\r\nend","test_suite":"%%\r\nn1 = 3;\r\nn2 = 5;\r\ntf_correct = 0;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 27;\r\nn2 = 123;\r\ntf_correct = 1;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 36;\r\nn2 = 49;\r\ntf_correct = 0;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 27;\r\nn2 = 28;\r\ntf_correct = 0;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 23;\r\nn2 = 69;\r\ntf_correct = 1;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 2;\r\nn2 = 3^5+1;\r\ntf_correct = 1;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":61785,"edited_by":223089,"edited_at":"2023-02-02T13:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":"2023-02-02T13:04:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-01-05T08:30:44.000Z","updated_at":"2025-12-07T18:53:39.000Z","published_at":"2016-01-05T08:30:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two integers n1, n2 greater than 1, find out if they have common divisors or are prime to each other. Return \\\"true\\\" if they have common divisors and \\\"false\\\" if they are prime to each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61052,"title":"Compute the Dedekind psi function","description":"Write a function to compute the Dedekind psi function. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 10.5px; transform-origin: 408px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/DedekindFunction.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eDedekind psi function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = DedekindPsi(n)\r\n y = psi(n);\r\nend","test_suite":"%%\r\nn = 1;\r\ny = DedekindPsi(n);\r\ny_correct = 1;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8;\r\ny = DedekindPsi(n);\r\ny_correct = 12;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 49;\r\ny = DedekindPsi(n);\r\ny_correct = 56;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 312;\r\ny = DedekindPsi(n);\r\ny_correct = 672;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1441;\r\ny = DedekindPsi(n);\r\ny_correct = 1584;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8028;\r\ny = DedekindPsi(n);\r\ny_correct = 16128;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 14035;\r\ny = DedekindPsi(n);\r\ny_correct = 19296;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 85432;\r\ny = DedekindPsi(n);\r\ny_correct = 131040;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6645344;\r\ny = DedekindPsi(n);\r\ny_correct = 10402560;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5533221188;\r\ny = DedekindPsi(n);\r\ny_correct = 9083498112;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\np = primes(1e8);\r\nq = p(randi(length(p)));\r\ny = DedekindPsi(q);\r\nassert(isequal(y,q+1))\r\n\r\n%%\r\np = primes(200);\r\nq = p(randi(length(p)));\r\nn = randi(5);\r\nx = q^n;\r\ny = DedekindPsi(x);\r\nassert(isequal(y,x+x/q))\r\n\r\n%%\r\np = primes(200);\r\nk = unique(randi(length(p),[1 randi(5)]));\r\nq = p(k);\r\nx = prod(q);\r\ny = DedekindPsi(x);\r\nassert(isequal(y,prod(q+1)))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-10-25T15:14:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-25T15:09:34.000Z","updated_at":"2026-02-26T13:49:01.000Z","published_at":"2025-10-25T15:14:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/DedekindFunction.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDedekind psi function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43085,"title":"Primes Checker","description":"Given variable inputs\r\nCheck if they are prime numbers","description_html":"\u003cp\u003eGiven variable inputs\r\nCheck if they are prime numbers\u003c/p\u003e","function_template":"function y = isOrArePrimes(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(isOrArePrimes(x),y_correct))\r\n%%\r\nx = 1;\r\ny = 7;\r\ny_correct = [0 1];\r\nassert(isequal(isOrArePrimes(x,y),y_correct))\r\n%%\r\nx = 2;\r\ny = 17;\r\nz = 20;\r\ny_correct = [1 1 0];\r\nassert(isequal(isOrArePrimes(x,y,z),y_correct))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":0,"created_by":13865,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2016-10-29T17:09:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-06T01:20:45.000Z","updated_at":"2026-02-11T18:07:13.000Z","published_at":"2016-10-06T01:23:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven variable inputs Check if they are prime numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1298,"title":"P-smooth numbers","description":"This Challenge is to find \u003chttps://en.wikipedia.org/wiki/Smooth_number P-smooth number\u003e partial sets given P and a max series value.\r\n\r\nA P-smooth number set of N contains a subset of 1:N integers whose prime factors are all \u003c=P.\r\n\r\nFor P=3 and N=16: P-smooth subset is [1 2 3 4 6 8 9 12 16]. Values 5,7,10,13,14,and 15 are primes \u003e3 or values divisible by primes\u003e3.\r\n\r\nvs = find_psmooth(P,N)\r\n\r\n\r\nSample \u003chttps://oeis.org/A051038 OEIS 11-smooth numbers\u003e\r\n\r\nWhere are P-smooth numbers utilized or present themselves?\r\nUpcoming Challenge solved by P-smooth numbers.","description_html":"\u003cp\u003eThis Challenge is to find \u003ca href = \"https://en.wikipedia.org/wiki/Smooth_number\"\u003eP-smooth number\u003c/a\u003e partial sets given P and a max series value.\u003c/p\u003e\u003cp\u003eA P-smooth number set of N contains a subset of 1:N integers whose prime factors are all \u0026lt;=P.\u003c/p\u003e\u003cp\u003eFor P=3 and N=16: P-smooth subset is [1 2 3 4 6 8 9 12 16]. Values 5,7,10,13,14,and 15 are primes \u0026gt;3 or values divisible by primes\u0026gt;3.\u003c/p\u003e\u003cp\u003evs = find_psmooth(P,N)\u003c/p\u003e\u003cp\u003eSample \u003ca href = \"https://oeis.org/A051038\"\u003eOEIS 11-smooth numbers\u003c/a\u003e\u003c/p\u003e\u003cp\u003eWhere are P-smooth numbers utilized or present themselves?\r\nUpcoming Challenge solved by P-smooth numbers.\u003c/p\u003e","function_template":"function vs = find_psmooth(pmax,vmax)\r\n% pmax is prime max\r\n% vmax is max value of set 1:vmax\r\n vs=1;\r\nend","test_suite":"%%\r\nvs = find_psmooth(2,16);\r\nassert(isequal(vs,[1 2 4 8 16]))\r\n%%\r\nvs = find_psmooth(3,128);\r\nassert(isequal(vs,[1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128]))\r\n%%\r\nvs = find_psmooth(11,73);\r\nassert(isequal(vs,[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72]))\r\n%%\r\npmax=7; vmax=120;\r\nvs = find_psmooth(pmax,vmax);\r\nvs=unique(vs); % Validity checks\r\nvs(vs\u003evmax)=[];\r\nvs(vs\u003c1)=[];\r\nvs=floor(vs);\r\nlength(vs)\r\nif length(vs)==50 % Known length\r\n pass=true;\r\nelse\r\n pass=false;\r\nend\r\npv=primes(vmax);\r\npv(pv\u003c=pmax)=[];\r\nfor i=pv\r\n if any(mod(vs,i)==0) % check for prime divisors \u003epmax\r\n pass=false;\r\n break;\r\n end\r\nend\r\nassert(pass)\r\n%%\r\npmax=11; vmax=300;\r\nvs = find_psmooth(pmax,vmax);\r\nvs=unique(vs); % Validity checks\r\nvs(vs\u003evmax)=[];\r\nvs(vs\u003c1)=[];\r\nvs=floor(vs);\r\nlength(vs)\r\nif length(vs)==104 % Known length\r\n pass=true;\r\nelse\r\n pass=false;\r\nend\r\npv=primes(vmax);\r\npv(pv\u003c=pmax)=[];\r\nfor i=pv\r\n if any(mod(vs,i)==0) % check for prime divisors \u003epmax\r\n pass=false;\r\n break;\r\n end\r\nend\r\nassert(pass)\r\n%%\r\npmax=13; vmax=900;\r\nvs = find_psmooth(pmax,vmax);\r\nvs=unique(vs); % Validity checks\r\nvs(vs\u003evmax)=[];\r\nvs(vs\u003c1)=[];\r\nvs=floor(vs);\r\nlength(vs)\r\nif length(vs)==231% Known length\r\n pass=true;\r\nelse\r\n pass=false;\r\nend\r\npv=primes(vmax);\r\npv(pv\u003c=pmax)=[];\r\nfor i=pv\r\n if any(mod(vs,i)==0) % check for prime divisors \u003epmax\r\n pass=false;\r\n break;\r\n end\r\nend\r\nassert(pass)\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":97,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":44,"created_at":"2013-02-23T23:06:45.000Z","updated_at":"2026-02-07T16:12:25.000Z","published_at":"2016-02-21T23:06:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to find\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Smooth_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eP-smooth number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e partial sets given P and a max series value.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA P-smooth number set of N contains a subset of 1:N integers whose prime factors are all \u0026lt;=P.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor P=3 and N=16: P-smooth subset is [1 2 3 4 6 8 9 12 16]. Values 5,7,10,13,14,and 15 are primes \u0026gt;3 or values divisible by primes\u0026gt;3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evs = find_psmooth(P,N)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSample\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A051038\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS 11-smooth numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere are P-smooth numbers utilized or present themselves? Upcoming Challenge solved by P-smooth numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50933,"title":"Find pairs of primes with the same digit sum","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86px 8px; transform-origin: 86px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe activities in the paper “\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A007513/a007513.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eA New Function from a Table of Primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.5px 8px; transform-origin: 176.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e” involve listing sets of consecutive primes such that the first and last numbers in the set have the same digit sum. For example, if the set size is 7, the first set that qualifies is 5, 7, 11, 13, 17, 19, 23 because the digit sums of 5 and 23 are both 5. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.5px 8px; transform-origin: 126.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes two numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89px 8px; transform-origin: 89px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as input and all sets of size \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.5px 8px; transform-origin: 63.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of primes less than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.5px 8px; transform-origin: 58.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that the first and last numbers in the set have the same digit sum. Return a two-column matrix with the first prime in the set in the first column and the last prime in the set in the second column. Sort the matrix with the first column in increasing order.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = primesEqDigSum1(m,n)\r\n y = f(m,n)\r\nend","test_suite":"%%\r\nm = 2;\r\nn = 100;\r\nassert(isempty(primesEqDigSum1(m,n)))\r\n\r\n%%\r\nm = 2;\r\nn = 2000;\r\ny_correct = [523 541; 1069 1087; 1259 1277; 1759 1777; 1913 1931];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 3;\r\nn = 1000;\r\ny_correct = [109 127; 113 131; 313 331; 503 521; 691 709; 709 727; 769 787; 839 857; 859 877; 863 881; 919 937; 953 971];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 4;\r\nn = 500;\r\ny_correct = [79 97; 139 157; 173 191; 233 251; 239 257; 349 367; 379 397; 439 457; 443 461];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 500;\r\ny_correct = [2 11; 19 37; 23 41; 43 61; 53 71; 149 167; 163 181; 179 197; 263 281; 449 467];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 7;\r\nn = 500;\r\ny_correct = [5 23; 191 227; 193 229; 281 317; 337 373; 373 409];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 10;\r\nn = 500;\r\ny_correct = [17 53; 37 73; 109 163; 173 227];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 19;\r\nn = 5000;\r\ny = primesEqDigSum1(m,n);\r\nassert(isequal(size(y,1),46) \u0026\u0026 isequal(sum(y),[110158 116332]) \u0026\u0026 isequal(y(31:37,1)',[3319 3491 3547 3583 3931 4057 4139]))\r\n\r\n%%\r\nm = 23;\r\nn = 50000;\r\ny = primesEqDigSum1(m,n);\r\nassert(isequal(size(y,1),415) \u0026\u0026 isequal(sum(y),[8631611 8718173]) \u0026\u0026 isequal(y(53,:),[3671 3851]))\r\n\r\n%%\r\nm = 53;\r\nn = 1e6;\r\ny = primesEqDigSum1(m,n);\r\nassert(isequal(size(y,1),5697) \u0026\u0026 isequal(sum(y),[2788369873 2792164201]) \u0026\u0026 isequal(y(3121,:),[538777 539479]))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-14T05:04:14.000Z","updated_at":"2025-08-01T21:24:16.000Z","published_at":"2021-03-14T05:11:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe activities in the paper “\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A007513/a007513.pdf\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA New Function from a Table of Primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e” involve listing sets of consecutive primes such that the first and last numbers in the set have the same digit sum. For example, if the set size is 7, the first set that qualifies is 5, 7, 11, 13, 17, 19, 23 because the digit sums of 5 and 23 are both 5. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes two numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and all sets of size \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of primes less than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that the first and last numbers in the set have the same digit sum. Return a two-column matrix with the first prime in the set in the first column and the last prime in the set in the second column. Sort the matrix with the first column in increasing order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44099,"title":"Find my secret function II","description":"If give my function a x value it will give me a y value, so find the secret of it:\r\nExamples:\r\n\r\ninput x=23 ---- \u003e\u003e\u003e output y=100\r\n\r\ninput x=21 ---- \u003e\u003e\u003e output y= 77\r\n\r\nHint: use tags\r\n","description_html":"\u003cp\u003eIf give my function a x value it will give me a y value, so find the secret of it:\r\nExamples:\u003c/p\u003e\u003cp\u003einput x=23 ---- \u0026gt;\u0026gt;\u0026gt; output y=100\u003c/p\u003e\u003cp\u003einput x=21 ---- \u0026gt;\u0026gt;\u0026gt; output y= 77\u003c/p\u003e\u003cp\u003eHint: use tags\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 23;\r\ny_correct = 100;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 21;\r\ny_correct =77;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = magic(1000);\r\ny_correct = 3.755040202300000e+10;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = magic(5);\r\ny_correct =100;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 1:220;\r\ny_correct = 4438;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":37163,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2017-04-25T11:26:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-04-23T19:43:02.000Z","updated_at":"2026-01-03T11:33:47.000Z","published_at":"2017-04-25T11:26:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf give my function a x value it will give me a y value, so find the secret of it: Examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput x=23 ---- \u0026gt;\u0026gt;\u0026gt; output y=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput x=21 ---- \u0026gt;\u0026gt;\u0026gt; output y= 77\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: use tags\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47808,"title":"Check if the input is an interprime","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 70.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 331.5px 35.4px; transform-origin: 331.5px 35.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 308.5px 10.4px; text-align: left; transform-origin: 308.5px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMore information about interprimes on \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Interprime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 328.5px 20px; transform-origin: 328.5px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 328.5px 10px; transform-origin: 328.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisInterprime(2) = 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 328.5px 10px; transform-origin: 328.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisInterprime(4) = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = isInterprime(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n%%\r\ninterprimeList = [4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99];\r\nfor idx = 1:100\r\n x = randi([2 99]);\r\n y_correct = 0;\r\n if ismember(x,interprimeList)\r\n y_correct = 1;\r\n end\r\n assert(isequal(isInterprime(x),y_correct))\r\nend\r\n\r\n%%\r\nx = 4676;\r\ny_correct = 1;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 46725;\r\ny_correct = 1;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 4622;\r\ny_correct = 0;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n%%\r\nx = 467475;\r\ny_correct = 1;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 467476;\r\ny_correct = 0;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n%% \r\nx = 499994;\r\ny_correct = 1;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n ","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":"2020-12-28T11:41:15.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2020-12-04T17:23:08.000Z","updated_at":"2026-01-16T17:38:20.000Z","published_at":"2020-12-04T17:23:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore information about interprimes on \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Interprime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[isInterprime(2) = 0;\\nisInterprime(4) = 1;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60975,"title":"Check Legendre's conjecture","description":"Context and problem statement\r\nLegendre's conjecture states for a given positive integer n, there always exists at least one prime number p between n² and (n+1²) :\r\n\r\n\r\n\r\nFor a given input n, List the prime number(s) p in the interval ]n^2; (n+1)^2[.\r\n\r\nExamples\r\n\r\nn = 1 =\u003e p = [2, 3];\r\nn = 2 =\u003e p = [5, 7];\r\nn = 10 =\u003e p = [101, 103, 107, 109, 113];\r\nn = 20 =\u003e p = [401, 409, 419, 421, 431, 433, 439];\r\n\r\nForbidden functions / expressions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nProblem 60972. Check Bertrand-Chebyshev's theorem about prime numbers\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 697.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 348.733px; transform-origin: 408px 348.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eContext and problem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.825px 8px; transform-origin: 174.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLegendre's conjecture states for a given positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 144.308px 8px; transform-origin: 144.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethere always exists at least one prime number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3417px 8px; transform-origin: 30.3417px 8px; unicode-bidi: 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margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"224\" height=\"19.5\" style=\"width: 224px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.0667px 8px; transform-origin: 54.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.675px 8px; transform-origin: 81.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, List the prime number(s) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90px 8px; transform-origin: 90px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in the interval ]n^2; (n+1)^2[.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 1 =\u0026gt; p = [2, 3];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 2 =\u0026gt; p = [5, 7];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 124.742px 8px; transform-origin: 124.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 10 =\u0026gt; p = [101, 103, 107, 109, 113];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 156.375px 8px; transform-origin: 156.375px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 20 =\u0026gt; p = [401, 409, 419, 421, 431, 433, 439];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/60972\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 60972. Check Bertrand-Chebyshev's theorem about prime numbers\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = check_legendre_conjecture(n)\r\n p = n;\r\nend","test_suite":"%%\r\nn = 1\r\np_correct = [2, 3];\r\nassert(isequal(check_legendre_conjecture(n),p_correct))\r\n\r\n%%\r\nn = 2\r\np_correct = [5, 7];\r\nassert(isequal(check_legendre_conjecture(n),p_correct))\r\n\r\n%%\r\nn = 10\r\np_correct = [101, 103, 107, 109, 113];\r\nassert(isequal(check_legendre_conjecture(n),p_correct))\r\n\r\n%%\r\nn = 20\r\np_correct = [401, 409, 419, 421, 431, 433, 439];\r\nassert(isequal(check_legendre_conjecture(n),p_correct))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('check_legendre_conjecture.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:05:15.000Z","deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-21T08:10:57.000Z","updated_at":"2026-02-12T07:21:34.000Z","published_at":"2025-07-21T08:28:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eContext and problem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLegendre's conjecture states for a given positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethere always exists at least one prime number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en²\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and (n+1²) :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall n \\\\in \\\\mathbb{N}^*, \\\\exists p \\\\in \\\\mathbb{P}, \\\\mathbf{n^2 \u0026lt; p \u0026lt; (n+1)^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, List the prime number(s) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the interval ]n^2; (n+1)^2[.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 1 =\u0026gt; p = [2, 3];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 2 =\u0026gt; p = [5, 7];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 10 =\u0026gt; p = [101, 103, 107, 109, 113];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 20 =\u0026gt; p = [401, 409, 419, 421, 431, 433, 439];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/problems/60972\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 60972. Check Bertrand-Chebyshev's theorem about prime numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44098,"title":"Find my secret function I","description":"If give my function a x value it will give me a y value, so find the secret of it:\r\nExamples:\r\n\r\ninput x=[2 5 6 8 9] ---- \u003e\u003e\u003e output y=7\r\n\r\ninput x =[1 1 1;\r\n 2 4 8;\r\n 3 9 27] \r\n---- \u003e\u003e\u003e output y= 23\r\n\r\nHint: use tags\r\n","description_html":"\u003cp\u003eIf give my function a x value it will give me a y value, so find the secret of it:\r\nExamples:\u003c/p\u003e\u003cp\u003einput x=[2 5 6 8 9] ---- \u0026gt;\u0026gt;\u0026gt; output y=7\u003c/p\u003e\u003cp\u003einput x =[1 1 1;\r\n 2 4 8;\r\n 3 9 27] \r\n---- \u0026gt;\u0026gt;\u0026gt; output y= 23\u003c/p\u003e\u003cp\u003eHint: use tags\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = magic(9);\r\ny_correct =79;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = magic(5);\r\ny_correct =23;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = magic(1000);\r\ny_correct =999983;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [1 2 5 4 5 6 8 9 52 56 58];\r\ny_correct =53;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":37163,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":"2017-04-25T11:17:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-04-23T19:42:59.000Z","updated_at":"2025-12-28T17:10:21.000Z","published_at":"2017-04-25T11:17:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf give my function a x value it will give me a y value, so find the secret of it: Examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput x=[2 5 6 8 9] ---- \u0026gt;\u0026gt;\u0026gt; output y=7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput x =[1 1 1; 2 4 8; 3 9 27] ---- \u0026gt;\u0026gt;\u0026gt; output y= 23\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: use tags\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":55275,"title":"List the semiprimes","description":"A semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers and are semiprimes, but and are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems 52859, 52990, and 53740. \r\nWrite a function to list the semiprime numbers less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.167px 8px; transform-origin: 297.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"6 = 2x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"9 = 3x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are semiprimes, but \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"8 = 2x2x2\" style=\"width: 84px; height: 18px;\" width=\"84\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"30 = 2x3x5\" style=\"width: 91.5px; height: 18px;\" width=\"91.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 205.517px 8px; transform-origin: 205.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52859\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52859\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52990\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52990\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53740\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e53740\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.75px 8px; transform-origin: 264.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = semiprimes(n)\r\n s = primes(n)/2;\r\nend","test_suite":"%%\r\nn = 100; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 1000; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95 106 111 115 118 119 121 122 123 129 133 134 141 142 143 145 146 155 158 159 161 166 169 177 178 183 185 187 194 201 202 203 205 206 209 213 214 215 217 218 219 221 226 235 237 247 249 253 254 259 262 265 267 274 278 287 289 291 295 298 299 301 302 303 305 309 314 319 321 323 326 327 329 334 335 339 341 346 355 358 361 362 365 371 377 381 382 386 391 393 394 395 398 403 407 411 413 415 417 422 427 437 445 446 447 451 453 454 458 466 469 471 473 478 481 482 485 489 493 497 501 502 505 511 514 515 517 519 526 527 529 533 535 537 538 542 543 545 551 553 554 559 562 565 566 573 579 581 583 586 589 591 597 611 614 622 623 626 629 633 634 635 649 655 662 667 669 671 674 679 681 685 687 689 694 695 697 698 699 703 706 707 713 717 718 721 723 731 734 737 745 746 749 753 755 758 763 766 767 771 778 779 781 785 789 791 793 794 799 802 803 807 813 815 817 818 831 835 838 841 842 843 849 851 862 865 866 869 871 878 879 886 889 893 895 898 899 901 905 913 914 917 921 922 923 926 933 934 939 943 949 951 955 958 959 961 965 973 974 979 982 985 989 993 995 998];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 10000; \r\ns = semiprimes(n);\r\nlen_correct = 2625;\r\nsum_correct = 12736914;\r\nvar_correct = 8.447173943104530e+06;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-8)\r\n\r\n%%\r\nn = 100000; \r\ns = semiprimes(n);\r\nlen_correct = 23378;\r\nsum_correct = 1138479765;\r\nvar_correct = 8.471797671132822e+08;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-6)\r\n\r\n%%\r\nn = 800000; \r\ns = semiprimes(n);\r\nlen_correct = 169660;\r\nsum_correct = 66262251604;\r\nvar_correct = 5.417425253731966e+10;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-4)\r\n\r\n%%\r\nfiletext = fileread('semiprimes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-08-02T01:42:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-02T01:34:03.000Z","updated_at":"2025-08-03T17:11:25.000Z","published_at":"2022-08-02T01:42:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"6 = 2x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6 = 2\\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"9 = 3x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e9 = 3 \\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are semiprimes, but \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"8 = 2x2x2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8 = 2\\\\times2 \\\\times 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"30 = 2x3x5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e30 = 2\\\\times 3 \\\\times 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52859\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52859\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52990\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52990\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53740\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e53740\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51466,"title":"List prime anagrams of a number","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.667px 7.91667px; transform-origin: 380.667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 172 is not prime, but its anagrams 127 and 271 are. Write a function that lists the unique prime anagrams of a number in increasing order. Leading zeros are allowed; for example, a prime anagram of 902 is 29. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = primeAnagrams(n)\r\n y = primes(n);\r\nend","test_suite":"%%\r\nn = 712;\r\ny = primeAnagrams(n);\r\ny_correct = [127 271];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 137;\r\ny = primeAnagrams(n);\r\ny_correct = [137 173 317];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 209;\r\ny = primeAnagrams(n);\r\ny_correct = 29;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 237;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 500;\r\ny = primeAnagrams(n);\r\ny_correct = 5;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 911;\r\ny = primeAnagrams(n);\r\ny_correct = [191 911];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1203;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 1913;\r\ny = primeAnagrams(n);\r\ny_correct = [1193 1319 1913 1931 3119 3191 3911 9311];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1973;\r\ny = primeAnagrams(n);\r\ny_correct = [1973 3719 3917 7193 9137 9173 9371];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 2648;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 5738;\r\ny = primeAnagrams(n);\r\ny_correct = [5387 5783 7583 7853 8537 8573 8753];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 11379;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 13379;\r\ny = primeAnagrams(n);\r\ny_correct = [13397 17393 19373 31379 31397 31793 31973 33179 33791 37139 39317 39371 71339 71933 79133 91373 91733 93371];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 13579;\r\ny = primeAnagrams(n);\r\ny_correct = [13597 13759 15739 15937 15973 17359 17539 19753 31957 37159 37591 37951 39157 51973 53197 53719 53791 53917 57139 57193 71359 71593 73951 75193 75391 75913 75931 79153 79531 91573 91753 95317 95713 95731];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 13779;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 13799;\r\ny = primeAnagrams(n);\r\ny_correct = [13799 13997 17939 19379 19739 19793 19937 19973 31799 37199 37991 39719 39791 39971 71399 71993 79139 79193 79319 91397 93179 93719 93971 97931 99137 99173 99317 99371 99713];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 54321;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 113377;\r\ny = primeAnagrams(n);\r\ny_correct = [117373 133717 137713 171733 173137 173713 311737 313717 317371 317731 373171 717133 717331 731173 731713 737131];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 113399;\r\ny = primeAnagrams(n);\r\ny_correct = [131939 133919 191339 193139 199313 313991 319391 319931 393191 399131 913139 919313 931193 931319 931913 991313];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 246803;\r\ny = primeAnagrams(n);\r\ny_correct = [24683 28463 28643 42683 42863 48623 62483 64283 82463 84263 86243 86423 206483 208463 246803 248063 260483 264083 268043 268403 280463 286043 402863 408263 408623 420683 486023 486203 604823 608423 624803 802463 802643 820643 824063 826403 842063 860423 864203];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1234567;\r\ny = primeAnagrams(n);\r\nlen_correct = 534;\r\nsum_correct = 2405142318;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nn = 3139793;\r\ny = primeAnagrams(n);\r\nlen_correct = 103;\r\nsum_correct = 544898129;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nn = 3917458;\r\ny = primeAnagrams(n);\r\nlen_correct = 708;\r\nsum_correct = 4185941334;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nn = 13456789;\r\ny = primeAnagrams(n);\r\nlen_correct = 4192;\r\nsum_correct = 249146788612;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct) \u0026\u0026 isequal(y(2096),59468713))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-18T14:18:17.000Z","updated_at":"2025-11-29T20:34:18.000Z","published_at":"2021-04-18T14:21:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 172 is not prime, but its anagrams 127 and 271 are. Write a function that lists the unique prime anagrams of a number in increasing order. Leading zeros are allowed; for example, a prime anagram of 902 is 29. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60988,"title":"List numbers that cannot be expressed as the sum of two primes","description":"The Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the other numbers, such as 1, 2, 3, and 11, which cannot? \r\nWrite a function that returns the nth number that cannot be expressed as the sum of two prime numbers.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 36px; transform-origin: 408px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the other numbers, such as 1, 2, 3, and 11, which cannot? \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the nth number that cannot be expressed as the sum of two prime numbers.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = notSum2Primes(n)\r\n y = x;\r\nend","test_suite":"%%\r\nassert(isequal(notSum2Primes(1),1))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(2),2))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(3),3))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(53),185))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(467),1365))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(3035),8101))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(25043),62663))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(453101),1073835))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(1200000),2807765))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(notSum2Primes(4521)),30313))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-29T02:06:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-29T02:04:28.000Z","updated_at":"2026-04-03T11:25:30.000Z","published_at":"2025-07-29T02:06:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the other numbers, such as 1, 2, 3, and 11, which cannot? \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the nth number that cannot be expressed as the sum of two prime numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60969,"title":"Check p = 4n +/- 1, the generic formula for odd prime numbers","description":"Problem statement\r\n\r\nFor all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 :\r\n\r\n\r\n\r\nCheck this formula for some given odd primes in a vector by computing n for each p.\r\n\r\nExamples\r\n\r\np = 17 =\u003e n = 4;\r\n\r\np = 19 =\u003e n = 5;\r\n\r\n p = [3, 5, 7, 11, 13, 17, 19] =\u003e n = [1, 1, 2, 3, 3, 4, 5];\r\n\r\np = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]\r\n =\u003e n = [1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 15, 17, 18, 18, 20, 21, 22, 24];\r\n\r\n\r\nForbidden functions / expressions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\n\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 919.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 459.733px; transform-origin: 408px 459.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.1333px 8px; transform-origin: 80.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor all odd prime number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4583px 8px; transform-origin: 96.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, there exists a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3333px 8px; transform-origin: 30.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esuch that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep = 4n +/- 1 :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"231\" height=\"18\" style=\"width: 231px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 222.1px 8px; transform-origin: 222.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCheck this formula for some given odd primes in a vector by computing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.9417px 8px; transform-origin: 15.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eeach\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e p.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = 17 =\u0026gt; n = 4;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = 19 =\u0026gt; n = 5;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 164.367px 8px; transform-origin: 164.367px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [3, 5, 7, 11, 13, 17, 19] =\u0026gt; n = [1, 1, 2, 3, 3, 4, 5];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 280.842px 8px; transform-origin: 280.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 287.408px 8px; transform-origin: 287.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e =\u0026gt; n = [1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 15, 17, 18, 18, 20, 21, 22, 24];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = check_odd_primes_gen_formula(p)\r\n n = p;\r\nend","test_suite":"%%\r\np = 17;\r\nn_correct = 4;\r\nassert(isequal(check_odd_primes_gen_formula(p),n_correct))\r\n\r\n\r\n%%\r\np = 19;\r\nn_correct = 5;\r\nassert(isequal(check_odd_primes_gen_formula(p),n_correct))\r\n\r\n\r\n%%\r\np = [3, 5, 7, 11, 13, 17, 19];\r\nn_correct = [1, 1, 2, 3, 3, 4, 5];\r\nassert(isequal(check_odd_primes_gen_formula(p),n_correct))\r\n\r\n\r\n%%\r\np = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\r\nn_correct = [1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 15, 17, 18, 18, 20, 21, 22, 24];\r\nassert(isequal(check_odd_primes_gen_formula(p),n_correct))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('check_odd_primes_gen_formula.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-20T05:09:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-20T04:24:51.000Z","updated_at":"2026-02-12T07:13:21.000Z","published_at":"2025-07-20T05:09:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor all odd prime number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, there exists a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003esuch that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 4n +/- 1 :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall p \\\\in \\\\mathbb{P}, p \u0026gt; 2 \\\\Rightarrow \\\\exists n \\\\in \\\\mathbb{N}, p = 4n \\\\pm 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck this formula for some given odd primes in a vector by computing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eeach\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e p.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 17 =\u0026gt; n = 4;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 19 =\u0026gt; n = 5;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [3, 5, 7, 11, 13, 17, 19] =\u0026gt; n = [1, 1, 2, 3, 3, 4, 5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e =\u0026gt; n = [1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 15, 17, 18, 18, 20, 21, 22, 24];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ePrime numbers properties I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47798,"title":"Check if the input is a balanced prime","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 90.1425px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.491px 45.0712px; transform-origin: 406.497px 45.0712px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.5882px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10.2941px; text-align: left; transform-origin: 383.496px 10.2941px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMore about Balanced Primes on \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Balanced_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 59.5588px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.493px 29.7794px; transform-origin: 403.498px 29.7794px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisBalancedPrime(3) = false;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisBalancedPrime(7) = false;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisBalancedPrime(5) = true; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); \"\u003e% since (3+7)/2 = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = isBalancedPrime(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 1;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nlist = [5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103];\r\nfor idx = 1:50\r\n x = randi([10 1103]);\r\n if ismember(x,list)\r\n y_correct = 1;\r\n else\r\n y_correct = 0;\r\n end\r\n assert(isequal(isBalancedPrime(x),y_correct))\r\nend\r\n\r\n\r\n%%\r\nx = 81001;\r\ny_correct = 1;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 81402;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 177487;\r\ny_correct = 1;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 467101;\r\ny_correct = 1;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 467102;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2020-12-04T16:29:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-04T16:26:34.000Z","updated_at":"2020-12-04T16:29:03.000Z","published_at":"2020-12-04T16:26:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore about Balanced Primes on \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Balanced_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[isBalancedPrime(3) = false;\\nisBalancedPrime(7) = false;\\nisBalancedPrime(5) = true; % since (3+7)/2 = 5]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":248,"title":"Twins in a Window","description":"\u003chttp://en.wikipedia.org/wiki/Twin_primes Twin primes\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\r\n\r\nExamples:\r\n\r\n Input lowVal = 10, highVal = 50\r\n Output p is [ 11 13\r\n 17 19\r\n 29 31\r\n 41 43 ]\r\n\r\n Input lowVal = 1000, highVal = 1050\r\n Output p is [ 1019 1021\r\n 1031 1033 ]\r\n","description_html":"\u003cp\u003e\u003ca href=\"http://en.wikipedia.org/wiki/Twin_primes\"\u003eTwin primes\u003c/a\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e Input lowVal = 10, highVal = 50\r\n Output p is [ 11 13\r\n 17 19\r\n 29 31\r\n 41 43 ]\u003c/pre\u003e\u003cpre\u003e Input lowVal = 1000, highVal = 1050\r\n Output p is [ 1019 1021\r\n 1031 1033 ]\u003c/pre\u003e","function_template":"function p = window_twins(lowVal,highVal)\r\n p = 0;\r\nend","test_suite":"%%\r\nlowVal = 10;\r\nhighVal = 50;\r\np = [11 13\r\n 17 19\r\n 29 31\r\n 41 43];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n\r\n%%\r\nlowVal = 1000;\r\nhighVal = 1050;\r\np = [1019 1021\r\n 1031 1033];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n\r\n%%\r\nlowVal = 3120;\r\nhighVal = 3300;\r\np = [ 3167 3169\r\n 3251 3253\r\n 3257 3259];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":161,"test_suite_updated_at":"2012-02-03T17:12:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-03T16:30:52.000Z","updated_at":"2025-12-17T11:07:45.000Z","published_at":"2012-02-03T17:12:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Twin_primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwin primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input lowVal = 10, highVal = 50\\n Output p is [ 11 13\\n 17 19\\n 29 31\\n 41 43 ]\\n\\n Input lowVal = 1000, highVal = 1050\\n Output p is [ 1019 1021\\n 1031 1033 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60970,"title":"Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3","description":"Problem statement\r\n\r\nFor all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 :\r\n\r\n\r\n\r\nCheck this formula for some given odd primes in a vector by computing n for each p.\r\n\r\nExamples\r\n\r\np = 17 =\u003e n = 3;\r\n\r\np = 19 =\u003e n = 3;\r\n\r\n p = [5, 7, 11, 13, 17, 19] =\u003e n = [1, 1, 2, 2, 3, 3];\r\n\r\np = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\r\n =\u003e n = [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16];\r\n\r\n\r\nForbidden functions / expressions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\n\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 919.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 459.733px; transform-origin: 408px 459.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.1333px 8px; transform-origin: 80.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor all odd prime number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.7333px 8px; transform-origin: 37.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003egreater than\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e 3\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4583px 8px; transform-origin: 96.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, there exists a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3333px 8px; transform-origin: 30.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esuch that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep = 6n +/- 1 :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"231\" height=\"18\" style=\"width: 231px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 222.1px 8px; transform-origin: 222.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCheck this formula for some given odd primes in a vector by computing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.9417px 8px; transform-origin: 15.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eeach\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e p.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = 17 =\u0026gt; n = 3;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = 19 =\u0026gt; n = 3;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 148.817px 8px; transform-origin: 148.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [5, 7, 11, 13, 17, 19] =\u0026gt; n = [1, 1, 2, 2, 3, 3];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 275.4px 8px; transform-origin: 275.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 266.008px 8px; transform-origin: 266.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e =\u0026gt; n = [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = check_odd_primes_gen_formula3(p)\r\n n = p;\r\nend","test_suite":"%%\r\np = 17;\r\nn_correct = 3;\r\nassert(isequal(check_odd_primes_gen_formula3(p),n_correct))\r\n\r\n\r\n%%\r\np = 19;\r\nn_correct = 3;\r\nassert(isequal(check_odd_primes_gen_formula3(p),n_correct))\r\n\r\n\r\n%%\r\np = [5, 7, 11, 13, 17, 19];\r\nn_correct = [1, 1, 2, 2, 3, 3];\r\nassert(isequal(check_odd_primes_gen_formula3(p),n_correct))\r\n\r\n\r\n%%\r\np = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\r\nn_correct = [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16];\r\nassert(isequal(check_odd_primes_gen_formula3(p),n_correct))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('check_odd_primes_gen_formula3.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-20T05:22:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-20T04:25:50.000Z","updated_at":"2026-02-12T07:15:38.000Z","published_at":"2025-07-20T05:22:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor all odd prime number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003egreater than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, there exists a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esuch that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 6n +/- 1 :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall p \\\\in \\\\mathbb{P}, p \u0026gt; 3 \\\\Rightarrow \\\\exists n \\\\in \\\\mathbb{N}, p = 6n \\\\pm 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck this formula for some given odd primes in a vector by computing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eeach\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e p.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 17 =\u0026gt; n = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 19 =\u0026gt; n = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [5, 7, 11, 13, 17, 19] =\u0026gt; n = [1, 1, 2, 2, 3, 3];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e =\u0026gt; n = [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1761,"title":"Primes Faster for Large N","description":"This Challenge is to improve the \"primes\" function for speed. This may be accomplished by fixing memory usage.\r\n\r\nThe Matlab function \"primes\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \"out of memory\", significant slow down, or Matlab freeze.\r\n\r\nCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\r\n\r\nThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\r\n\r\nThe reference solution can process N=2^33 on a 16GB machine in 284sec.\r\n\r\n*Input:* N (max of primes to find)\r\n\r\n*Output:* vector of primes (all primes less than or equal to N)\r\n\r\n*Scoring:* Time to find all primes \u003c 2^28\r\n\r\n*Hints:*\r\n\r\n 1) Doubles use 8 bytes; logicals use 1 byte\r\n 2) The method p = p(p\u003e0); is good but can be improved\r\n 3) The method p = 1:2:n; creates a double and is a little slow\r\n 4) Usage of profiler and Task Manager combined give performance insights\r\n\r\n*Related:* \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit Primes 2^30\u003e\r\n\r\n*Matlab 2014a incorporated the speed enhancement of logicals*","description_html":"\u003cp\u003eThis Challenge is to improve the \"primes\" function for speed. This may be accomplished by fixing memory usage.\u003c/p\u003e\u003cp\u003eThe Matlab function \"primes\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \"out of memory\", significant slow down, or Matlab freeze.\u003c/p\u003e\u003cp\u003eCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\u003c/p\u003e\u003cp\u003eThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\u003c/p\u003e\u003cp\u003eThe reference solution can process N=2^33 on a 16GB machine in 284sec.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e N (max of primes to find)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e vector of primes (all primes less than or equal to N)\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Time to find all primes \u0026lt; 2^28\u003c/p\u003e\u003cp\u003e\u003cb\u003eHints:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) Doubles use 8 bytes; logicals use 1 byte\r\n2) The method p = p(p\u0026gt;0); is good but can be improved\r\n3) The method p = 1:2:n; creates a double and is a little slow\r\n4) Usage of profiler and Task Manager combined give performance insights\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eRelated:\u003c/b\u003e \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit\"\u003ePrimes 2^30\u003c/a\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eMatlab 2014a incorporated the speed enhancement of logicals\u003c/b\u003e\u003c/p\u003e","function_template":"function p = primes_faster(n) % The mathworks primes function\r\n%PRIMES Generate list of prime numbers.\r\n% PRIMES(N) is a row vector of the prime numbers less than or \r\n% equal to N. A prime number is one that has no factors other\r\n% than 1 and itself.\r\n%\r\n% Class support for input N:\r\n% float: double, single\r\n%\r\n% See also FACTOR, ISPRIME.\r\n\r\n% Copyright 1984-2004 The MathWorks, Inc. \r\n% $Revision: 1.16.4.3 $ $Date: 2010/08/23 23:13:13 $\r\n\r\nif length(n)~=1 \r\n error(message('MATLAB:primes:InputNotScalar')); \r\nend\r\nif n \u003c 2, p = zeros(1,0,class(n)); return, end\r\np = 1:2:n;\r\nq = length(p);\r\np(1) = 2;\r\nfor k = 3:2:sqrt(n)\r\n if p((k+1)/2)\r\n p(((k*k+1)/2):k:q) = 0;\r\n end\r\nend\r\np = p(p\u003e0);\r\n\r\nend","test_suite":"feval(@assignin,'caller','score',30); %\r\n%%\r\ntic\r\nassert(isequal(primes_faster(1),primes(1)))\r\nassert(isequal(primes_faster(2),primes(2)))\r\nfor i=1:100\r\n n=randi(2000,1);\r\n assert(isequal(primes_faster(n),primes(n)))\r\nend\r\ntoc\r\n%%\r\ntic\r\nta=clock;\r\n p = primes_faster(2^28);\r\nt1=etime(clock,ta); % time in sec\r\n\r\nfprintf('P 2^28 %12i %10.3f\\n',length(p),t1)\r\n\r\nassert(isequal(size(unique(p),2),14630843))\r\n\r\nptr=randi(7603553,1,10); % small to avoid timeout\r\n\r\npchk=double(p(ptr));\r\n\r\nassert(all(isprime(pchk)))\r\n\r\nfeval( @assignin,'caller','score',floor(min(30,t1)) );\r\ntoc","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2013-08-07T00:21:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-30T02:37:44.000Z","updated_at":"2025-12-15T18:33:37.000Z","published_at":"2013-07-30T04:30:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to improve the \\\"primes\\\" function for speed. This may be accomplished by fixing memory usage.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Matlab function \\\"primes\\\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \\\"out of memory\\\", significant slow down, or Matlab freeze.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody appears to have 2GB of RAM based upon \\\"out of memory\\\" messages observed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution can process N=2^33 on a 16GB machine in 284sec.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e N (max of primes to find)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector of primes (all primes less than or equal to N)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Time to find all primes \u0026lt; 2^28\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1) Doubles use 8 bytes; logicals use 1 byte\\n2) The method p = p(p\u003e0); is good but can be improved\\n3) The method p = 1:2:n; creates a double and is a little slow\\n4) Usage of profiler and Task Manager combined give performance insights]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrimes 2^30\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMatlab 2014a incorporated the speed enhancement of logicals\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60972,"title":"Check Bertrand-Chebyshev's theorem about prime numbers","description":"Historical context\r\nBertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory stating that for every integer greater than 1, there always exists at least on prime number between it and its double : \r\n\r\n\r\n\r\nProblem statement\r\nFor a given input n, List the prime number(s) p in the interval ]n; 2n[.\r\n\r\nExamples\r\n\r\nn = 2 =\u003e p = 3;\r\nn = 3 =\u003e p = 5;\r\nn = 7 =\u003e p = [11, 13];\r\nn = 47 =\u003e p = [53, 59, 61, 67, 71, 73, 79, 83, 89];\r\n\r\nForbidden functions / expressions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 697.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 348.733px; transform-origin: 408px 348.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory stating that for every integer greater than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 223.658px 8px; transform-origin: 223.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethere always exists at least on prime number between it and its double : \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"223\" height=\"19.5\" style=\"width: 223px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.0667px 8px; transform-origin: 54.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.675px 8px; transform-origin: 81.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, List the prime number(s) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.8917px 8px; transform-origin: 66.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in the interval ]n; 2n[.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.6833px 8px; transform-origin: 46.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 2 =\u0026gt; p = 3;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.6833px 8px; transform-origin: 46.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 3 =\u0026gt; p = 5;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 68.3333px 8px; transform-origin: 68.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 7 =\u0026gt; p = [11, 13];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 152.467px 8px; transform-origin: 152.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 47 =\u0026gt; p = [53, 59, 61, 67, 71, 73, 79, 83, 89];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = check_Bertrand_Chebyshev_theorem(n)\r\n p = n;\r\nend","test_suite":"%%\r\nn = 2;\r\np_correct = 3;\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%%\r\nn = 3;\r\np_correct = 5;\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%%\r\nn = 7;\r\np_correct = [11, 13];\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%%\r\nn = 11;\r\np_correct = [13, 17, 19];\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%%\r\nn = 47;\r\np_correct = [53, 59, 61, 67, 71, 73, 79, 83, 89];\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('check_Bertrand_Chebyshev_theorem.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:03:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-20T04:28:51.000Z","updated_at":"2026-02-12T07:17:44.000Z","published_at":"2025-07-21T04:30:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory stating that for every integer greater than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethere always exists at least on prime number between it and its double : \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall n \\\\in \\\\mathbb{N}^* - \\\\{ 1 \\\\}, \\\\exists p \\\\in \\\\mathbb{P}, \\\\mathbf{n \u0026lt; p \u0026lt; 2n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, List the prime number(s) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the interval ]n; 2n[.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 2 =\u0026gt; p = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 3 =\u0026gt; p = 5;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 7 =\u0026gt; p = [11, 13];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 47 =\u0026gt; p = [53, 59, 61, 67, 71, 73, 79, 83, 89];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42749,"title":"Find the nearest prime","description":"Given a positive integer 'n', the task is to find a prime number greater than or equal to 'n'. \r\n\r\nExample 1\r\n\r\nIf given 'n' is 10, then the closest prime number greater than 10 is 11 at a distance of 1. So 11 must be returned. \r\n\r\nExample 2\r\n\r\nIf the given 'n' is 17, then the closest prime number is itself at a distance of 0. So 17 must be returned. \r\n\r\nThe returned prime number must be greater than or equal to 'n'. \r\n","description_html":"\u003cp\u003eGiven a positive integer 'n', the task is to find a prime number greater than or equal to 'n'.\u003c/p\u003e\u003cp\u003eExample 1\u003c/p\u003e\u003cp\u003eIf given 'n' is 10, then the closest prime number greater than 10 is 11 at a distance of 1. So 11 must be returned.\u003c/p\u003e\u003cp\u003eExample 2\u003c/p\u003e\u003cp\u003eIf the given 'n' is 17, then the closest prime number is itself at a distance of 0. So 17 must be returned.\u003c/p\u003e\u003cp\u003eThe returned prime number must be greater than or equal to 'n'.\u003c/p\u003e","function_template":"function y = closestPrime(n)\r\n y = 2; \r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 3;\r\nassert(isequal(closestPrime(n),y_correct))\r\n\r\n%%\r\nn = 20;\r\ny_correct = 23;\r\nassert(isequal(closestPrime(n),y_correct))\r\n\r\n%%\r\nn = 86;\r\ny_correct = 89;\r\nassert(isequal(closestPrime(n),y_correct))\r\n\r\n%%\r\nn = 250;\r\ny_correct = 251;\r\nassert(isequal(closestPrime(n),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":66083,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":104,"test_suite_updated_at":"2016-02-23T21:20:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-02-23T21:05:45.000Z","updated_at":"2025-12-11T05:21:59.000Z","published_at":"2016-02-23T21:20:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer 'n', the task is to find a prime number greater than or equal to 'n'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf given 'n' is 10, then the closest prime number greater than 10 is 11 at a distance of 1. So 11 must be returned.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the given 'n' is 17, then the closest prime number is itself at a distance of 0. So 17 must be returned.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe returned prime number must be greater than or equal to 'n'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60965,"title":"List the near-square primes, p = n² + 1 (Landau's 4th problem)","description":"Historical context\r\n\r\nAt the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as \"unattackable at the present state of mathematics\" and are now known as Landau's problems (source : Wiki)\r\n\r\nProblem statement\r\n\r\nThe 4th Landau's problem aalso known as the 'near square primes' asked whether there are infinitely many primes which are of the form . Your task here is to list such primes below a given input integer m.\r\n\r\nExamples\r\n\r\nm = 20 =\u003e p = [2, 5, 17] ;\r\nm = 200 =\u003e p = [2, 5, 17, 37, 101, 197] ;\r\nm = 2000 =\u003e p = [2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601] ;\r\n\r\nFobidden functions\r\nregexp\r\nstr2num\r\nassignin\r\necho\r\n\r\nSee also\r\n\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 719.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 359.517px; transform-origin: 408px 359.517px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.375px 8px; transform-origin: 375.375px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAt the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as \"unattackable at the present state of mathematics\" and are now known as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.825px 8px; transform-origin: 65.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eLandau's problems \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.725px 8px; transform-origin: 44.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(source : Wiki)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.275px 8px; transform-origin: 376.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe 4th Landau's problem aalso known as the 'near square primes' asked whether there are infinitely many primes which are of the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"110.5\" height=\"19\" style=\"width: 110.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.775px 8px; transform-origin: 211.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eYour task here is to list such primes below a given input integer\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 78.575px 8px; transform-origin: 78.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 20 =\u0026gt; p = [2, 5, 17] ;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 125.25px 8px; transform-origin: 125.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 200 =\u0026gt; p = [2, 5, 17, 37, 101, 197] ;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 230.275px 8px; transform-origin: 230.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 2000 =\u0026gt; p = [2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601] ;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9167px 8px; transform-origin: 64.9167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFobidden functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e I\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = list_the_near_square_primes(m)\r\n p = m;\r\nend","test_suite":"%%\r\nm = 20;\r\np_correct = [2,5,17];\r\nassert(isequal(list_the_near_square_primes(m),p_correct))\r\n\r\n\r\n%%\r\nm = 200;\r\np_correct = [2,5,17,37,101,197];\r\nassert(isequal(list_the_near_square_primes(m),p_correct))\r\n\r\n\r\n%%\r\nm = 2000;\r\np_correct = [2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601];\r\nassert(isequal(list_the_near_square_primes(m),p_correct))\r\n\r\n\r\n%% Test forbidden functions\r\nfiletext = fileread('list_the_near_square_primes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:04:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":55,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-17T04:36:44.000Z","updated_at":"2026-02-13T13:18:04.000Z","published_at":"2025-07-17T05:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAt the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as \\\"unattackable at the present state of mathematics\\\" and are now known as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eLandau's problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(source : Wiki)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 4th Landau's problem aalso known as the 'near square primes' asked whether there are infinitely many primes which are of the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = n^2 + 1, n \\\\in \\\\mathbb{N}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYour task here is to list such primes below a given input integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 20 =\u0026gt; p = [2, 5, 17] ;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 200 =\u0026gt; p = [2, 5, 17, 37, 101, 197] ;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 2000 =\u0026gt; p = [2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601] ;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFobidden functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52288,"title":"List Honaker primes","description":"The number 131 is the 32nd prime number. It is a Honaker prime because the sum of its digits (1+3+1) equals the sum of the digits of the index in the list of primes (3+2). \r\nWrite a function to list Honaker primes less than or equal to the input number.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.7417px 7.79167px; transform-origin: 79.7417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 131 is the 32\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003end\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 289px 7.79167px; transform-origin: 289px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e prime number. It is a Honaker prime because the sum of its digits (1+3+1) equals the sum of the digits of the index in the list of primes (3+2). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 239.083px 7.79167px; transform-origin: 239.083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list Honaker primes less than or equal to the input number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = HonakerPrimes(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 1000;\r\ny_correct = [131 263 457];\r\nassert(isequal(HonakerPrimes(n),y_correct))\r\n\r\n%%\r\nn = 6500;\r\ny = HonakerPrimes(n);\r\ny40_45_correct = [5741 5801 5843 5927 6301 6311];\r\nassert(isequal(y(40:45),y40_45_correct))\r\n\r\n%%\r\nn = 100000;\r\ns = sum(HonakerPrimes(n));\r\nsum_correct = 18350014;\r\nassert(isequal(s,sum_correct))\r\n\r\n%%\r\nn = 250000;\r\ny = HonakerPrimes(n);\r\nz_correct = 62.432176393547657;\r\nz = prod(y(2:2:end)./y(1:2:end));\r\nassert(abs(z-z_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 1.5e6;\r\ny = HonakerPrimes(n);\r\nz_correct = 147.5463941840111;\r\nz = prod(y(2:2:end)./y(1:2:end));\r\nassert(abs(z-z_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 5e6;\r\ny = HonakerPrimes(n);\r\nylast5_correct = [4991453 4991473 4991771 4993403 4998001];\r\nz_correct = 276.8019673660703;\r\nz = prod(y(2:2:end)./y(1:2:end-1));\r\nassert(isequal(y(end-4:end),ylast5_correct) \u0026\u0026 abs(z-z_correct)\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('HonakerPrimes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-14T03:41:59.000Z","updated_at":"2025-11-29T20:37:54.000Z","published_at":"2021-07-14T03:43:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 131 is the 32\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003end\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e prime number. It is a Honaker prime because the sum of its digits (1+3+1) equals the sum of the digits of the index in the list of primes (3+2). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list Honaker primes less than or equal to the input number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52293,"title":"Palindromic Primes","description":"A Palindromic Prime is a prime number that is also a palindromic number. (Wiki, OEIS) \r\n\r\nIf given a monotonic series (increment=1) or a single number, give the corresonding palindromic prime.\r\nElse, if given a random array of numbers, check if the numbers in the array are palindromic prime or not.\r\nTake base 10 as the reference.\r\n\r\nExample\r\ninput = 2:5;\r\noutput = [3 5 7 11];\r\n\r\ninput = 17;\r\noutput = 787;\r\n\r\ninput = [7 23 47 11 4 10];\r\noutput = [1 0 0 1 0 0];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 374.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 187.233px; transform-origin: 407px 187.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA Palindromic Prime is a prime number that is also a palindromic number. (\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Palindromic_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWiki\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002385\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOEIS\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 322.5px 8px; transform-origin: 322.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf given a monotonic series (increment=1) or a single number, give the corresonding palindromic prime.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 328px 8px; transform-origin: 328px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eElse, if given a random array of numbers, check if the numbers in the array are palindromic prime or not.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.5px 8px; transform-origin: 98.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTake base 10 as the reference.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.5px 8px; transform-origin: 26.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 163.467px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 81.7333px; transform-origin: 404px 81.7333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003einput = 2:5;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; tab-size: 4; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eoutput = [3 5 7 11];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; tab-size: 4; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003einput = 17;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eoutput = 787;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; 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tab-size: 4; transform-origin: 104px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003einput = [7 23 47 11 4 10];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eoutput = [1 0 0 1 0 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = palinprime(x)\r\n%{Enter your code here%}\r\n\r\n%Stay home, stay safe\r\n%Wear a mask and sanitize\r\n\r\nend","test_suite":"%%\r\nx = 17;\r\ny = 787;\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [101 111 121 131 141 151];\r\ny = [1 0 0 1 0 1];\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = 1:4;\r\ny = [2, 3, 5, 7];\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [22, 58, 84, 85, 94, 136, 160];\r\ny = zeros(1,7);\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\n%The only 2 digit palindromic prime\r\nx = 5;\r\ny = 11;\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [69 420 666];\r\ny = [0 0 0];\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = 11;\r\ny = 313;\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [363 373 383];\r\ny = [0 1 1];\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = 1;\r\ny = 2;\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [313, 323, 333, 343, 353];\r\ny = [1 0 0 0 1];\r\nassert(isequal(palinprime(x),y))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":223089,"edited_by":223089,"edited_at":"2022-06-04T20:18:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2021-07-15T05:24:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-14T10:18:02.000Z","updated_at":"2026-01-21T12:33:19.000Z","published_at":"2021-07-14T12:33:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Palindromic Prime is a prime number that is also a palindromic number. (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Palindromic_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWiki\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A002385\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf given a monotonic series (increment=1) or a single number, give the corresonding palindromic prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eElse, if given a random array of numbers, check if the numbers in the array are palindromic prime or not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTake base 10 as the reference.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[input = 2:5;\\noutput = [3 5 7 11];\\n\\ninput = 17;\\noutput = 787;\\n\\ninput = [7 23 47 11 4 10];\\noutput = [1 0 0 1 0 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60946,"title":"Fermat primes","description":"Historical context\r\n\r\n\r\nThe french mathematician Pierre de Fermat found the formula to find some prime numbers. He thought / conjectured all these numbers where primes, but P(5) is actually the first not prime Fermat number.\r\n\r\n\r\nProblem statement\r\n\r\nFor a given integer m, , list the Fermat prime numbers less or equal to m in a vector fp. Also compute their frequency / ratio f compare to all the primes in the same range. If , your function should return fp = [] and f = 0.\r\n\r\nExamples\r\n\r\nIf m = 10 then fp = [3, 5] and f = 2/3 since 3 = P(0), 5 = P(1), and there are in total three primes in the range [3; 10] ;\r\nIf m = 300 then fp = [3, 5, 17, 257] and f = 4/61 since 3 = P(0), 5 = P(1), 17 = P(2), 257 = P(3) and there are in total 61 prime numbers in the range [3; 300] ; \r\nIf m = 2 then fp = [] and f = 0;\r\n\r\n\r\nTip \r\n\r\n here.\r\n\r\n\r\nFobidden functions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\n\r\n\r\nSee also\r\nProblem 60942. Euler primes\r\nPrime numbers properties II","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1001.03px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 500.517px; transform-origin: 408px 500.517px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 22.5px; text-align: left; transform-origin: 385px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 193.7px 8px; transform-origin: 193.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe french mathematician Pierre de Fermat found the formula \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"96\" height=\"23.5\" style=\"width: 96px; height: 23.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.625px 8px; transform-origin: 132.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to find some prime numbers. He thought / conjectured all these numbers where primes, but P(5) is actually the first not prime Fermat number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.2917px 8px; transform-origin: 60.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.225px 8px; transform-origin: 6.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAkCAYAAAAeor16AAADoklEQVRoQ+2YTahOQRjH792Tj50NCxaUsvFVUpSPkrLzsZV8laRQLHSzQCTJwsfKwgILFlYslfKxwoIFigUrIvb8f5mnpnlnzp175n3PPbdm6t9533Nm5sz85pnneeaMj9VSRGC8qHVtPFYBFhpBBVgBFhIobF4tsAIsJFDYvFrgf4DzpQPSDmmNY/pe10fSySbGfQO4WIP9WGgUU20OvGfSUumFa2wQ+QvIZalO+wbwr5vEEV1fTZVEy/rv1O6LdNhbPKBel3a6Pg/peiPWf98AftUgF7iBYg2jBnlQ79go7UrA/637s6Qn0taZAJAxMqkzHYG8p/dgXT8SAJ/rPtv5fgpy3yzQn0cMJGCxhq4K2xvfuFsC9kDpM0AbbAjymx4cS01oiGQJaB8kXMnaVL8xgDREm6QV0kLpjWfCp/Qb34SvCiMUvuSKe5b0Gy0n2SVIi8zMu2mLRz8mAG+lNOHMl/maCWPGi6Rf0hYHwn+2XvfeRp61ZBZtNmqQzOu2M4JJrb1pCwOLMP7HQSOsU1gRAD92/1fretz9Pq0rC2DPiFyj8lnDBhn256/eLf0h0R4oTQDNgeIDXktzHTwi1kXphMQKXZM2SHsk/5mBT0W42Himcg9LOStZ0stY7kiNJ4eMF7B9N0v4WT+hjgaSFEA6+e5ehgXNkbY5QNzGwpgAPpCyXbIThIX+YftAm3sIzo5cF7zxZXDKqnJTtfZ7HAZywRRAgsFd15CV5YzonwwswaRKuDKcJihs5/NZw8yrFAN3VU2jJ4S8LrNqWXLPjpodtkgBNP9H/UuSvy1W6f/LxKowSd83DuM4Nl3gjJVZ4ZQAGnWsb3mwNcz/8QICiA/J941hu6zl9ipNNzgbis0pmg/GLNC3sFj0MR8X63DSo08GxRAcvvRhB1s1NTSzwKhLigFssjA/uMQ6NP9nXy94OYl3biS2BWAygLvsrhncR1aF3Ughxx341BYDaOkL0W1dMHlyJcsHlwQd+v6PZ+RNRO9o/pSYLgvQJTgWmNPWUymW/hALyD72SVlnYd/CwuDBnC24xOBiaeccGCD8lBqPQQFE3k2CPqrEO7ZmfjaBvyev/CTNk/ZKHGOPNo0ptEDfwsIAwQDshbHPO5b6EK2w0lHkZQnDbX2bMU9IfHGxgm//LD1wBtPY+Uz4GtOaThcN+wbQglDbuUdztbad5bSrAHMoNdTpG8DC6XTfvAIsZF4BVoCFBAqbVwusAAsJFDb/B1Yz0yUhbiKsAAAAAElFTkSuQmCC\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 144.3px 8px; transform-origin: 144.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elist the Fermat prime numbers less or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.1083px 8px; transform-origin: 38.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a vector f\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.6167px 8px; transform-origin: 98.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Also compute their frequency / ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.242px 8px; transform-origin: 146.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecompare to all the primes in the same range. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8583px 8px; transform-origin: 82.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eyour function should return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.1333px 8px; transform-origin: 23.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e fp = [] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.0833px 8px; transform-origin: 18.0833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e f = 0.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.9833px 8px; transform-origin: 21.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e f\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 28.5833px 8px; transform-origin: 28.5833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [3, 5]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.975px 8px; transform-origin: 21.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 2/3 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 56.0083px 8px; transform-origin: 56.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3 = P(0), 5 = P(1),\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 169.192px 8px; transform-origin: 169.192px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and there are in total three primes in the range [3; 10] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.875px 8px; transform-origin: 25.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 300\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e f\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 55.8083px 8px; transform-origin: 55.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [3, 5, 17, 257]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.8667px 8px; transform-origin: 25.8667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 4/61 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 86.9333px 8px; transform-origin: 86.9333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3 = P(0), 5 = P(1), 17 = P(2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 32.875px 8px; transform-origin: 32.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e257 = P(3)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 66.125px 8px; transform-origin: 66.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand there are in total 61\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 85.5833px 8px; transform-origin: 85.5833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eprime numbers in the range\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 31.1px 8px; transform-origin: 31.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e [3; 300] ; \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 20.0333px 8px; transform-origin: 20.0333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003efp = []\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 14.2px 8px; transform-origin: 14.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9167px 8px; transform-origin: 64.9167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFobidden functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/60942-euler-primes\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 60942. Euler primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95759\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties II\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [fp, f] = fermat_primes(n)\r\n fp = n;\r\n f = 1;\r\nend","test_suite":"%%\r\nm = 10;\r\nfp_correct = [3, 5];\r\nf_correct = 2/3;\r\n[fp,f] = fermat_primes(m);\r\nassert(isequal([fp,f],[fp_correct,f_correct]));\r\n\r\n%%\r\nm = 300;\r\nfp_correct = [3, 5, 17, 257];\r\nf_correct = 4/61;\r\n[fp,f] = fermat_primes(m);\r\nassert(isequal([fp,f],[fp_correct,f_correct]));\r\n\r\n%%\r\nm = 2;\r\nfp_correct = [];\r\nf_correct = 0;\r\n[fp,f] = fermat_primes(m);\r\nassert(isequal([fp,f],[fp_correct,f_correct]));\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('fermat_primes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T06:52:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2025-07-09T05:57:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-06-27T05:33:53.000Z","updated_at":"2026-03-16T20:10:35.000Z","published_at":"2025-06-27T06:14:34.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe french mathematician Pierre de Fermat found the formula \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbf{P(n) = 2^{2^n} + 1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to find some prime numbers. He thought / conjectured all these numbers where primes, but P(5) is actually the first not prime Fermat number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em \\\\geq 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003elist the Fermat prime numbers less or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in a vector f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Also compute their frequency / ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ecompare to all the primes in the same range. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em \u0026lt; 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eyour function should return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e fp = [] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e f = 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [3, 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 2/3 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3 = P(0), 5 = P(1),\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and there are in total three primes in the range [3; 10] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 300\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [3, 5, 17, 257]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 4/61 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3 = P(0), 5 = P(1), 17 = P(2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e257 = P(3)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand there are in total 61\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eprime numbers in the range\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e [3; 300] ; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efp = []\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \\\\leq 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e here.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFobidden functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/problems/60942-euler-primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 60942. Euler primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95759\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties II\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60561,"title":"Determine whether a number is a Blum integer","description":"A Blum integer is a semiprime—that is, the product of two distinct primes—whose factors have the form for some integer . The number 21 is a Blum integer because its two prime factors, 3 and 7, have the form with and . The number 123 is a semiprime because it is , but it is not a Blum integer because 41 is not 3 more than a multiple of 4. The number 1463 is not a Blum integer: although its prime factors are distinct and each 3 more than a multiple of 4, there are three of them, not two. \r\nWrite a function to determine whether the numbers in a matrix are Blum integers. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.60833px 8px; transform-origin: 6.60833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Blum_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eBlum integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.775px 8px; transform-origin: 14.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55275\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esemiprime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 228.683px 8px; transform-origin: 228.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, the product of two distinct primes—whose factors have the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42\" height=\"18\" alt=\"4k+3\" style=\"width: 42px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1083px 8px; transform-origin: 31.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for some integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 273.808px 8px; transform-origin: 273.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The number 21 is a Blum integer because its two prime factors, 3 and 7, have the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42\" height=\"18\" alt=\"4k+3\" style=\"width: 42px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.3333px 8px; transform-origin: 16.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36\" height=\"18\" alt=\"k = 0\" style=\"width: 36px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36\" height=\"18\" alt=\"k = 1\" style=\"width: 36px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 145.083px 8px; transform-origin: 145.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The number 123 is a semiprime because it is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42\" height=\"18\" alt=\"3x41\" style=\"width: 42px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.633px 8px; transform-origin: 188.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but it is not a Blum integer because 41 is not 3 more than a multiple of 4. The number 1463 is not a Blum integer: although its prime factors are distinct and each 3 more than a multiple of 4, there are three of them, not two. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.917px 8px; transform-origin: 251.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether the numbers in a matrix are Blum integers. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isBlum(x)\r\n y = false;\r\nend","test_suite":"%%\r\nx = 21;\r\nassert(isBlum(x))\r\n\r\n%%\r\nx = 25;\r\nassert(~isBlum(x))\r\n\r\n%%\r\nx = 123;\r\nassert(~isBlum(x))\r\n\r\n%%\r\nx = 123;\r\nassert(~isBlum(x))\r\n\r\n%%\r\nx = 737;\r\nassert(isBlum(x))\r\n\r\n%%\r\nx = 1463;\r\nassert(~isBlum(x))\r\n\r\n%%\r\nx = [37533 37581 37601 37617 37641 37669 37709 37721 37749 37753 37769];\r\nassert(all(isBlum(x)))\r\n\r\n%%\r\nx = 4+[37533 37581 37601 37617 37641 37669 37709 37721 37749 37753 37769];\r\nassert(sum(isBlum(x))==1)\r\n\r\n%% \r\nx = [74089 74301 74401 74549 74669 74773 74881\r\n 74141 74309 74417 74553 74689 74801 74901\r\n 74213 74329 74429 74557 74701 74809 74913\r\n 74233 74369 74461 74569 74721 74813 74917\r\n 74249 74389 74473 74577 74741 74829 74937\r\n 74281 74393 74537 74621 74757 74833 74957\r\n 74289 74397 74541 74641 74769 74837 74977];\r\nassert(isequal(isBlum(x),true(7)))\r\n\r\n%% \r\nx = [74089 74301 74401 74549 74669 74773 74881\r\n 74141 74309 74417 74553 74689 74801 74901\r\n 74213 74329 74429 74557 74701 74809 74913\r\n 74233 74369 74461 74569 74721 74813 74917\r\n 74249 74389 74473 74577 74741 74829 74937\r\n 74281 74393 74537 74621 74757 74833 74957\r\n 74289 74397 74541 74641 74769 74837 74977];\r\nA = isBlum(x+16);\r\ny = A*2.^(6:-1:0)';\r\ny_correct = [16 9 0 66 4 20 17]';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = randi(1000);\r\nx = 2*randi(450000,1,n);\r\nassert(all(~isBlum(x)))\r\n\r\n%%\r\nx = reshape([97091 106789 109033 147703 186819 267349 345133 472647 480241 491283 510839 524249 87893 128567 185019 226173 273351 325969 377121 405283 440487 478509 506273 518377],[4 3 2]);\r\ny = isBlum(x);\r\ny_correct = reshape(logical([0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1]),[4 3 2]);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = [504737 539969 619369];\r\nassert(isequal(isBlum(x),logical([1 1 0])))\r\n\r\n%%\r\nf = 4*(1:200)+3;\r\nf1 = f(isprime(f));\r\nassert(isequal(isBlum(f1.*f1'),logical(~eye(length(f1)))))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-26T00:46:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-25T03:32:30.000Z","updated_at":"2025-07-31T19:37:37.000Z","published_at":"2024-06-25T03:33:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Blum_integer\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBlum integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55275\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esemiprime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, the product of two distinct primes—whose factors have the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"4k+3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4k+3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for some integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\\n\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The number 21 is a Blum integer because its two prime factors, 3 and 7, have the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"4k+3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4k+3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The number 123 is a semiprime because it is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"3x41\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\\\\times41\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, but it is not a Blum integer because 41 is not 3 more than a multiple of 4. The number 1463 is not a Blum integer: although its prime factors are distinct and each 3 more than a multiple of 4, there are three of them, not two. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether the numbers in a matrix are Blum integers. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60942,"title":"Euler primes","description":"Historical context\r\n\r\n\r\nThe great swiss mathematician Leonhard Euler found the formula to give some prime numbers.\r\n\r\n\r\nProblem statement\r\n\r\nFor a given integer m, m \u003e= 41, list the Euler prime numbers less or equal to m in a vector ep. Also compute their frequency / ratio f compare to all the primes in the same range. If m is not a positive integer greater or equal to 41, your function should return ep = [] and f = 0.\r\n\r\nExamples (check the tests for more)\r\n\r\nIf m = 41 then ep = 41 and f = 1 since 41 = P(0) and it is the only prime number m greater or equal and less or equal to 41;\r\nIf m = 100 then ep = [41, 43, 47, 53, 61, 71, 83, 97] and f = 8/13 since 41 = P(0), 43 = P(1), 47 = P(2), 53 = P(3), 61 = P(4), 71 = P(5), 83 = P(6), and 97 = P(7), and in total there are 13 prime numbers in the range [41; 100] ; \r\nIf m = 19 then ep = [] and f = 0;\r\n\r\n\r\nTip \r\n\r\nn is less or equal to 107 here.\r\n\r\n\r\nFobidden functions\r\n\r\nregexp\r\nstr2num\r\nassignin\r\n\r\nSee also\r\nProblem 60944. Ulam primes first formula, Problem 60943. Ulam primes second formula\r\nPrime numbers properties II","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 988.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 494.233px; transform-origin: 408px 494.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; 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\"\u003e\u003cspan style=\"\"\u003eThe great swiss mathematician Leonhard Euler found the formula \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"125\" height=\"19.5\" style=\"width: 125px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.1833px 8px; transform-origin: 92.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to give some prime numbers.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.2917px 8px; transform-origin: 60.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.225px 8px; transform-origin: 6.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.075px 8px; transform-origin: 26.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em \u0026gt;= 41\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.475px 8px; transform-origin: 138.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elist the Euler prime numbers less or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.1667px 8px; transform-origin: 36.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 8px; transform-origin: 7.78333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.3833px 8px; transform-origin: 96.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Also compute their frequency / ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 286.658px 8px; transform-origin: 286.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecompare to all the primes in the same range. If m is not a positive integer greater or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.6667px 8px; transform-origin: 11.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e41, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.35px 8px; transform-origin: 63.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eyour function should return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.6917px 8px; transform-origin: 24.6917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e ep = [] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.0833px 8px; transform-origin: 18.0833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e f = 0.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.6167px 8px; transform-origin: 34.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3333px 8px; transform-origin: 79.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(check the tests for more)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 51.0833px; transform-origin: 392px 51.0833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.9833px 8px; transform-origin: 21.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 41\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 23.925px 8px; transform-origin: 23.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eep = 41\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 16.1417px 8px; transform-origin: 16.1417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 1 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 28.9833px 8px; transform-origin: 28.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e41 = P(0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 99.575px 8px; transform-origin: 99.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and it is the only prime number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 108.533px 8px; transform-origin: 108.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e greater or equal and less or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 10.1167px 8px; transform-origin: 10.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e41;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.875px 8px; transform-origin: 25.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 100\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 110.258px 8px; transform-origin: 110.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eep = [41, 43, 47, 53, 61, 71, 83, 97]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.8667px 8px; transform-origin: 25.8667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 8/13 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 141.192px 8px; transform-origin: 141.192px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e41 = P(0), 43 = P(1), 47 = P(2), 53 = P(3), 61 = P(4), 71 = P(5), 83 = P(6), and 97 = P(7), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand in total there are\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.6667px 8px; transform-origin: 11.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e 13 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 85.5833px 8px; transform-origin: 85.5833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eprime numbers in the range\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 34.9917px 8px; transform-origin: 34.9917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e [41; 100] ; \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 23.925px 8px; transform-origin: 23.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 19 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 20.8083px 8px; transform-origin: 20.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eep = []\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 14.2px 8px; transform-origin: 14.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is less or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e107\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9167px 8px; transform-origin: 64.9167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFobidden functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/60944-ulam-primes-first-formula\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-style: italic; \"\u003eProblem 60944. Ulam primes first formula\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/60943-ulam-primes-second-formula\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-style: italic; \"\u003eProblem 60943. Ulam primes second formula\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95759\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties II\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [ep,f] = euler_primes(m)\r\n ep = m;\r\n f = 1;\r\nend","test_suite":"%%\r\nm = 41;\r\nep_correct = 41;\r\nf_correct = 1;\r\n[ep,f] = euler_primes(m);\r\nassert(isequal([ep,f],[ep_correct,f_correct]));\r\n\r\n%%\r\nm = 100;\r\nep_correct = [41, 43, 47, 53, 61, 71, 83, 97];\r\nf_correct = 8/13;\r\n[ep,f] = euler_primes(m);\r\nassert(isequal([ep,f],[ep_correct,f_correct]));\r\n\r\n%%\r\nm = 200;\r\nep_correct = [41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197];\r\nf_correct = 13/34;\r\n[ep,f] = euler_primes(m);\r\nassert(isequal([ep,f],[ep_correct,f_correct]));\r\n\r\n%%\r\nm = 19;\r\nep_correct = [];\r\nf_correct = 0;\r\n[ep,f] = euler_primes(m);\r\nassert(isequal([ep,f],[ep_correct,f_correct]));\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('euler_primes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T06:49:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2025-07-09T05:56:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-06-26T14:44:30.000Z","updated_at":"2026-03-16T19:16:06.000Z","published_at":"2025-06-26T15:44:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe great swiss mathematician Leonhard Euler found the formula \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbf{P(n) = n^2 + n + 41}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to give some prime numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em \u0026gt;= 41\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003elist the Euler prime numbers less or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Also compute their frequency / ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ecompare to all the primes in the same range. If m is not a positive integer greater or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e41, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eyour function should return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e ep = [] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e f = 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(check the tests for more)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 41\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eep = 41\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 1 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e41 = P(0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and it is the only prime number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e greater or equal and less or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e41;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eep = [41, 43, 47, 53, 61, 71, 83, 97]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 8/13 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e41 = P(0), 43 = P(1), 47 = P(2), 53 = P(3), 61 = P(4), 71 = P(5), 83 = P(6), and 97 = P(7), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand in total there are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 13 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eprime numbers in the range\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e [41; 100] ; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 19 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eep = []\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is less or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e107\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFobidden functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/problems/60944-ulam-primes-first-formula\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 60944. Ulam primes first formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/problems/60943-ulam-primes-second-formula\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 60943. Ulam primes second formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95759\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties II\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50948,"title":"Identify prime words","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6083px 7.91667px; transform-origin: 13.6083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=9CcI5M1LfRs\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eNumberphile video on evil primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 236.375px 7.91667px; transform-origin: 236.375px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Tony Padilla introduced the “Jesus prime” 105,192,119, which is formed by concatenating the positions of the letters of ‘Jesus’ in the English alphabet: 10, 5, 19, 21, 19. In general, a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.625px 7.91667px; transform-origin: 34.625px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eprime word\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.91667px; transform-origin: 20.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e could be defined as a word such that the number formed by concatenating the positions of the letters in the alphabet is prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.425px 7.91667px; transform-origin: 368.425px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a string and identifies prime words. It should delete apostrophes and hyphens (e.g. “don’t” = “dont”, “un-ionized” = “unionized”) and treat other punctuation as spaces. The function should return an array of 0’s and 1’s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isPrimeWord(s)\r\n tf = isprime(s);\r\nend","test_suite":"%%\r\nassert(isPrimeWord('Croatia'))\r\n\r\n%%\r\nassert(~isPrimeWord('Serbia'))\r\n\r\n%%\r\nassert(isPrimeWord('frenetic'))\r\n\r\n%%\r\nassert(~isPrimeWord('frantic'))\r\n\r\n%%\r\nassert(isPrimeWord('smiling'))\r\n\r\n%%\r\nassert(~isPrimeWord('frowning'))\r\n\r\n%%\r\nassert(isPrimeWord('ziti'))\r\n\r\n%%\r\nassert(~isPrimeWord('spaghetti'))\r\n\r\n%%\r\nassert(isPrimeWord('tick'))\r\n\r\n%%\r\nassert(~isPrimeWord('tock'))\r\n\r\n%%\r\nassert(isPrimeWord('madam'))\r\n\r\n%%\r\nassert(~isPrimeWord('Adam')) \r\n\r\n%%\r\nassert(isPrimeWord('RFQ'))\r\n\r\n%%\r\nassert(~isPrimeWord('FAQ'))\r\n\r\n%%\r\nassert(isPrimeWord('Jesus'))\r\n\r\n%%\r\nassert(~isPrimeWord('Moses')) \r\n\r\n%%\r\nassert(isPrimeWord('adieu'))\r\n\r\n%%\r\nassert(~isPrimeWord('milieu'))\r\n\r\n%%\r\nassert(isPrimeWord('wallow'))\r\n\r\n%%\r\nassert(~isPrimeWord('swallow')) \r\n\r\n%%\r\ns = 'slim pickings';\r\nassert(all(isPrimeWord(s)))\r\n\r\n%%\r\ns = 'mellow fellow';\r\nassert(all(isPrimeWord(s)))\r\n\r\n%%\r\ns = 'Ms. Zadora stuck a cornucopia full of Bing cherries into her knapsack.';\r\ntf_correct = [1 1 1 0 1 0 0 1 0 0 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%%\r\ns = 'The dog and pig are going to India.';\r\ntf_correct = [0 1 0 1 0 1 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%%\r\ns = 'Liam, is Mauritius in Africa? I know that Mali and Libya are.';\r\ntf_correct = [1 1 1 0 1 0 0 0 1 0 1 0];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%% Maria Bamford\r\nq = char(39);\r\ns = ['I was in a lot of plays. We had a weird drama teacher in that he was incredibly enthusiastic about a high school drama program and would talk to all the kids for hours. He ended up marrying one of the kids, but that' q 's neither here nor there.'];\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[28 32 42]))\r\n\r\n%% Maria Bamford\r\nq = char(39);\r\ns = ['I do wanna get married. It just sounds great. You get to go grocery shopping together, rent videos, and the kissing and the hugging and the kissing and the hugging under the cozy covers. Mmmm! But sometimes I worry that I don' q 't wanna get married as much as I want to get dipped in a vat of warm, rising bread dough. That might feel pretty good, too.'];\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[3 15 34 43]))\r\n\r\n%% Monty Python\r\ns = 'I cut down trees, I eat my lunch, I go to the lavatory. On Wednesday I go shopping and have buttered scones for tea.';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[4 18]))\r\n\r\n%% Monty Python\r\ns = 'Strange women lying in ponds, distributing swords, is no basis for a system of government!';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[8 10]))\r\n\r\n%% Monty Python\r\ns = 'My hovercraft is full of eels.';\r\ntf_correct = [0 0 1 0 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n \r\n%% Basil Fawlty\r\ns = 'Well may I ask what you expected to see out of a Torquay hotel bedroom window? Sydney Opera House perhaps? The Hanging Gardens of Babylon? Herds of wildebeest sweeping majestically';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[18 23]))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-03-14T22:44:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-14T16:24:34.000Z","updated_at":"2026-01-20T19:15:07.000Z","published_at":"2021-03-14T16:29:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=9CcI5M1LfRs\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNumberphile video on evil primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, Tony Padilla introduced the “Jesus prime” 105,192,119, which is formed by concatenating the positions of the letters of ‘Jesus’ in the English alphabet: 10, 5, 19, 21, 19. In general, a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprime word\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e could be defined as a word such that the number formed by concatenating the positions of the letters in the alphabet is prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a string and identifies prime words. It should delete apostrophes and hyphens (e.g. “don’t” = “dont”, “un-ionized” = “unionized”) and treat other punctuation as spaces. The function should return an array of 0’s and 1’s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":54900,"title":"Find the number of primes less than input","description":"Given an integer n, determine the number of primes less than or equal to n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.5px 8px; transform-origin: 237.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an integer n, determine the number of primes less than or equal to n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(n)\r\n y = n;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 25;\r\ny_correct = 9;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 37;\r\ny_correct = 12;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 5;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":2434635,"edited_by":223089,"edited_at":"2022-10-20T07:05:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":49,"test_suite_updated_at":"2022-10-20T07:05:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-12T15:13:37.000Z","updated_at":"2026-02-15T08:35:09.000Z","published_at":"2022-07-12T15:13:37.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer n, determine the number of primes less than or equal to n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57600,"title":"Extract the prime numbers","description":"Given a list of elements, extract the prime numbers from that array.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 10.4972px; transform-origin: 406.996px 10.5043px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a list of elements, extract the prime numbers from that array.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1,3,4,6,7,9,3,5,11,6432,636451,323423,5454,44363,223,55345,677,5343];\r\ny_correct = [3 7 3 5 11 223 677];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [1,3,4,6,7,9,3,5,11,6432,636,451,3234,23,54,54,443,63,2,23,553,45,677,5,343];\r\ny_correct = [3 7 3 5 11 23 443 2 23 677 5];\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-20T10:59:03.000Z","updated_at":"2026-02-12T19:14:16.000Z","published_at":"2023-01-20T10:59:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of elements, extract the prime numbers from that array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2411,"title":"Largest Prime Number","description":"Given a matrix X, find the largest prime number in X.","description_html":"\u003cp\u003eGiven a matrix X, find the largest prime number in X.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = max(x);\r\nend","test_suite":"%%\r\nx = [1 2 3 9 7];\r\ny_correct = 7;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n\r\n\r\n\r\n%%\r\n\r\nX=[1 2; 7 13;19 23];\r\ny_correct = 23;\r\nassert(isequal(your_fcn_name(X),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":27947,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":151,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-10T16:01:56.000Z","updated_at":"2026-03-04T14:01:30.000Z","published_at":"2014-07-10T16:01:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a matrix X, find the largest prime number in X.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1763,"title":"Primes for Large N: 2^30, System Memory Limit","description":"This Challenge is to further improve the \"primes\" function for speed/memory usage to the Limit of Cody Memory.\r\n\r\nThe Matlab function \"primes\" has a very efficient sieving method but it suffers from memory usage issues, especially on limited memory systems.\r\n\r\nThe \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1761-primes-faster-for-large-n Primes Faster Challenge\u003e gives the first half to maximizing the primes function for optimal memory usage and speed.\r\n\r\nCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\r\n\r\nThe test case of 2^30 pushes the upper limits of Cody memory.\r\n\r\nThe reference solution can process N=2^32 on an 8GB machine in 68sec.\r\n\r\n*Input:* N (max of primes to find)\r\n\r\n*Output:* vector of primes (all primes less than or equal to N)\r\n\r\n*Scoring:* Time to find all primes \u003c 2^30\r\n\r\n*Hints:*\r\n\r\n 1) Doubles use 8 bytes;\r\n 2) The primes method p(((k*k+1)/2):k:q) creates a vector using q/k*8 bytes. This is 8/3 the size of p for k=3 because k is a double. \r\n 3) Segmentation will keep memory usage below limits at the cost of time.\r\n 4) Cody Available Memory appears to be 537.27MB. XP Operating system eats memory.\r\n 5) Usage of profiler and Task Manager combined give performance insights.","description_html":"\u003cp\u003eThis Challenge is to further improve the \"primes\" function for speed/memory usage to the Limit of Cody Memory.\u003c/p\u003e\u003cp\u003eThe Matlab function \"primes\" has a very efficient sieving method but it suffers from memory usage issues, especially on limited memory systems.\u003c/p\u003e\u003cp\u003eThe \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1761-primes-faster-for-large-n\"\u003ePrimes Faster Challenge\u003c/a\u003e gives the first half to maximizing the primes function for optimal memory usage and speed.\u003c/p\u003e\u003cp\u003eCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\u003c/p\u003e\u003cp\u003eThe test case of 2^30 pushes the upper limits of Cody memory.\u003c/p\u003e\u003cp\u003eThe reference solution can process N=2^32 on an 8GB machine in 68sec.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e N (max of primes to find)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e vector of primes (all primes less than or equal to N)\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Time to find all primes \u0026lt; 2^30\u003c/p\u003e\u003cp\u003e\u003cb\u003eHints:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) Doubles use 8 bytes;\r\n2) The primes method p(((k*k+1)/2):k:q) creates a vector using q/k*8 bytes. This is 8/3 the size of p for k=3 because k is a double. \r\n3) Segmentation will keep memory usage below limits at the cost of time.\r\n4) Cody Available Memory appears to be 537.27MB. XP Operating system eats memory.\r\n5) Usage of profiler and Task Manager combined give performance insights.\r\n\u003c/pre\u003e","function_template":"function p = primes_faster_large(n)\r\n% Standard primes will not succeed\r\n p=[];\r\nreturn\r\n\r\n%PRIMES Generate list of prime numbers.\r\n% PRIMES(N) is a row vector of the prime numbers less than or \r\n% equal to N. A prime number is one that has no factors other\r\n% than 1 and itself.\r\n% Class support for input N:\r\n% float: double, single\r\n% See also FACTOR, ISPRIME.\r\n% Copyright 1984-2004 The MathWorks, Inc. \r\n% $Revision: 1.16.4.3 $ $Date: 2010/08/23 23:13:13 $\r\n\r\nif length(n)~=1 \r\n error(message('MATLAB:primes:InputNotScalar')); \r\nend\r\nif n \u003c 2, p = zeros(1,0,class(n)); return, end\r\np = 1:2:n;\r\nq = length(p);\r\np(1) = 2;\r\nfor k = 3:2:sqrt(n)\r\n if p((k+1)/2)\r\n p(((k*k+1)/2):k:q) = 0;\r\n end\r\nend\r\np = p(p\u003e0);\r\n\r\nend","test_suite":"feval(@assignin,'caller','score',55);\r\n%%\r\ntic\r\nassert(isequal(primes_faster_large(1),primes(1)))\r\nassert(isequal(primes_faster_large(2),primes(2)))\r\nfor i=1:10\r\n n=randi(2000,1);\r\n assert(isequal(primes_faster_large(n),primes(n)))\r\nend\r\ntoc\r\n%%\r\ntic\r\nta=clock;\r\n p = primes_faster_large(2^30);\r\nt1=etime(clock,ta); % time in sec\r\nfprintf('P 2^30 %12i %10.3f\\n',length(p),t1)\r\nassert(isequal(length(p),54400028))\r\nassert(all(diff(p)\u003e0))\r\n%assert(isequal(size(unique(p),2),54400028))\r\nptr=randi(7603553,1,10); % small to avoid timeout\r\npchk=double(p(ptr));\r\nassert(all(isprime(pchk)))\r\nfeval( @assignin,'caller','score',floor(min(55,t1)) );\r\ntoc\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2013-08-07T00:23:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-30T19:43:11.000Z","updated_at":"2025-06-07T08:19:24.000Z","published_at":"2013-07-31T04:12:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to further improve the \\\"primes\\\" function for speed/memory usage to the Limit of Cody Memory.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Matlab function \\\"primes\\\" has a very efficient sieving method but it suffers from memory usage issues, especially on limited memory systems.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1761-primes-faster-for-large-n\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrimes Faster Challenge\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e gives the first half to maximizing the primes function for optimal memory usage and speed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody appears to have 2GB of RAM based upon \\\"out of memory\\\" messages observed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test case of 2^30 pushes the upper limits of Cody memory.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution can process N=2^32 on an 8GB machine in 68sec.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e N (max of primes to find)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector of primes (all primes less than or equal to N)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Time to find all primes \u0026lt; 2^30\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1) Doubles use 8 bytes;\\n2) The primes method p(((k*k+1)/2):k:q) creates a vector using q/k*8 bytes. This is 8/3 the size of p for k=3 because k is a double. \\n3) Segmentation will keep memory usage below limits at the cost of time.\\n4) Cody Available Memory appears to be 537.27MB. XP Operating system eats memory.\\n5) Usage of profiler and Task Manager combined give performance insights.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50038,"title":"Number Puzzles - 014","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA number pr is a prime number and it is an average of the squares of four integers m, n, o, and p. Give an example of [m n o p pr]. The answer is not unique and, therefore, your answer will be checked against the requirement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = puzzle_014()\r\n y = [1 2 3 4 11];\r\nend","test_suite":"%%\r\ny=puzzle_014();\r\nassert(isequal(y(1)^2+y(2)^2+y(3)^2+y(4)^2,4*y(5)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-29T00:53:59.000Z","updated_at":"2026-02-24T10:37:44.000Z","published_at":"2021-01-29T00:53:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA number pr is a prime number and it is an average of the squares of four integers m, n, o, and p. Give an example of [m n o p pr]. The answer is not unique and, therefore, your answer will be checked against the requirement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55170,"title":"Find all prime factors of the input","description":"Given an input x, find its all prime factors. Return the vector with all factors in ascending order.\r\nEfficiency is the key here.\r\nExample 1:\r\nx = 4\r\ny = [2]\r\nExample 2:\r\nx = 6270\r\ny = [2 3 5 11 19]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 106.875px; transform-origin: 407px 106.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an input x, find its all prime factors. Return the vector with all factors in ascending order.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEfficiency is the key here.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ex = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ey = [2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ex = 6270\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ey = [2 3 5 11 19]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = get_prime_factors(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = [2];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [2];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 17;\r\ny_correct = [17];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 6270;\r\ny_correct = [2 3 5 11 19];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 83160;\r\ny_correct = [2 3 5 7 11];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 27;\r\ny_correct = [3];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 999613;\r\ny_correct = [999613];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n\r\n%%\r\nx = 99999989;\r\ny_correct = [99999989];\r\nassert(isequal(get_prime_factors(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2434370,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-13T19:38:39.000Z","updated_at":"2026-02-19T14:24:12.000Z","published_at":"2022-07-13T19:38:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input x, find its all prime factors. Return the vector with all factors in ascending order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEfficiency is the key here.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = 4\\ny = [2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = 6270\\ny = [2 3 5 11 19]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52298,"title":"Which Prime","description":"Given two prime numbers, specify the relation between them i.e. - \r\n'Twin Prime', 'Cousin Prime', 'Sexy Prime' or 'None'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.5px 8px; transform-origin: 207.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two prime numbers, specify the relation between them i.e. - \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.5px 8px; transform-origin: 1.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Twin_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwin Prime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e', '\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Cousin_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCousin Prime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e', '\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Sexy_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSexy Prime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e' or 'None'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = whichprime(x)\r\n%primes everywhere\r\n%sort accordingly\r\nend","test_suite":"%%\r\nx = [3 5];\r\ny = 'Twin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [17 37];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [3 7];\r\ny = 'Cousin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [5 11];\r\ny = 'Sexy Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [7 11];\r\ny = 'Cousin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [103 3];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [13 11];\r\ny = 'Twin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [101 107];\r\ny = 'Sexy Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [139 137];\r\ny = 'Twin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [397 401];\r\ny = 'Cousin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [3 11];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [313 307];\r\ny = 'Sexy Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [2 5];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [263 269];\r\ny = 'Sexy Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [101 103];\r\ny = 'Twin Prime';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [17 7];\r\ny = 'None';\r\nassert(isequal(whichprime(x),y))\r\n\r\n%%\r\nx = [17 13];\r\ny = 'Cousin Prime';\r\nassert(isequal(whichprime(x),y))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2021-07-14T13:56:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-14T13:39:21.000Z","updated_at":"2026-03-03T11:03:32.000Z","published_at":"2021-07-14T13:56:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two prime numbers, specify the relation between them i.e. - \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Twin_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwin Prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e', '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Cousin_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCousin Prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e', '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Sexy_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSexy Prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e' or 'None'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1375,"title":"select the primes of a vector","description":"Find the prime numbers in a vector","description_html":"\u003cp\u003eFind the prime numbers in a vector\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 2 3 4 5 31 67];\r\ny_correct = [2 3 5 31 67];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":12098,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":321,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-22T16:30:19.000Z","updated_at":"2026-02-17T14:58:03.000Z","published_at":"2013-03-22T16:30:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the prime numbers in a vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42483,"title":"Give prime Numbers upto n","description":"You are given a input number x; print all the prime numbers less than equal to x.","description_html":"\u003cp\u003eYou are given a input number x; print all the prime numbers less than equal to x.\u003c/p\u003e","function_template":"function y = prime(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 10;\r\ny_correct = [ 2 3 5 7 ];\r\nassert(isequal(prime(x),y_correct))\r\n\r\n%%\r\nx = 19;\r\ny_correct = [ 2 3 5 7 11 13 17 19 ];\r\nassert(isequal(prime(x),y_correct))\r\n\r\n%%\r\nx = 1;\r\ny_correct = [ ];\r\nassert(isequal(prime(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":47762,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":"2015-08-02T06:07:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-02T06:02:07.000Z","updated_at":"2026-02-19T14:24:46.000Z","published_at":"2015-08-02T06:07:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a input number x; print all the prime numbers less than equal to x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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5;\r\nassert(isequal(mostPrimes(x),y_correct));\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":16505,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":71,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-22T04:52:10.000Z","updated_at":"2025-12-18T06:07:24.000Z","published_at":"2014-05-22T04:52:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an vector x of integer numbers, find the element of x that has the most primes less than it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42513,"title":"Is it prime?","description":"Given a number, check whether it is prime or not.\r\n\r\nIf prime output is true, otherwise false.","description_html":"\u003cp\u003eGiven a number, check whether it is prime or not.\u003c/p\u003e\u003cp\u003eIf prime output is true, otherwise false.\u003c/p\u003e","function_template":"function y = prime(x)\r\n y = \r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = 'true';\r\nassert(isequal(prime(x),y_correct))\r\n\r\nx = 4;\r\ny_correct = 'false';\r\nassert(isequal(prime(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":4,"created_by":46868,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":151,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-18T11:21:38.000Z","updated_at":"2026-03-18T23:49:40.000Z","published_at":"2015-08-18T11:21:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a number, check whether it is prime or not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf prime output is true, otherwise false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60948,"title":"Check p² = 24k + 1, p \u003e 3, the 'golden prime squares' equation","description":"Historical context\r\nIn december 2023, I / Nicolas Douillet was working on prime squares properties and I found* the formula :\r\n\r\n \r\n\r\nwhich I named the ‘Christmas eve equation'. From it I then wrote :\r\n\r\n\r\n\r\nand I named it the ‘golden prime squares equation’. These two formulas, which are actually the same one, can easily be proven starting from (note this last formula applies not only to prime numbers). \r\n \r\n* Apparently, I rediscovered it since I found it a posteriori on this excellent French math website : Site de Gérard Villemin\r\n \r\nProblem statement\r\nYour goal here is to check this formula for the first primes less or equal to a given integer m (input). To do so you will simply compute k in a vector. For the two first cases where the formula doesn’t apply -2 and 3- your function should return 0.\r\n \r\nExamples\r\n\r\nIf m = 20 then k = [0, 0, 1, 2, 5, 7, 12, 15], since 5^2 = 24x1 + 1, 7^2 = 24x2 + 1, 11^2 = 24x5 + 1, etc…\r\n\r\nIf m = 40 then k = [0, 0, 1, 2, 5, 7, 12, 15, 22, 35, 40, 57] ; \r\n \r\nFobidden functions\r\n \r\nregexp\r\nstr2num\r\nassignin\r\n \r\nSee also (my file exchange contributions using this equation) :\r\n\r\nIsprime optimus [FAST]\r\nPrime number spiral (my corresponding contribution on my file exchange)\r\nPrime numbers properties II","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1019.47px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 509.733px; transform-origin: 408px 509.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn december 2023, I / \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/profile/authors/8668631?s_tid=user_nav_comm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eNicolas Douillet\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 210.05px 8px; transform-origin: 210.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e was working on prime squares properties and I found* the formula :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"251\" height=\"19\" style=\"width: 251px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.025px 8px; transform-origin: 99.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.7333px 8px; transform-origin: 58.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhich I named the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.4167px 8px; transform-origin: 76.4167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e‘Christmas eve equation'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0417px 8px; transform-origin: 68.0417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. From it I then wrote :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"249\" height=\"19\" style=\"width: 249px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.95px 8px; transform-origin: 57.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand I named it the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.2167px 8px; transform-origin: 99.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e‘golden prime squares equation’\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 215.483px 8px; transform-origin: 215.483px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. These two formulas, which are actually the same one, can easily be proven starting from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"111.5\" height=\"18\" style=\"width: 111.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.033px 8px; transform-origin: 182.033px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (note this last formula applies not only to prime numbers). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 299.367px 8px; transform-origin: 299.367px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e* Apparently, I rediscovered it since I found it a posteriori on this excellent French math website : \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSite de Gérard Villemin\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour goal here is to check this formula for the first primes less or equal to a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.4917px 8px; transform-origin: 45.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003egiven integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.16667px 8px; transform-origin: 8.16667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.8417px 8px; transform-origin: 97.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(input). To do so you will simply compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.575px 8px; transform-origin: 211.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a vector. For the two first cases where the formula doesn’t apply -\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e3\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.9083px 8px; transform-origin: 94.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- your function should return 0.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.9833px 8px; transform-origin: 21.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 20\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 82.6333px 8px; transform-origin: 82.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek = [0, 0, 1, 2, 5, 7, 12, 15]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 26.4333px 8px; transform-origin: 26.4333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^2 = 24x\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.075px 8px; transform-origin: 46.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 1, 7^2 = 24x\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.75px 8px; transform-origin: 15.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 1, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 7.4px 8px; transform-origin: 7.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e11\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 26.4333px 8px; transform-origin: 26.4333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^2 = 24x\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 32.0833px 8px; transform-origin: 32.0833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e + 1, etc…\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.9833px 8px; transform-origin: 21.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 40\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 133.575px 8px; transform-origin: 133.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek = [0, 0, 1, 2, 5, 7, 12, 15, 22, 35, 40, 57] ;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9167px 8px; transform-origin: 64.9167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFobidden functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161.05px 8px; transform-origin: 161.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(my file exchange contributions using this equation) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/171714-isprime-optimus-fast?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-style: italic; \"\u003eIsprime optimus [FAST]\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/171709-prime-numbers-spiral?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime number spiral (my corresponding contribution on my file exchange)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95759\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties II\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = golden_prime_squares(m)\r\n\r\n k = m;\r\n \r\nend","test_suite":"%%\r\nm = 4;\r\nk_correct = [0, 0];\r\nassert(isequal(golden_prime_squares(m),k_correct))\r\n\r\n%%\r\nm = 20;\r\nk_correct = [0, 0, 1, 2, 5, 7, 12, 15];\r\nassert(isequal(golden_prime_squares(m),k_correct))\r\n\r\n%%\r\nm = 40;\r\nk_correct = [0, 0, 1, 2, 5, 7, 12, 15, 22, 35, 40, 57];\r\nassert(isequal(golden_prime_squares(m),k_correct))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('golden_prime_squares.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T06:55:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2025-07-09T05:55:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-06-27T16:53:40.000Z","updated_at":"2026-03-11T11:59:56.000Z","published_at":"2025-06-27T17:08:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn december 2023, I / \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/profile/authors/8668631?s_tid=user_nav_comm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNicolas Douillet\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e was working on prime squares properties and I found* the formula :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall p \\\\in \\\\mathbb{p}, p \\\\geq 5 \\\\Rightarrow \\\\exists k \\\\in \\\\mathbb{N}, \\\\mathbf{p^2 = 24k + 25}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich I named the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e‘Christmas eve equation'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. From it I then wrote :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall p \\\\in \\\\mathbb{p}, p \\\\geq 5 \\\\Rightarrow \\\\exists k \\\\in \\\\mathbb{N}^*, \\\\mathbf{p^2 = 24k + 1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand I named it the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e‘golden prime squares equation’\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. These two formulas, which are actually the same one, can easily be proven starting from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 6n \\\\pm 1, p \\\\geq 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (note this last formula applies not only to prime numbers). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e* Apparently, I rediscovered it since I found it a posteriori on this excellent French math website : \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSite de Gérard Villemin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour goal here is to check this formula for the first primes less or equal to a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egiven integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(input). To do so you will simply compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in a vector. For the two first cases where the formula doesn’t apply -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e- your function should return 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 20\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek = [0, 0, 1, 2, 5, 7, 12, 15]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^2 = 24x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 1, 7^2 = 24x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 1, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e11\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^2 = 24x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e + 1, etc…\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 40\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek = [0, 0, 1, 2, 5, 7, 12, 15, 22, 35, 40, 57] ;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFobidden functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(my file exchange contributions using this equation) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/171714-isprime-optimus-fast?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIsprime optimus [FAST]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/171709-prime-numbers-spiral?s_tid=prof_contriblnk\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime number spiral (my corresponding contribution on my file exchange)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95759\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties II\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44266,"title":"Sort the prime numbers in each row of a matrix","description":"Considering a 3x3 matrix A, sort the prime numbers of each row in ascending order. For exemple:\r\n\r\n \r\n input A=[5 8 2 4;\r\n 1 11 1 5]\r\n \r\n output B=[2 8 5 4;\r\n 1 5 1 11]\r\n \r\n\r\nYou don't have to sort the other numbers, just the prime numbers.\r\nEnjoy!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 164.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.0833px; transform-origin: 407px 82.0833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 292px 8px; transform-origin: 292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsidering a matrix A, sort the prime numbers of each row in ascending order. For exemple:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 48px 8.5px; transform-origin: 48px 8.5px; \"\u003e input \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 40px 8.5px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 40px 8.5px; \"\u003eA=[5 8 2 4\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 96px 8.5px; transform-origin: 96px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 11 1 5]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 72px 8.5px; transform-origin: 72px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 28px 8.5px; transform-origin: 28px 8.5px; \"\u003eoutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 40px 8.5px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 40px 8.5px; \"\u003eB=[2 8 5 4\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 5 1 11]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 229px 8px; transform-origin: 229px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou don't have to sort the other numbers, just the prime numbers. Enjoy!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function B = SrtPrimesInRows(A)\r\n","test_suite":"%%\r\nA=[5 8 2 4;1 11 1 5] ; \r\nB_correct = [2 8 5 4;1 5 1 11];\r\nassert(isequal(SrtPrimesInRows(A),B_correct))\r\n%%\r\nA=[2 7 5; 1 11 2;2 2 2];\r\nB_correct=[2 5 7;1 2 11;2 2 2];\r\nassert(isequal(SrtPrimesInRows(A),B_correct))\r\n%%\r\nA=[111 12 134;333 654 100000;112227 38 1];\r\nB_correct=A;\r\nassert(isequal(SrtPrimesInRows(A),B_correct))\r\n%%\r\nA=ones(4);\r\nA(2,1:4)=[11 59 7 23];\r\nB_correct=[1 1 1 1;7 11 23 59;1 1 1 1;1 1 1 1];\r\nassert(isequal(SrtPrimesInRows(A),B_correct))\r\n%%\r\nA=reshape(flip(primes(40)),3,4);\r\nB_correct= flipud(reshape(primes(40),3,4));\r\nassert(isequal(SrtPrimesInRows(A),B_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":140751,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2021-04-20T15:13:52.000Z","rescore_all_solutions":false,"group_id":674,"created_at":"2017-07-20T15:29:29.000Z","updated_at":"2026-03-04T15:19:28.000Z","published_at":"2017-07-20T15:29:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsidering a matrix A, sort the prime numbers of each row in ascending order. For exemple:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ input A=[5 8 2 4;\\n 1 11 1 5]\\n\\noutput B=[2 8 5 4;\\n 1 5 1 11]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou don't have to sort the other numbers, just the prime numbers. Enjoy!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45543,"title":"Find the remainder with the factorial of PRIMES?","description":"* Take a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\r\n* calculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\r\n* As mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\r\n* Divide factorial with the remainder (if possible). e.g. 120/5 = 24\r\n\r\nDon't use builtin functions \r\n\r\n primes\r\n\r\n factorial\r\n\r\n mod","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 275.767px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 137.883px; transform-origin: 407px 137.883px; vertical-align: baseline; \"\u003e\u003cul style=\"block-size: 122.6px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 61.3px; transform-origin: 391px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 290px 8px; transform-origin: 290px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTake a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 355px 8px; transform-origin: 355px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecalculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 359px 8px; transform-origin: 359px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 197px 8px; transform-origin: 197px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDivide factorial with the remainder (if possible). e.g. 120/5 = 24\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDon't use builtin functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 51.0833px; transform-origin: 404px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eprimes\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003efactorial\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003emod\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'primes')))\r\nassert(isempty(strfind(filetext, 'factorial')))\r\nassert(isempty(strfind(filetext, 'mod')))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 630;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 49;\r\ny_correct = 3.232790518889602e+58;\r\nassert(abs(your_fcn_name(x)/1e58-y_correct/1e58)\u003c1e-2)\r\n\r\n%%\r\nx = 5;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 17;\r\ny_correct = 6.2270208e+09;\r\nassert(abs(your_fcn_name(x)/1e9-y_correct/1e9)\u003c1e-2)","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":26467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2021-05-20T10:42:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-20T09:50:35.000Z","updated_at":"2025-04-28T21:39:14.000Z","published_at":"2020-05-20T09:54:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTake a number greater than or equal to 2 and take its primes. e.g. 6 and its primes are 2 3 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ecalculate the factorial of its prime (nearest less) and calculate the sum from that number down to 1. e.g. 5! = 120 and sum 5 to 1 is 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs mod of the factorial of every number with 2 is zero, check the mod of the sum calculated with 10 e.g. mod of 15 with 10 is 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDivide factorial with the remainder (if possible). e.g. 120/5 = 24\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDon't use builtin functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[primes\\n\\nfactorial\\n\\nmod]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46848,"title":"Modulo of sum of square of first n primes with 24","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 199.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 99.8px; transform-origin: 407px 99.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the modulo of sum of square of first n primes with 24.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e For n = 1, mod(2^2,24) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e For n = 2, mod(2^2 + 3^2,24) = 13\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e For n = 4, mod(2^2 + 3^2 + 5^2 + 7^2,24) = 15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eNote: n can be very large.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint : refer tag or check the modulo of square of primes(greater than 3) with 24 to observe the pattern\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = modp24(n)\r\n %...rather than a brute force approach, try finding a pattern in primes square and 24 :)\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 4;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 2;\r\ny_correct = 13;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 4;\r\ny_correct = 15;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = 15;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 120;\r\ny_correct = 11;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 1000;\r\ny_correct = 3;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 10^9;\r\ny_correct = 3;\r\nassert(isequal(modp24(x),y_correct))\r\n%%\r\nx = 10^12 + 15;\r\ny_correct = 18;\r\nassert(isequal(modp24(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":442401,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2020-10-17T08:26:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-17T08:22:52.000Z","updated_at":"2026-03-16T11:31:29.000Z","published_at":"2020-10-17T08:26:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the modulo of sum of square of first n primes with 24.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e For n = 1, mod(2^2,24) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e For n = 2, mod(2^2 + 3^2,24) = 13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e For n = 4, mod(2^2 + 3^2 + 5^2 + 7^2,24) = 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: n can be very large.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint : refer tag or check the modulo of square of primes(greater than 3) with 24 to observe the pattern\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44861,"title":"Ratio between sums of prime and non-prime numbers","description":"Write a function that calculates the ratio between the sum of the prime numbers lower or equal than x, and the sum of the non-prime numbers lower than x.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 91.5px; vertical-align: baseline; perspective-origin: 332px 91.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function that calculates the ratio between the sum of the prime numbers less than or equal to x, and the sum of the non-prime numbers up to the greatest prime less than or equal to x.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if x = 7, then:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 20px; perspective-origin: 329px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003esum_prime = sum([2 3 5 7]) = 17\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003esum_non_prime = sum([1 4 6]) = 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, the desired ratio is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eprime_ratio = sum_prime / sum_non_prime = 17 / 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 7;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 28/38;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 20;\r\ny_correct = 77/113;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 31;\r\ny_correct = 160/336;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 32;\r\ny_correct = 160/336;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 42;\r\ny_correct = 238/623;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2020-09-29T13:58:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-03-01T22:30:26.000Z","updated_at":"2026-04-01T10:59:16.000Z","published_at":"2019-03-01T22:30:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that calculates the ratio between the sum of the prime numbers less than or equal to x, and the sum of the non-prime numbers up to the greatest prime less than or equal to x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if x = 7, then:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[sum_prime = sum([2 3 5 7]) = 17\\nsum_non_prime = sum([1 4 6]) = 11]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, the desired ratio is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[prime_ratio = sum_prime / sum_non_prime = 17 / 11]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52397,"title":"Find the nth composite number.","description":"Everyone heard about the nth prime number. Let's try to find out the nth composite. For example , 1 is the first composite, 10 is the 6th composite number. Write a program that takes the value of n and give the nth composite as output,","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEveryone heard about the nth prime number. Let's try to find out the nth composite. For example , 1 is the first composite, 10 is the 6th composite number. Write a program that takes the value of n and give the nth composite as output,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = nthcomposite(n)\r\n y = n;\r\nend","test_suite":"%%\r\nn = 10;\r\ny_correct = 16; \r\nassert(isequal(nthcomposite(n),y_correct))\r\n\r\n%%\r\nn = 2;\r\ny_correct = 4; \r\nassert(isequal(nthcomposite(n),y_correct))\r\n\r\n%%\r\nn = 100;\r\ny_correct = 132; \r\nassert(isequal(nthcomposite(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":1282418,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":"2021-08-01T15:00:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-31T21:09:28.000Z","updated_at":"2026-03-23T11:03:03.000Z","published_at":"2021-07-31T21:09:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEveryone heard about the nth prime number. Let's try to find out the nth composite. For example , 1 is the first composite, 10 is the 6th composite number. Write a program that takes the value of n and give the nth composite as output,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57869,"title":"Identify de Polignac numbers","description":"The numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, , and . The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\r\nWrite a function that determines whether an odd number is a de Polignac number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.55px 8px; transform-origin: 297.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"125 = 109+2^4\" style=\"width: 96px; height: 19px;\" width=\"96\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALEAAAAmCAYAAACLSno+AAAHVElEQVR4Xu1bW8htUxQ+553cnnig8ODkWnKJeBBHiSS5ptMfcnmQ5FIkDxJySfLgUnRSriWJFEcUObmkKOKBBx54cot3vq/mdxp7/nOuedlrr3+tteeqr/3/e83LGGN+c8wx5px7+7b2NAtM3ALbJy5/E79ZYFsjcSPB5C3QSDz5IWwKNBI3DkzeAo3Ekx/C2SpwFDR7EPgL+Bu4CHgbuMvXuJF4thyYtGIHQ/qfgeuB15wm/O5b4BPgCqtdI/Gkx3q2wt/tvPAh+PzDaPkI/r4TWPi+kXi2PJi0YiLrqdDiS6PJs/j7auAIS+4UiW9C4UuAM4D9gN+cO7/ZmyEhi7HuBnCae/kvPvcC93qChepyubgWOMC9PBaf7wKPZdQd0+jR6DdkCkTbHhYouxPfXQecBRwKlNgxs+uVF6MOtxsescPPgScAhQtWCJZ/D6BNjgPojRVikAfZ4QQbvxz4AWBgTSKRyHxoyJOAnwLqszN2JPKGLHRlRHjWfRq4ALgUeN9VZpD/DnAM8CiwKbgPdTKC7/4xNkuJ8xwK3OgVoiOgPTiYvwCHAySynpgdU30N+T41kUN6Uz7xj1xjgrcLYGL3MGBDjOhhBzs+G7jVEIkNK1bh368DCzPCWUYun0R+3n13Mj5v8QbAXyqs4CHFTkGBL1x7XAmeGXIkKvoiATnhSMIPOuo/iXecnOd7tqZt6ameAh4y9eml3gC0Moa8d4W4K6lCHV51er2Azz+BI4ENwDq5ezwdJYyIzP+tV14QNhROyOudiZILjHc16eZpSM6Q/T3VSbQPAQbfIZKpLqv5k0BLCN/5A6puuvpeySgs0ej3qEuCdk02rjy/uwHyycj69D42JpQ41pmEnEGt2HRAJwKxZb60Xa5ELwP+CsN2rA6hUEorOqMAhbOst0nfEInZ+FeAlnJfcAXdoY4V34Q8NNvhBPnRNejXt8vHQuBuBLCKj9kbcwDoPUODZ+2pcMFfeTihuXpZD2zracLTkZwTIXop4Vj+M4AeMuYZS9qkblzJY86Qbf0KKDw6Gn/b8JSyMCdifT4KUalzUWIXEloxTmjJ7/IeaotluHz6nlwKhTy86lpvzUlGjz3lRytLaWyrZZr5yo4eDdAniemUPgK6ViIbL1sPK/3sZKJj+NRxZ2GSpXYnQvYh2fgwWw4ldimbylD+APznKnaR2MbFsWw+1f9Y3iuU2ORZMgQkQZj82sOAjGrJIn2SONkZCmhV9zcK9L0/uUXuBQdaSmIaj66cSVooVssRXJ7Y9+QiMdvokiuH7DlybHUZhRKxBDkmH+vdB9wGhLanltFraBLLE/sOTbbxwxqtxFWemLHsSwDjJc4aZtw121zW+/ixnMjNQYgldnxXQ2IbhiwzyH3Eiuq/NJRQnK19Z5I/Z7++RN+hSawx9/MbhQ6U3YZLtBm3GS8E9kUBKU/Mwb/fkdc3Rk08Fktk2LaNj2J7h5oELN8Vdviyjo3EJaGELsJwz95/uvbrS8irskOSWEl+jEc6MzgBwnF/mBEAHzqShTA2RWJrCJ0cWWPGyBYzoOJpncLYclTqa0AHKn62yrKpbZmagduKOrWhBHOCywB6LtmpxpnEdB6SxIrr7aFW1ViUkFgdKLgu9YYM1q8BLgZi8bQGV23roOAgfMFj6OMBbclMeXeiNJTwB9ef8Ll7xUqYqshiKuX2F+tHBzax84Qi+WpIzA7sSUqOQiVC09vcAdi7At/h/90AycwjSD5j3ifuGoSSUKKrHTvhc2P1MZBYdyBihyBFBGbhWhJbb5wiMUn5FsDYetmjYruXHLu7UWyEgSvUhhK+mDY/yCVxStVVhxNK2D6GIKmDoJSs+97XktieGMVO19hJnwS2nqf0EtCYEjtl5KUHHKFB1U5N125ONhlQcJUkXgmB+/DEXXFpDoGpWOh+Rsjr8KY/kxkmMl1HmaFBGwuJlZHXHHDEPHH0YkwJe13ZVZE4l8C5fFhQrdYTp06MJPSL6C12/k9BmOA8DsTuaUhYGZcD1pUYVozboFW0u9JHUqqVqXRV6lJ4VSQmXw4Euq4J0DbMeYrPH0IkpnE2AHq+0GZ6ynh2o5oXQGIPL0lz47rr7J9tvQLQk06dwLRDbHPftxFXMV7B5A2u0I8IdFuQCe/pPU7DVZDYOjxexQw95zquVeU5IRLb65I6ndN9WO7p8Ven/h1XCWYvaeTYtishIXF115ae6yogJ/TI6XcrythQIjVYdj+csvJ0zr+bzQMAluvTJn2T2O5ipWxevTqFSMxZ/oDzfuqYcSh/WfCmM2jMcPboOCV06LSJk+A8gHvCvEO6F8gJN1J9jeG9iMmf5aS8p/2Fiw419OsO7vSQ1DWXr1J26JPEqV90+LJUJ7q1MXHKGDXvNXm+QWXeZ97Ts5epkWnd6uhS/G4ovux26GC2GxOJB1O6dTQvCzQSz2s811KbRuK1HPZ5Kd1IPK/xXEttGonXctjnpXQj8bzGcy21aSRey2Gfl9KNxPMaz7XU5n+Yxsk2AHmnJgAAAABJRU5ErkJggg==\" alt=\"329 = 73+2^8\" style=\"width: 88.5px; height: 19px;\" width=\"88.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 320.392px 8px; transform-origin: 320.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.042px 8px; transform-origin: 255.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isdePolignac(n)\r\n tf = isequal(n,p+2^k);\r\nend","test_suite":"%%\r\nassert(isdePolignac(1))\r\n\r\n%%\r\nassert(~isdePolignac(17))\r\n\r\n%%\r\nassert(~isdePolignac(75))\r\n\r\n%%\r\nassert(isdePolignac(127))\r\n\r\n%%\r\nassert(isdePolignac(331))\r\n\r\n%%\r\nassert(~isdePolignac(531))\r\n\r\n%%\r\nassert(isdePolignac(905))\r\n\r\n%%\r\nassert(isdePolignac(1619))\r\n\r\n%%\r\nassert(~isdePolignac(2261))\r\n\r\n%%\r\nassert(isdePolignac(7535))\r\n\r\n%%\r\nassert(~isdePolignac(10413))\r\n\r\n%%\r\nassert(isdePolignac(21453))\r\n\r\n%%\r\nassert(isdePolignac(45233))\r\n\r\n%%\r\nassert(~isdePolignac(70999))\r\n\r\n%%\r\nassert(~isdePolignac(96415))\r\n\r\n%%\r\nassert(~isdePolignac(121399))\r\n\r\n%%\r\nassert(isdePolignac(148243))\r\n\r\n%%\r\nassert(isdePolignac(172841))\r\n\r\n%%\r\nassert(isdePolignac(201599))\r\n\r\n%%\r\nassert(isdePolignac(227107))\r\n\r\n%%\r\nassert(isdePolignac(253151))\r\n\r\n%%\r\nassert(~isdePolignac(267267))\r\n\r\n%%\r\nassert(~isdePolignac(271271))\r\n\r\n%%\r\nassert(isdePolignac(273421))\r\n\r\n%%\r\nassert(isdePolignac(542459))\r\n\r\n%%\r\nassert(isdePolignac(2000039))\r\n\r\n%%\r\nassert(~isdePolignac(123456789))\r\n\r\n%%\r\nassert(isdePolignac(123456791))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,5893:2:5933)')'),288))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,21671:10:21791)')'),4624))\r\n\r\n%%\r\nfiletext = fileread('isdePolignac.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-29T05:27:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-29T05:27:08.000Z","updated_at":"2025-12-25T08:44:06.000Z","published_at":"2023-03-29T05:27:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"125 = 109+2^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125 = 109+2^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"329 = 73+2^8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e329 = 73+2^8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},null,{"id":44862,"title":"Ratio between sum of primes and sum of factors","description":"Write a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.","description_html":"\u003cp\u003eWrite a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 8;\r\ny_correct = 17/6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 28/7;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 1060/14;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2019-03-12T22:32:41.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2019-03-01T22:35:36.000Z","updated_at":"2026-03-16T13:27:48.000Z","published_at":"2019-03-01T22:35:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60661,"title":"The Prime Days of Christmas","description":"On the first day of Christmas my true love sent to me partridges in a pear tree.\r\nOn the second day of Christmas my true love sent to me turtle doves, and partridges in a pear tree.\r\nOn the third day of Christmas my true love sent to me French hens, turtle doves, and partridges in a pear tree.\r\nOn the fourth day of Christmas my true love sent to me calling birds, French hens, turtle doves, and partridges in a pear tree.\r\nOn the fifth day of Christmas my true love sent to me golden rings, calling birds, French hens, turtle doves, and partridges in a pear tree.\r\nAnd so on ...\r\n denotes the -th prime. Suppose that there are days of Christmas. How many gifts am I receiving in total?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 276px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 138px; transform-origin: 407px 138px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11.25px; text-align: left; transform-origin: 384px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the first day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11.25px; text-align: left; transform-origin: 384px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the second day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e turtle doves, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.75px; text-align: left; transform-origin: 384px 21.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the third day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e French hens, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e turtle doves, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the fourth day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAAAoCAYAAACCV8YCAAAAAXNSR0IArs4c6QAAA/ZJREFUaEPtmUmoVEcUhr/nRMSJEBcRQUUQcROFYBYKLhKcEJwIOCYoaFQIARGDokZFVFRQF3GOieKAilkkIYjzAM4LURyQbBxQERWcYhJxqh/Pxfvuu/d2Nd3Cu3lV0Ivue6q6+qv/DHW6hjCqRqCmaiuFhQgwqyiCADPArCKBKi4VlBlgVpFAFZcKyqwNczjwqyff3cAE4FFkH2C+I9cC+BEY5wlzGrACeB1g1iX2GfAzsBz4E3iRAXU68DUwFDgTtwnKfEujMfADcBzYl6PMtsAWe/4VcD/ArEuruYPYCziao0jN6g3sAZYCC+MurodBmZ4B0ljNAr4HBpqKa832gdkM0Mk9tpNoArSyVZTJXvnvp9CWuS6epcx2wEigH9AN6Agstsw1EfjGPtP8s8B3wKlCY/LbfK6Ll3LzT4FdQGdA8u7uIP4CHAIEfJWDOcjkPtaVFNf89uRl9RGwDejvZZ1ttM7VgVOBfypcRx4cufgw4GDaenlu3tcy2xPgAiBVXoktMglYa++l4v0Vbjg+vb7BjFxcIU5l0Z1yYEYnscAmSnlSZHyMAbbaB3ouJf1fR+TiK10img+8LAdmG+An4Etgk6unvgX+TiygE9r8npRZnw7Fy8XzYuYngO6eXYA01ekL5trrL4OuUJAcshsFqMDVOg/qEyXPvUQu/gEgb7ydNS8rZg4GfgPOuzg5wgG5mljgQ2Cje65gnKVcTdFh6Mbw0DZSRJiRi+vePifLxbOUqauVYuXMHFB9gB1AS1OdwCeHatMldhjnyoRZXxJQPHeUTLJpyoxkPQCY7MoglRfxIUjqliibb7DSIxlPZT8E6OGaBx2cXfuCwvR28Sxlqr78w1Sn04gX5FEMVEl0GRifKJci6J3cHXc2sMiuX3qveFM0N/d28SyYUf14AhjtgF2PyVLNAGV5XS3VGL2Y4t6qxQTymCu6T5qKiwgz7uLyst9LJaykm8dd+IDBvAc0Ar4AlllSEqybGYtLzYqp81xnpWmBYUYu3jpFVKk/PQlT9/Dt1o46DNy1TK6r5A1LOqdzmhsfG0QlsFvWIFF8LaIyIxeXJ84AnperTClKPT1dIZPxstRacm+1py5ZWSX7SOlFhFnq96YW1fEP1RRQ2/5IqQI15Zt0kjrBNQ7qM3uu9t0Ua4yomaqQoTLpv7J3WoAJcTdXj1KdIN1WVjt16g+jf8v4DfG7eta0vQXN6l4Y4jC7uv7lTmu1pdWXXgtm1KQNys0FVaXOeoPxOaAEVOlocDFTVzd1hXpaKSOAT63lpitjJYV2g4NZqfrCfCPg84dagOVJIMD0BOVjFmD6UPK0CTA9QfmYBZg+lDxtAkxPUD5mbwDkr8spiLbU7wAAAABJRU5ErkJggg==\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e calling birds, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e French hens, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e turtle doves, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the fifth day of Christmas my true love sent to me \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49\" height=\"20\" style=\"width: 49px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e golden rings, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e calling birds, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAAAoCAYAAACCV8YCAAAAAXNSR0IArs4c6QAABJFJREFUaEPtmXnIVUUYxn+mBYIalbigoAkRRegfUoKKoKIG0WZFVlqKLQoqiLihoiAoGBUYSpmR7YtFiIjiLuKG+ofigugfLqBERJRG2uo88U6d79xzzr13OB+cL2bgcr/v3Jn3vvPMM8+73HbEURoC7UqzFA0RwSyRBBHMCGaJCJRoKjIzglkiAmGmegH3A9uSyyMzs8FsD8wBluVgfRp4xr1ORjDrs/Fu4HNgUM7UlQb2jQhmMZi6rTPcFR4CvAf8npr+J3AK+CFtJl7zWmB7AuuAN4Ct9Un834wIZi1ak4FHAL3/GMFsBoGWc7vZ1X4MuAAcAjYAO4HvgL+LTDfCzNuAjsDPZqyDuwKdzehPwF/hvldu5VjgmxyvPnL7Xwycz/M6C0xpxjhgNHAf0AdYDrwFvAK8as9k87CJ9cHKwRLmkPbbG+hvkXwkcGfC1DHH0KnAgSzzRcwc6BLTr4B+LqItAAY4ED8wygvwVaYt+4DxRScWsK+7gE+d02MC1iaXvAvMBH4NtNMFeMqtn+tSpXvNhq7+BOBsM9F8lEWzq8BxY6WSVT9eA96xf8TiFtVAoPN+WVXA9P70AFYYiHqmvxcBvyX3mcdMPRcblwJXjHkS4eR4AfjEHoiZYtL/eXQHxPTHnQTuB563IPXvnvPAvN1px1rgacu5pgG/pJB6EfiwlZhZ1UPxAUq3VbexRazIA1MC/LVj2z3GyjTrtE6RTS9ph0CXFGhIsBWkJprO7LAad1e91KKqCCb8UjD+zMnfYGAooHhRl5nKs5RfKXo9C5xJbfQO4H33+ZMp5kqwFfmPApussyKpEMA1jYE2AF7aRa/lCspJAv0zL4uZ6pgIgPkFV3wY8AXQyURZwGsI3OvAlgQL/dVoRlerFoA8qN4v5dkNaWZX4GOnBw8DU0x0kyekBF45p6K5GgFKPaSntzjw+wIXgT8SC9Qw2GxA68o3MqoKppc/7UcturpdI+WXG411aZEVk5+zlEidk0lOBpLpUhoozdeBPGBfng5ijQBblTmq/OYBL9sVP5K12fQznz9mhX8Jr6K8SksZPVGwUwE53Jg7veSkvjUAlqYrb1bD93XTfF8q+73o8yXW66yp09OambzC200XvrcrrNJKX6KgtNB1VS4V7EjVgtKpl6yOLyzDWgOZAJuSqzcT6yRlqy0G6DY+YYl6blaSBjMZ+rVInRJFcpWS0kIFHZVTjTQ3vIYKVDn6bUhbKwCU0CUikg5fUfohI4E6R7uB9fZeKFNpMBWl9wCZSWmgl0qX3nY5mcrTRy1tCjRV7WVpMD3VdRoqFy+X5L6vlmoS3ZLsV8JMEkzlTuoEqSMirZhlelGGozoYHZRae+fKMFhFG0kwFTS+NH3Myi9D/fdFgJrMap60yM1CjVZxnQdT70p11piTIwAFoGaGQFPjVFFfDFeXSemD0iPV6bMtoDVjs03NFYiqNhRxHwRuNe+vGRiK3jU/aebsULYUCVWKiuV7LY3Su+r0tpywN3SojfwG1JChOCm70RFxCUQgMjMQuKxlEcwIZokIlGgqMjOCWSICJZq6CXYR2ykCf1AuAAAAAElFTkSuQmCC\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e French hens, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e turtle doves, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e partridges in a pear tree.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAnd so on ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11.25px; text-align: left; transform-origin: 384px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"13.5\" height=\"20\" style=\"width: 13.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e denotes the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th prime. Suppose that there are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e days of Christmas. How many gifts am I receiving in total?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function total = prime_days_of_christmas(n)\r\n total = 364;\r\nend","test_suite":"%%\r\nassert(isequal(prime_days_of_christmas(12), 824))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(2), 7))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(6), 103))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(10), 467))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(1), 2))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(25), 8600))\r\n\r\n%%\r\nassert(isequal(prime_days_of_christmas(365), 47830218))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":332395,"edited_by":332395,"edited_at":"2024-07-30T08:36:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-07-30T08:36:00.000Z","updated_at":"2026-04-02T15:11:40.000Z","published_at":"2024-07-30T08:36:54.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the first day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the second day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_2 = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e turtle doves, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the third day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_3 = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e French hens, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_2 = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e turtle doves, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the fourth day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_4 = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e calling birds, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_3 = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e French hens, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_2 = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e turtle doves, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the fifth day of Christmas my true love sent to me \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_5 =11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e golden rings, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_4 = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e calling birds, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_3 = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e French hens, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_2 = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e turtle doves, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1 = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e partridges in a pear tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnd so on ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e denotes the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th prime. Suppose that there are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e days of Christmas. How many gifts am I receiving in total?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3020,"title":"Prime Letters = Removing","description":"Given a string, remove all the letters which in ASCII Code are prime numbers.\r\n\r\nFor Example:\r\n\r\n s1 = 'Determine which array elements are prime'\r\n\r\nBecomes:\r\n\r\n s2 = 'Dtrin which rry lnts r pri'","description_html":"\u003cp\u003eGiven a string, remove all the letters which in ASCII Code are prime numbers.\u003c/p\u003e\u003cp\u003eFor Example:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003es1 = 'Determine which array elements are prime'\r\n\u003c/pre\u003e\u003cp\u003eBecomes:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003es2 = 'Dtrin which rry lnts r pri'\r\n\u003c/pre\u003e","function_template":"function y = primeLetters(x)\r\n y = x;\r\nend","test_suite":"%%\r\ns1 = 'Determine which array elements are prime'\r\ns2 = 'Dtrin which rry lnts r pri'\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'YeS, I SaY, make me SOme egg, aCe'\r\ns2 = ', , , '\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'qwertyuiopasdfghjklzxcvbnmQWERTYUIOPASDFGHJKLZXCVBNM'\r\ns2 = 'wrtyuiopsdfhjlzxcvbnQWERTUPADFHJKLZXVBNM'\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'DISSappearIng'\r\ns2 = 'Dpprn'\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'One, twO, three'\r\ns2 = 'n, tw, thr'\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'GaSSeS GO'\r\ns2 = ' '\r\nassert(isequal(primeLetters(s1),s2))\r\n\r\n%%\r\ns1 = 'SageS Must SaY See'\r\ns2 = ' Must '\r\nassert(isequal(primeLetters(s1),s2))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":4690,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":114,"test_suite_updated_at":"2017-09-27T16:27:47.000Z","rescore_all_solutions":false,"group_id":32,"created_at":"2015-02-15T21:22:59.000Z","updated_at":"2026-03-19T20:01:04.000Z","published_at":"2015-02-15T21:24:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string, remove all the letters which in ASCII Code are prime numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor Example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[s1 = 'Determine which array elements are prime']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBecomes:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[s2 = 'Dtrin which rry lnts r pri']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56260,"title":"Leonardo primes","description":"Leonardo numbers are defined by following recurrence relation:\r\n\r\n\r\n\r\nLeonard prime is Leonardo number which is also prime (see https://en.wikipedia.org/wiki/Leonardo_number). \r\n\r\nFor given n, find all Leonardo primes.\r\n\r\nExample:\r\nn=5;\r\nLeoNumbers=[1 1 3 5 9 15];\r\nPrimes=[2 3 5 7 11 13];\r\nLeoPrimes=[3 5];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 392.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 196.375px; transform-origin: 407px 196.375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLeonardo numbers are defined by following recurrence relation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 61px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 30.5px; text-align: left; transform-origin: 384px 30.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-24px\"\u003e\u003cimg 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+1IYjNL4tK2/M8nIKiHgsQZ+kaTXzIicGBTGOHjPLErwRkZQbEmwjaiSxCRCg194Heti4pVgd4LnTdPw9UOQESQiuDoTBAescKmeNc5tu0D8vhHoCgGTka6QdD1DIDAkGUnfzucqLsuzl27OAZwxjovQFkNgtUqbnZGR3NL3NEn3kPStBT1CBwbAhK8lMBkhbVNJKhNUL6hd5kWRu2Jk+SMyHUFfZv2qk8FPcumlHgKdYW1c5eGTRGHYjKCqGbsXSk5G/j0SEzr3wSqfgd8pjcD2QZyR3FXpvEu37/qNQFsEbijphAgmWXXe5HYd5AGrcwGu06f80l2loskP8VdIIhDomxZ4n9Zpc4hnCGhKHBfO/Xmerxf0C7DnldzSd1mWWKKfImp6Qdzmud3nBz9qm6Ml/SIY3rlzGsUl98OSfl9h0JMvDEgK9icERsMne56LcJp0jIGmklgOw9Unx4/VNEN8Qm5zEQJ8S3zrd4qf9OwXwtbrsyEVtUTP62isCOwWknoiWZMThkK0UyQQ2Ct+XdJekRAWJwkihVO4lB8fJggYm666xvNLd5VHaMpRg6qedpCS812N/TINRvT9JpII1IZ5BEINCmQOYkK0deKlbHHGmEdGuPUgSeBQpPDioWHrkW7qvItaBlEXBz1+0PPYY3LH/XQWVr5qoaKeQc1TpaLJRVeoXgiWxkS9fckkYSx7ywih/vOxfh0z/crtRpg4JE3zvI8mMiR30wgYASNgBIxANQJVZARGg7qFmw8SjSZlnsdN0s3hajsvTkmSntwvIqzOSlfoByz1mPAswe0VEdsyYx5ipGCN3NQiucm4Szybu/aakJRA2HUaASNgBIzAKBBYpKbpsoOJjKDGqUrT3GVbs3VBrB4/QTLCOK4l6Y0R9AzxIBbWuS1OSdxctxEwAkbACBiBXhAwGekF5pUbYX4w+MU7iYKxIGosJ8lbGVK/aASMgBEwAmNDoG8yskhNUwobbEaIYLfIpbhU213USyZiDFnxGiJjMePAwMrFCBgBI2AEjMBaINAXGalrwFoCVMgIXjqoa35ZooHCdTJHGPaSKJBCELepRZQtDJGrNwJGwAgYgSkj0BcZqeva2zWWyQMnuUqROG+KJfeHrwqSM8Uxuc9GwAgYASNgBM5HoC8ykmKE7LEk6FnX07JTqDjwRiHz4VRLnqmYMTRNnDTVcbvfRsAIGAEjsAEI9EVGgJIganjT9OliS/x/YpIcIunkCc8neQlQ05DBlzLVlNITngJ33QgYASNgBEoh0CcZ2UXSWyRhxJonvys1NurFTuTACMhGyOopF2xfyLFDWZaxeMrjdN+NgBEwAkZgwxDok4wkQ0zCw+Kiumoo3bpTRNAw4vp/NeLiTyGU7qKx5dmMl4Xnr4uRnzMCRsAIGAEjMDgCfZIRBrtrRGB9SuSUKQkARp94nRCn44clG+qp7pyMfGnCrso9weVmjIARMAJGYCoI9E1GaI/kOWTze2pB6QheNAQHI4EeNiPrUHIy8rWebW/WAT+PwQgYASNgBEaKQN9kBBggCs+XdGohotAX4el7Sk1G+kbc7RkBI2AEjEAvCAxBRhgYKZkPD0PM0zse6fUl7SfpeZFFuOPqB6vOZGQw6N2wETACRsAIlERgKDKSCMnjwrMGG4guCkTkzpKOWjMiAjYmI12sENdhBIyAETACo0NgSDICGDtIwuX3+5LaersQZXU3ST8oaIsy5ASajAyJvts2AkbACBiBYggMTUaKDWwNKzYZWcNJ9ZCMgBEwAkagv3Dwxro9AiYj7TF0DUbACBgBIzBCBCwZGeGkzOmSych05so9NQJGwAgYgQYImIw0AGvgR3GHJnIt5VeS9g336IG75eaNgBEwAkbACLRDwGSkHX59vv1KSY+IBs8O9+WP9NkBt2UEjIAR2FAEtpN0o7gE4rXJhfDjkk6Q9MsNxaTTYZuMdApn0cpKkpErRkTXm0g6YGYU/yXpA5KOk/SjoiOcfuWXlfRASReR9OzpD2fhCG4maa/YnG+QPfm7WC8fknT8mnq2tZla9tyrSjpI0m0k3VjStyWRb+rNkUvrL20aGPm7HOo3lfTQ+EYY+1Dl2pJeH+lCDpV05pyOkOeM7xnScaQkssG/PMjJO2MsZw01iJG3W3tPNBkZ+Uxm3StJRlIzl5f0ttgk+TfaRDX0h+nANEhP+eDIDn2IJBJBPl3SswbpSf+N3jLSLtAyROThkt7egat+/yMp3+L2ES+IVBUEfpwt4Me6ebGk88p3p9cWEgl5rKS7SRpDSos8E/p9Jb21AhHOSPKbkecM1TgxsVKU72MiivhjvEduQa7xnmgy0uv32KqxWTJyF0kntapx68s5GWFjvL2kUzpuY52qI07OAyRdQRIHDZvSJTaYjKA2vJ+kX6zTJHc4FiRJb5D0FknvkvTjSB56L0kPi7XDdweGJ3bY7tBV7S6Jw56EpRzotxsJGakjGblcRAonHtY9Q4oFnpydO0pCZb5uxLHNell5TzQZaQN7v+8i1mUjoxBC/x6SvtlxFxA/vlvS1SV9Mm5xVs3MB5lAe5Q/S8qJ3BgkIxeVRHZsslc/OW50HS+X86vjEOWGSHmuJG6b4OGyLQI7SXqVpPdVSI7ymzZk9k2SDh7gtl1qzaC2PDfguH+oo8YgGamzRlGjfUzSd52ctA5cWnlPNBmphe8oHurDtTdvA1HxE7NNZBQgjLgTiCUR8+49EskICSmZQ8jCzQtJuPI2mBqkdRy2LlsRwMYG6QBqCm7TswW7hFeEuo8koveJyNR9YtnHmkl7zFTICOlFkFJNpb+sF+bxCEnY+2Fk+6c+F1HWVqM90WRkoFlaodnSZITbC8kFUTVQ5ulQV+j6RrzS6MPrAZE+DhbsY7AxwiBxSpt1D/BvaeLRIdE8eUHjSco0FJZ9rJmpkZGp9TeRkXQR+YKkF4RReRUJLvktNNoTTUZKTkW3dZdW0+BRw83+VpLOkHR3SV/vdghrXVujD68HJPo4WG4bImyGc6ykR61hgsoepuqCJtLBx20WycjP+2w8btSlpWljO9w5A68sCQNbcqRR8m953hS8Oi5ufR/wdZfEJSU9SBIkmEvDaZJeGGr4vhwSGu2JJiN1p3b450obsCJG/nAY0WE3ggX5bzsYNofiLSR9WtI5UR9SmCtJ+idJ+Oyjlz1a0nsjeeKdIqYK9g7cvLF9GLsvf90Pj03v1pK+ErEKOoC4sorSZIS9g3lJXkOoHzjIuih4mlxX0ickJTdXjAWvFuvlerHB4r30vbDXYePFowm7B9wwsa+amu1KkozMqkgZE15LiN1LHn6l1wxrYyxkZOdQqT4k9qd5kuBS/eX7ubSka0hiPeMej70F5OHXYdiMu/F+knAbfuqKKtBZUoIrNQE0MaAuTUrq7onn7xkmI11snf3UUdq1F/UMLocUjBDZ0NtmUsaok48IA8fc2PYfJXGrxhNlD0mfk3TvID8cbrz3N5LuGv2Zgi1Ckw8PIvY4SS8taBdQ+mC5lKTXhQStS88rjKchGay/n8b8Y6GP3QveXcSnwMjzZeF2jqcGNz7WF+oi1tNQNhdtdoKkJuUSgOvrrDqHbwYvGw4SAm6VKKXXzFjICGsMArBnFkiybzLCGkYKzVwj9aawJ7wkvI3Yg1HX3SGId9sLYhUpIVYKEs1SMVKa7IkmIyW+6EJ1liQjfxsHIxshBde7tm7DuLs+Iw6NKq+ffOND5MnHh9HVf4c0hABsn+mwP4Wm5YJqG3144Q58eEFCUvpguWbcrnCP7MrzilsiEha8kRIRyeeNvxNkCsLB4fHl8OCB8OJhluJGdNWf0msmr59AaMRnQcdPbJ8qCci1QvpTipCUXjNjISMJ93wN901GUh+QSLPPJUJPiAAibUNMIJ1JbdaVGhRSAqmF8PM9oZqClODB1bX0udGeaMlIn9tNu7ZKkpHcEJGgPsQ9+E6L7rKpsWFCLOYFwMptVBCvQ17+N3sen/53ZFITxPFjLo0+vBgIGxFY47XUtci09MGSvAwYCmuTzTOp4VaZJ6RhSIogpp+aU0GyUeHGeFgQkiQVQZXB/z8yk5oM5UXQdPzsw4jkkQ5yS17kss962S0igXYd36L0mhkbGZklt1VBz0qpadIaSao5YvTgGo/rM+pPyDju4JCQO8b3BTFpK61O7c6SEogPDgyoN7siJY32RJORptvGcM+XtBnp2hCRDRMRJAfUvEM22ajgv4+tCjcCbrgcIKxLpCT8NDEUyyMqrjJTbbwYGn140Tl0xNyC/xgHaNONpu146cYqY6bfqNOeFOMg6irztGqhPiQiqGPYEKsO2dxGBZLKOsHGKAUHy+O81PUEq2OouGxMTdbnvLr+OVRe2AvMI2LpXQgD6lQOr1UCow21ZlL/Sx/uy+Yr//vQZCQnf6+VBEE4StIXo5NJcrNrwQCUVaQE0kOYfILytSmN9kSTkTZQ9/suNz6MPCl4u+wfFtJte9G1ISKRCvmwyOGA0eq8kmxUEE/+Z4QR/0k8nNsjoDriw6hT2m60qxzMqV+NPrxsMIjnCYYFcftGnUFmz7QdL1WtMuYUlXKf2LBSmOyG3b/gcew+EBUjnp6XqyRfEz8LKQprLBEXDKHfL+k3kV+pDpZjICNIBJl/bALqhtHHsBtVFsaXTQ+ModaMycjWryOXSDOPXEyQzqRLSZI+4l2FxKTpXNf9HjkDMJBmHaIKpGA8jtSGs2bV0mhPNBlZFeb+3ysVZ6RrQ0S8GjAMW+TmifEWxArdJR8YN1kISSopEiy/T8XFuNGHl401SRk4VMl/0ZUHSEmRezr4IZ5tQ8AzfiRgSMYWRW/NowN/MLy9EnkFziTu7kq33scXTqAz1JkY3NYlIvQrfT9IUeoS9TrjKblmTEa2zkAukeYCl+e4yaWPpSIbc/7zXWG7hoqQQsJG4pKwttqqARvtiSYjdT7RcTxTioysEgIekTh5Noi2mRvaJWIDk18kts/Fo8krItfvp7G2tSDvc+YafXgzHWNTQu3BhtCVbUzJg2WVEPAQGA5RjEvzkm6HGDsvMprO1z9SwfdkleRj7dLFuOT6SUQEF2+y9Tbd+JkDov1C/nEF7aKUXDMmI9vOUC6R5kKG5+Dns0dy6WPX3oSEFyCswr9mJASVJ+o/iHFXWaMb7YkmI118wv3UUYqMNA0Bn7JYcrDMGlRx4PxHGGVivDqvJPFjlUtoHgm2KxfjPmao0Yc30yHiZ2AH8cwVYwlUja/UwbJKCHj00mx0r5nZcOk3awGVwyKj6XxNVEliEqHBs2cKyR0hIuQLQqU0L0MvBwbu7fOMcInNw5qBmGF03kUptWbyvtlm5P/RyCXSVXZHSfqISjJP0NdmnqtICBI57FS+2iEJSX1stCeajLSZ2n7fLUFGZkPAE/eDjKKLCjpFLK4xtsuZPO9wW0O3uSivRi5+hI3P3uxyLxtcjJGyYAyLd8+Z/ULeqLVGH95MzWljws4BVU1TQ9Y+yUiu5yaqIwkbv7UAKfYY1i7Bm2bnOq0F4j4sCrKXrwlsa2ZJcBJ3J5degvURWI6108bDp9ECqPkwBz62AfQL7595EhEkjwR6m5frJ80DB9myb7Zm187PabJJEViHNGDNJdKzkr60lxKfKakd8RaDoJC0r6nkooqEsGYwFufb7WK/qVpjjfZEk5G6n+nwz5UgI/kmzwiXJVTDuhv3Sz6G2VTxdQ+WXPxYdbAkLxsOOsaMGyNxJTBwbCrK7nPWGn14Mx1LpBBsugqpXupgyfXc6JeZo3mugGyCbLTooAmQNhtIL9k+/GJJUsa0Jn5fIc7Oxd0cpNifEBgNj4Rlnil9rg/awlsINRKRN/mOqqQe2M5ApLgNY7Q+z2gxEVgMDLvKlFxqzVgysnWlpf08BXzM1bOzake+Hdz/j2uYqX2WhCCJRvXN91iShFgy0vfO0nN7JcgIkgcWJ4cChVs5hz4+54kt82H8XWyOj5dEqO4q9UkKnIYBJoZY88JWJ/Ejt74qkXouxkXlg6897XUdh6Pr6SN8OQG5uOVX2cG1KEg5AAAF6ElEQVQsa48xYtHeVU6SEgcLByVrBBUDhYBJxMfA1iPNN+QAtQy3TogVkrJ5EVqTOy5eVymsfBVOyfOqSkWTjxO1BfEZkNg1MQhdNjdd/B3sIN/cRuuUKqKev5fGnUKI4x7etpRYM3mfwABCimSoyk6ibf+bvo9X0gmSMMSuwjsnul1GGc4l0lUqmvxiQyZn9kqCktUl1/Sb/YhQCUR4pe/YJUHWIT2lJCGz+DfaEy0Zabp8h3u+SzLCgcnt8YAINdxkVPM+yvQBERVz0U0tD/IzK12hH9hP8OGRvIr/IsqmzTEWDgIixRKUCONTROcU+gsxwT3ulJoh34nZwW24K/1w1wcLY2QNkjcokde6czLP4yaJyXEpnGfwnHtezbMhYh0j0kZKgLsvB0xTUXbdsaz6HG7LeM7UwY6Depm7dAry9vdLpFNN+tv1mkltI/FDQsba4ScVos1yGfpsEMi+gtQhbcVWCeJPThgKFzAkEPSHBKGoyTAcZW1xAaMgrT0+jLAhvKv2N5dIV8XESQQTo27awaYKjOqSiDSP9B0vHWJU/aDJQmjx7Mp7oslIC9R7frVLMlKi64mMcPguuuWWaHsd6mR+kTx1RUY4rIjkyO0PSUZXRo5dYp3ICGLjquiXXba1jnVBzlBhLVKVNRn3FNZMk/Fs6rPMI945SFJKxSbpHFuTkc4hLVahyUgxaEdRcddkZBSDWtIJk5F2s9Q1GWnXG79tBFogYDLSAryeX00JlWgWcfTYgoHVVdP0DNtkmuNgQSzcNi/QZAYcdiWosxapaaY0nj77mkTxqDNRd3YVa6TPMbgtI3ABAiYj01kMKRYFBqCULjLrdjn6ugasXba5TnVt4i23rgHrOs1zV2NJZIT6FhmMd9We6zECRREwGSkKb6eV54Z8VDy2gGB1XXs7BWVNKivhGTEFaOq69k5hLH33MUkiCS7YVWyavsfg9oyAJSMTXQMEjcLim1IVMGzoYWH3QGyERUHPhu7jGNtPqcIx/iUPxaaU5DpJHJlFQc82BY8m40ySUox/UXW5GIFJI2DJyLSmj1TSBL7BfgT3UXzITx7REIgqSKwHsolysLrUQyDhdsjI5rNe79s9RRA1DtSuvIja9WY6b4MbgdNw36yToXg6I3NPNxIBk5FpTXvKC0OOD0pVwJwhR0TODYL04I8/G7J7yH6NvW0kSgcWThM+VgwIOEVoaoxY8+R3Y+3vGPqVJErEGDl4AgEBx4CZ+zByBExGRj5BFd1DpA8J4UaEdASvGvIVjKWQg4RAPl1mEx3L2Er0IxE4ElURubVuYKMSfRmiTvYgDDAJGEdkzlUDSQ3R96HahMAREJBgVicO1Qm3awS6RMBkpEs0+6uLZHVvlHQjSeQ2OKhhzoKSPYUsccslHLc3yuVIE5QMA0RsJn64/PG1fAL1IwSbIG3klHFZjACEHzdw1HpnGSwjsA4ImIxMdxb3jHwD3Cg59AmzTl6OMRT6hmSEzL6OfzB/RvCieVFESsTWZlML+xDh9FM+DUtH5q+EnUMVir2I7bI29YtZw3GbjEx7Ukmshv0IkSzxrkHcTfKyoQtuvmQnpXDYkjzPZVsEfABviwfEjNwtp4YRtNfLVgRSsr1zNlSl5zWxxgiYjEx/ckn6dFR41nBTwrWWRE9DFw6Xw0KNRMK4TbOFWIY/wesQt5PFdayJAJeNoeu/k5DscEnHSjq968onXh979T6S/iEkI5YeTXxC3f2ttzNjMn0EdoismGR3PGJEcQcgJOi1IUcfNSG5YKFBRMgaCok0Edn2+4OQkM4dz5oxJvcbYreAiOwtCVsxjFZNRIaYBbdZFAFLRorC68olbScJA0VSWJ9nRIQKC2kWePhQqV4QkGs8RlA5WqImgQffEDmp/uJvyAisIwImI+s4qx6TETACRsAIGIEJIWAyMqHJcleNgBEwAkbACKwjAiYj6zirHpMRMAJGwAgYgQkhYDIyoclyV42AETACRsAIrCMCJiPrOKsekxEwAkbACBiBCSHwf866QgLAcriVAAAAAElFTkSuQmCC\" width=\"273.5\" height=\"61\" style=\"width: 273.5px; height: 61px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLeonard prime is Leonardo number which is also prime (see \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Leonardo_number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Leonardo_number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find all Leonardo primes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.75px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.875px; transform-origin: 404px 40.875px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=5;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eLeoNumbers=[1 1 3 5 9 15];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ePrimes=[2 3 5 7 11 13];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eLeoPrimes=[3 5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function LeoPrimes = LeonardoPrimes(n)\r\n LeoPrimes=n;\r\nend","test_suite":"%%\r\nn = 5;\r\nLeoPrimes_correct = [3,5];\r\nassert(isequal(LeonardoPrimes(n),LeoPrimes_correct))\r\n\r\n%%\r\nn = 0;\r\n%LeoPrimes_correct = [];\r\nassert(isempty(LeonardoPrimes(n)))\r\n\r\n%%\r\nn = 25;\r\nLeoPrimes_correct = [3,5,41,67,109,1973,5167];\r\nassert(isequal(LeonardoPrimes(n),LeoPrimes_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":2663765,"edited_by":2663765,"edited_at":"2022-10-10T14:54:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":"2022-10-10T13:22:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-10T12:53:17.000Z","updated_at":"2026-01-13T16:14:23.000Z","published_at":"2022-10-10T12:53:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeonardo numbers are defined by following recurrence relation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL(n) = \\n \\\\begin{cases}\\n 1 \u0026amp; \\\\mbox{if }~n = 0 \\\\\\\\\\n 1 \u0026amp; \\\\mbox{if }~n = 1 \\\\\\\\\\n L(n - 1) + L(n - 2) + 1 \u0026amp; \\\\mbox{if }~n \u0026gt; 1 \\\\\\\\\\n \\\\end{cases}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeonard prime is Leonardo number which is also prime (see \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Leonardo_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Leonardo_number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find all Leonardo primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n=5;\\nLeoNumbers=[1 1 3 5 9 15];\\nPrimes=[2 3 5 7 11 13];\\nLeoPrimes=[3 5];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47803,"title":"Check if the input is a strong prime","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 109.995px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.491px 54.9977px; transform-origin: 406.497px 54.9977px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.5882px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10.2941px; text-align: left; transform-origin: 383.496px 10.2941px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMore information about strong primes on \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Strong_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 79.4118px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.493px 39.7059px; transform-origin: 403.498px 39.7059px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisStrongPrime(11) = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisStrongPrime(2) = 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisStrongPrime(9) = 0; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisStrongPrime(227) = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = isStrongPrime(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nstrongPrimeList = [11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499];\r\nfor idx = 1:100\r\n x = randi([2 500]);\r\n y_correct = 0;\r\n if ismember(x, strongPrimeList)\r\n y_correct = 1;\r\n end\r\n assert(isequal(isStrongPrime(x),y_correct))\r\nend\r\n\r\n%%\r\nx = 4673;\r\ny_correct = 1;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 4677;\r\ny_correct = 0;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 46747;\r\ny_correct = 1;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 46748;\r\ny_correct = 0;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 467317;\r\ny_correct = 1;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n\r\n%%\r\nx = 467318;\r\ny_correct = 0;\r\nassert(isequal(isStrongPrime(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-04T16:46:35.000Z","updated_at":"2026-04-03T03:56:15.000Z","published_at":"2020-12-04T16:46:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore information about strong primes on \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Strong_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[isStrongPrime(11) = 1;\\nisStrongPrime(2) = 0;\\nisStrongPrime(9) = 0; \\nisStrongPrime(227) = 1;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42704,"title":"prime to each other","description":"Given two integers n1, n2 greater than 1, find out if they have common divisors or are prime to each other. Return \"true\" if they have common divisors and \"false\" if they are prime to each other.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two integers n1, n2 greater than 1, find out if they have common divisors or are prime to each other. Return \"true\" if they have common divisors and \"false\" if they are prime to each other.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = prime_to_each_other(n1, n2)\r\n tf = false;\r\nend","test_suite":"%%\r\nn1 = 3;\r\nn2 = 5;\r\ntf_correct = 0;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 27;\r\nn2 = 123;\r\ntf_correct = 1;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 36;\r\nn2 = 49;\r\ntf_correct = 0;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 27;\r\nn2 = 28;\r\ntf_correct = 0;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 23;\r\nn2 = 69;\r\ntf_correct = 1;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))\r\n\r\n%%\r\nn1 = 2;\r\nn2 = 3^5+1;\r\ntf_correct = 1;\r\nassert(isequal(prime_to_each_other(n1, n2),tf_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":61785,"edited_by":223089,"edited_at":"2023-02-02T13:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":"2023-02-02T13:04:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-01-05T08:30:44.000Z","updated_at":"2025-12-07T18:53:39.000Z","published_at":"2016-01-05T08:30:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two integers n1, n2 greater than 1, find out if they have common divisors or are prime to each other. Return \\\"true\\\" if they have common divisors and \\\"false\\\" if they are prime to each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61052,"title":"Compute the Dedekind psi function","description":"Write a function to compute the Dedekind psi function. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 10.5px; transform-origin: 408px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/DedekindFunction.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eDedekind psi function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = DedekindPsi(n)\r\n y = psi(n);\r\nend","test_suite":"%%\r\nn = 1;\r\ny = DedekindPsi(n);\r\ny_correct = 1;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8;\r\ny = DedekindPsi(n);\r\ny_correct = 12;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 49;\r\ny = DedekindPsi(n);\r\ny_correct = 56;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 312;\r\ny = DedekindPsi(n);\r\ny_correct = 672;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1441;\r\ny = DedekindPsi(n);\r\ny_correct = 1584;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8028;\r\ny = DedekindPsi(n);\r\ny_correct = 16128;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 14035;\r\ny = DedekindPsi(n);\r\ny_correct = 19296;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 85432;\r\ny = DedekindPsi(n);\r\ny_correct = 131040;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6645344;\r\ny = DedekindPsi(n);\r\ny_correct = 10402560;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5533221188;\r\ny = DedekindPsi(n);\r\ny_correct = 9083498112;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\np = primes(1e8);\r\nq = p(randi(length(p)));\r\ny = DedekindPsi(q);\r\nassert(isequal(y,q+1))\r\n\r\n%%\r\np = primes(200);\r\nq = p(randi(length(p)));\r\nn = randi(5);\r\nx = q^n;\r\ny = DedekindPsi(x);\r\nassert(isequal(y,x+x/q))\r\n\r\n%%\r\np = primes(200);\r\nk = unique(randi(length(p),[1 randi(5)]));\r\nq = p(k);\r\nx = prod(q);\r\ny = DedekindPsi(x);\r\nassert(isequal(y,prod(q+1)))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-10-25T15:14:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-25T15:09:34.000Z","updated_at":"2026-02-26T13:49:01.000Z","published_at":"2025-10-25T15:14:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/DedekindFunction.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDedekind psi function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43085,"title":"Primes Checker","description":"Given variable inputs\r\nCheck if they are prime numbers","description_html":"\u003cp\u003eGiven variable inputs\r\nCheck if they are prime numbers\u003c/p\u003e","function_template":"function y = isOrArePrimes(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(isOrArePrimes(x),y_correct))\r\n%%\r\nx = 1;\r\ny = 7;\r\ny_correct = [0 1];\r\nassert(isequal(isOrArePrimes(x,y),y_correct))\r\n%%\r\nx = 2;\r\ny = 17;\r\nz = 20;\r\ny_correct = [1 1 0];\r\nassert(isequal(isOrArePrimes(x,y,z),y_correct))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":0,"created_by":13865,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2016-10-29T17:09:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-06T01:20:45.000Z","updated_at":"2026-02-11T18:07:13.000Z","published_at":"2016-10-06T01:23:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven variable inputs Check if they are prime numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1298,"title":"P-smooth numbers","description":"This Challenge is to find \u003chttps://en.wikipedia.org/wiki/Smooth_number P-smooth number\u003e partial sets given P and a max series value.\r\n\r\nA P-smooth number set of N contains a subset of 1:N integers whose prime factors are all \u003c=P.\r\n\r\nFor P=3 and N=16: P-smooth subset is [1 2 3 4 6 8 9 12 16]. Values 5,7,10,13,14,and 15 are primes \u003e3 or values divisible by primes\u003e3.\r\n\r\nvs = find_psmooth(P,N)\r\n\r\n\r\nSample \u003chttps://oeis.org/A051038 OEIS 11-smooth numbers\u003e\r\n\r\nWhere are P-smooth numbers utilized or present themselves?\r\nUpcoming Challenge solved by P-smooth numbers.","description_html":"\u003cp\u003eThis Challenge is to find \u003ca href = \"https://en.wikipedia.org/wiki/Smooth_number\"\u003eP-smooth number\u003c/a\u003e partial sets given P and a max series value.\u003c/p\u003e\u003cp\u003eA P-smooth number set of N contains a subset of 1:N integers whose prime factors are all \u0026lt;=P.\u003c/p\u003e\u003cp\u003eFor P=3 and N=16: P-smooth subset is [1 2 3 4 6 8 9 12 16]. Values 5,7,10,13,14,and 15 are primes \u0026gt;3 or values divisible by primes\u0026gt;3.\u003c/p\u003e\u003cp\u003evs = find_psmooth(P,N)\u003c/p\u003e\u003cp\u003eSample \u003ca href = \"https://oeis.org/A051038\"\u003eOEIS 11-smooth numbers\u003c/a\u003e\u003c/p\u003e\u003cp\u003eWhere are P-smooth numbers utilized or present themselves?\r\nUpcoming Challenge solved by P-smooth numbers.\u003c/p\u003e","function_template":"function vs = find_psmooth(pmax,vmax)\r\n% pmax is prime max\r\n% vmax is max value of set 1:vmax\r\n vs=1;\r\nend","test_suite":"%%\r\nvs = find_psmooth(2,16);\r\nassert(isequal(vs,[1 2 4 8 16]))\r\n%%\r\nvs = find_psmooth(3,128);\r\nassert(isequal(vs,[1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128]))\r\n%%\r\nvs = find_psmooth(11,73);\r\nassert(isequal(vs,[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72]))\r\n%%\r\npmax=7; vmax=120;\r\nvs = find_psmooth(pmax,vmax);\r\nvs=unique(vs); % Validity checks\r\nvs(vs\u003evmax)=[];\r\nvs(vs\u003c1)=[];\r\nvs=floor(vs);\r\nlength(vs)\r\nif length(vs)==50 % Known length\r\n pass=true;\r\nelse\r\n pass=false;\r\nend\r\npv=primes(vmax);\r\npv(pv\u003c=pmax)=[];\r\nfor i=pv\r\n if any(mod(vs,i)==0) % check for prime divisors \u003epmax\r\n pass=false;\r\n break;\r\n end\r\nend\r\nassert(pass)\r\n%%\r\npmax=11; vmax=300;\r\nvs = find_psmooth(pmax,vmax);\r\nvs=unique(vs); % Validity checks\r\nvs(vs\u003evmax)=[];\r\nvs(vs\u003c1)=[];\r\nvs=floor(vs);\r\nlength(vs)\r\nif length(vs)==104 % Known length\r\n pass=true;\r\nelse\r\n pass=false;\r\nend\r\npv=primes(vmax);\r\npv(pv\u003c=pmax)=[];\r\nfor i=pv\r\n if any(mod(vs,i)==0) % check for prime divisors \u003epmax\r\n pass=false;\r\n break;\r\n end\r\nend\r\nassert(pass)\r\n%%\r\npmax=13; vmax=900;\r\nvs = find_psmooth(pmax,vmax);\r\nvs=unique(vs); % Validity checks\r\nvs(vs\u003evmax)=[];\r\nvs(vs\u003c1)=[];\r\nvs=floor(vs);\r\nlength(vs)\r\nif length(vs)==231% Known length\r\n pass=true;\r\nelse\r\n pass=false;\r\nend\r\npv=primes(vmax);\r\npv(pv\u003c=pmax)=[];\r\nfor i=pv\r\n if any(mod(vs,i)==0) % check for prime divisors \u003epmax\r\n pass=false;\r\n break;\r\n end\r\nend\r\nassert(pass)\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":97,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":44,"created_at":"2013-02-23T23:06:45.000Z","updated_at":"2026-02-07T16:12:25.000Z","published_at":"2016-02-21T23:06:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to find\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Smooth_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eP-smooth number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e partial sets given P and a max series value.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA P-smooth number set of N contains a subset of 1:N integers whose prime factors are all \u0026lt;=P.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor P=3 and N=16: P-smooth subset is [1 2 3 4 6 8 9 12 16]. Values 5,7,10,13,14,and 15 are primes \u0026gt;3 or values divisible by primes\u0026gt;3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evs = find_psmooth(P,N)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSample\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A051038\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS 11-smooth numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere are P-smooth numbers utilized or present themselves? Upcoming Challenge solved by P-smooth numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50933,"title":"Find pairs of primes with the same digit sum","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86px 8px; transform-origin: 86px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe activities in the paper “\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A007513/a007513.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eA New Function from a Table of Primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.5px 8px; transform-origin: 176.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e” involve listing sets of consecutive primes such that the first and last numbers in the set have the same digit sum. For example, if the set size is 7, the first set that qualifies is 5, 7, 11, 13, 17, 19, 23 because the digit sums of 5 and 23 are both 5. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.5px 8px; transform-origin: 126.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes two numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89px 8px; transform-origin: 89px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as input and all sets of size \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.5px 8px; transform-origin: 63.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of primes less than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.5px 8px; transform-origin: 58.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that the first and last numbers in the set have the same digit sum. Return a two-column matrix with the first prime in the set in the first column and the last prime in the set in the second column. Sort the matrix with the first column in increasing order.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = primesEqDigSum1(m,n)\r\n y = f(m,n)\r\nend","test_suite":"%%\r\nm = 2;\r\nn = 100;\r\nassert(isempty(primesEqDigSum1(m,n)))\r\n\r\n%%\r\nm = 2;\r\nn = 2000;\r\ny_correct = [523 541; 1069 1087; 1259 1277; 1759 1777; 1913 1931];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 3;\r\nn = 1000;\r\ny_correct = [109 127; 113 131; 313 331; 503 521; 691 709; 709 727; 769 787; 839 857; 859 877; 863 881; 919 937; 953 971];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 4;\r\nn = 500;\r\ny_correct = [79 97; 139 157; 173 191; 233 251; 239 257; 349 367; 379 397; 439 457; 443 461];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 500;\r\ny_correct = [2 11; 19 37; 23 41; 43 61; 53 71; 149 167; 163 181; 179 197; 263 281; 449 467];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 7;\r\nn = 500;\r\ny_correct = [5 23; 191 227; 193 229; 281 317; 337 373; 373 409];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 10;\r\nn = 500;\r\ny_correct = [17 53; 37 73; 109 163; 173 227];\r\nassert(isequal(primesEqDigSum1(m,n),y_correct))\r\n\r\n%%\r\nm = 19;\r\nn = 5000;\r\ny = primesEqDigSum1(m,n);\r\nassert(isequal(size(y,1),46) \u0026\u0026 isequal(sum(y),[110158 116332]) \u0026\u0026 isequal(y(31:37,1)',[3319 3491 3547 3583 3931 4057 4139]))\r\n\r\n%%\r\nm = 23;\r\nn = 50000;\r\ny = primesEqDigSum1(m,n);\r\nassert(isequal(size(y,1),415) \u0026\u0026 isequal(sum(y),[8631611 8718173]) \u0026\u0026 isequal(y(53,:),[3671 3851]))\r\n\r\n%%\r\nm = 53;\r\nn = 1e6;\r\ny = primesEqDigSum1(m,n);\r\nassert(isequal(size(y,1),5697) \u0026\u0026 isequal(sum(y),[2788369873 2792164201]) \u0026\u0026 isequal(y(3121,:),[538777 539479]))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-14T05:04:14.000Z","updated_at":"2025-08-01T21:24:16.000Z","published_at":"2021-03-14T05:11:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe activities in the paper “\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A007513/a007513.pdf\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA New Function from a Table of Primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e” involve listing sets of consecutive primes such that the first and last numbers in the set have the same digit sum. For example, if the set size is 7, the first set that qualifies is 5, 7, 11, 13, 17, 19, 23 because the digit sums of 5 and 23 are both 5. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes two numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and all sets of size \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of primes less than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that the first and last numbers in the set have the same digit sum. Return a two-column matrix with the first prime in the set in the first column and the last prime in the set in the second column. Sort the matrix with the first column in increasing order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44099,"title":"Find my secret function II","description":"If give my function a x value it will give me a y value, so find the secret of it:\r\nExamples:\r\n\r\ninput x=23 ---- \u003e\u003e\u003e output y=100\r\n\r\ninput x=21 ---- \u003e\u003e\u003e output y= 77\r\n\r\nHint: use tags\r\n","description_html":"\u003cp\u003eIf give my function a x value it will give me a y value, so find the secret of it:\r\nExamples:\u003c/p\u003e\u003cp\u003einput x=23 ---- \u0026gt;\u0026gt;\u0026gt; output y=100\u003c/p\u003e\u003cp\u003einput x=21 ---- \u0026gt;\u0026gt;\u0026gt; output y= 77\u003c/p\u003e\u003cp\u003eHint: use tags\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 23;\r\ny_correct = 100;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 21;\r\ny_correct =77;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = magic(1000);\r\ny_correct = 3.755040202300000e+10;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = magic(5);\r\ny_correct =100;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = 1:220;\r\ny_correct = 4438;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":37163,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2017-04-25T11:26:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-04-23T19:43:02.000Z","updated_at":"2026-01-03T11:33:47.000Z","published_at":"2017-04-25T11:26:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf give my function a x value it will give me a y value, so find the secret of it: Examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput x=23 ---- \u0026gt;\u0026gt;\u0026gt; output y=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput x=21 ---- \u0026gt;\u0026gt;\u0026gt; output y= 77\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: use tags\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47808,"title":"Check if the input is an interprime","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 70.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 331.5px 35.4px; transform-origin: 331.5px 35.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 308.5px 10.4px; text-align: left; transform-origin: 308.5px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMore information about interprimes on \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Interprime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 328.5px 20px; transform-origin: 328.5px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 328.5px 10px; transform-origin: 328.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisInterprime(2) = 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 328.5px 10px; transform-origin: 328.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisInterprime(4) = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = isInterprime(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n%%\r\ninterprimeList = [4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99];\r\nfor idx = 1:100\r\n x = randi([2 99]);\r\n y_correct = 0;\r\n if ismember(x,interprimeList)\r\n y_correct = 1;\r\n end\r\n assert(isequal(isInterprime(x),y_correct))\r\nend\r\n\r\n%%\r\nx = 4676;\r\ny_correct = 1;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 46725;\r\ny_correct = 1;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 4622;\r\ny_correct = 0;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n%%\r\nx = 467475;\r\ny_correct = 1;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 467476;\r\ny_correct = 0;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n%% \r\nx = 499994;\r\ny_correct = 1;\r\nassert(isequal(isInterprime(x),y_correct))\r\n\r\n ","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":"2020-12-28T11:41:15.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2020-12-04T17:23:08.000Z","updated_at":"2026-01-16T17:38:20.000Z","published_at":"2020-12-04T17:23:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore information about interprimes on \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Interprime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[isInterprime(2) = 0;\\nisInterprime(4) = 1;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60975,"title":"Check Legendre's conjecture","description":"Context and problem statement\r\nLegendre's conjecture states for a given positive integer n, there always exists at least one prime number p between n² and (n+1²) :\r\n\r\n\r\n\r\nFor a given input n, List the prime number(s) p in the interval ]n^2; (n+1)^2[.\r\n\r\nExamples\r\n\r\nn = 1 =\u003e p = [2, 3];\r\nn = 2 =\u003e p = [5, 7];\r\nn = 10 =\u003e p = [101, 103, 107, 109, 113];\r\nn = 20 =\u003e p = [401, 409, 419, 421, 431, 433, 439];\r\n\r\nForbidden functions / expressions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nProblem 60972. Check Bertrand-Chebyshev's theorem about prime numbers\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 697.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 348.733px; transform-origin: 408px 348.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eContext and problem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.825px 8px; transform-origin: 174.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLegendre's conjecture states for a given positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 144.308px 8px; transform-origin: 144.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethere always exists at least one prime number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3417px 8px; transform-origin: 30.3417px 8px; unicode-bidi: 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margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"224\" height=\"19.5\" style=\"width: 224px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.0667px 8px; transform-origin: 54.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.675px 8px; transform-origin: 81.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, List the prime number(s) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90px 8px; transform-origin: 90px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in the interval ]n^2; (n+1)^2[.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 1 =\u0026gt; p = [2, 3];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 2 =\u0026gt; p = [5, 7];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 124.742px 8px; transform-origin: 124.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 10 =\u0026gt; p = [101, 103, 107, 109, 113];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 156.375px 8px; transform-origin: 156.375px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 20 =\u0026gt; p = [401, 409, 419, 421, 431, 433, 439];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/60972\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 60972. Check Bertrand-Chebyshev's theorem about prime numbers\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = check_legendre_conjecture(n)\r\n p = n;\r\nend","test_suite":"%%\r\nn = 1\r\np_correct = [2, 3];\r\nassert(isequal(check_legendre_conjecture(n),p_correct))\r\n\r\n%%\r\nn = 2\r\np_correct = [5, 7];\r\nassert(isequal(check_legendre_conjecture(n),p_correct))\r\n\r\n%%\r\nn = 10\r\np_correct = [101, 103, 107, 109, 113];\r\nassert(isequal(check_legendre_conjecture(n),p_correct))\r\n\r\n%%\r\nn = 20\r\np_correct = [401, 409, 419, 421, 431, 433, 439];\r\nassert(isequal(check_legendre_conjecture(n),p_correct))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('check_legendre_conjecture.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:05:15.000Z","deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-21T08:10:57.000Z","updated_at":"2026-02-12T07:21:34.000Z","published_at":"2025-07-21T08:28:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eContext and problem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLegendre's conjecture states for a given positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethere always exists at least one prime number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en²\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and (n+1²) :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall n \\\\in \\\\mathbb{N}^*, \\\\exists p \\\\in \\\\mathbb{P}, \\\\mathbf{n^2 \u0026lt; p \u0026lt; (n+1)^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, List the prime number(s) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the interval ]n^2; (n+1)^2[.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 1 =\u0026gt; p = [2, 3];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 2 =\u0026gt; p = [5, 7];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 10 =\u0026gt; p = [101, 103, 107, 109, 113];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 20 =\u0026gt; p = [401, 409, 419, 421, 431, 433, 439];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/problems/60972\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 60972. Check Bertrand-Chebyshev's theorem about prime numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44098,"title":"Find my secret function I","description":"If give my function a x value it will give me a y value, so find the secret of it:\r\nExamples:\r\n\r\ninput x=[2 5 6 8 9] ---- \u003e\u003e\u003e output y=7\r\n\r\ninput x =[1 1 1;\r\n 2 4 8;\r\n 3 9 27] \r\n---- \u003e\u003e\u003e output y= 23\r\n\r\nHint: use tags\r\n","description_html":"\u003cp\u003eIf give my function a x value it will give me a y value, so find the secret of it:\r\nExamples:\u003c/p\u003e\u003cp\u003einput x=[2 5 6 8 9] ---- \u0026gt;\u0026gt;\u0026gt; output y=7\u003c/p\u003e\u003cp\u003einput x =[1 1 1;\r\n 2 4 8;\r\n 3 9 27] \r\n---- \u0026gt;\u0026gt;\u0026gt; output y= 23\u003c/p\u003e\u003cp\u003eHint: use tags\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = magic(9);\r\ny_correct =79;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = magic(5);\r\ny_correct =23;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = magic(1000);\r\ny_correct =999983;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [1 2 5 4 5 6 8 9 52 56 58];\r\ny_correct =53;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":37163,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":"2017-04-25T11:17:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-04-23T19:42:59.000Z","updated_at":"2025-12-28T17:10:21.000Z","published_at":"2017-04-25T11:17:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf give my function a x value it will give me a y value, so find the secret of it: Examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput x=[2 5 6 8 9] ---- \u0026gt;\u0026gt;\u0026gt; output y=7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput x =[1 1 1; 2 4 8; 3 9 27] ---- \u0026gt;\u0026gt;\u0026gt; output y= 23\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: use tags\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":55275,"title":"List the semiprimes","description":"A semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers and are semiprimes, but and are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems 52859, 52990, and 53740. \r\nWrite a function to list the semiprime numbers less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.167px 8px; transform-origin: 297.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"6 = 2x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"9 = 3x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are semiprimes, but \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"8 = 2x2x2\" style=\"width: 84px; height: 18px;\" width=\"84\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"30 = 2x3x5\" style=\"width: 91.5px; height: 18px;\" width=\"91.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 205.517px 8px; transform-origin: 205.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52859\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52859\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52990\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52990\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53740\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e53740\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.75px 8px; transform-origin: 264.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = semiprimes(n)\r\n s = primes(n)/2;\r\nend","test_suite":"%%\r\nn = 100; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 1000; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95 106 111 115 118 119 121 122 123 129 133 134 141 142 143 145 146 155 158 159 161 166 169 177 178 183 185 187 194 201 202 203 205 206 209 213 214 215 217 218 219 221 226 235 237 247 249 253 254 259 262 265 267 274 278 287 289 291 295 298 299 301 302 303 305 309 314 319 321 323 326 327 329 334 335 339 341 346 355 358 361 362 365 371 377 381 382 386 391 393 394 395 398 403 407 411 413 415 417 422 427 437 445 446 447 451 453 454 458 466 469 471 473 478 481 482 485 489 493 497 501 502 505 511 514 515 517 519 526 527 529 533 535 537 538 542 543 545 551 553 554 559 562 565 566 573 579 581 583 586 589 591 597 611 614 622 623 626 629 633 634 635 649 655 662 667 669 671 674 679 681 685 687 689 694 695 697 698 699 703 706 707 713 717 718 721 723 731 734 737 745 746 749 753 755 758 763 766 767 771 778 779 781 785 789 791 793 794 799 802 803 807 813 815 817 818 831 835 838 841 842 843 849 851 862 865 866 869 871 878 879 886 889 893 895 898 899 901 905 913 914 917 921 922 923 926 933 934 939 943 949 951 955 958 959 961 965 973 974 979 982 985 989 993 995 998];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 10000; \r\ns = semiprimes(n);\r\nlen_correct = 2625;\r\nsum_correct = 12736914;\r\nvar_correct = 8.447173943104530e+06;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-8)\r\n\r\n%%\r\nn = 100000; \r\ns = semiprimes(n);\r\nlen_correct = 23378;\r\nsum_correct = 1138479765;\r\nvar_correct = 8.471797671132822e+08;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-6)\r\n\r\n%%\r\nn = 800000; \r\ns = semiprimes(n);\r\nlen_correct = 169660;\r\nsum_correct = 66262251604;\r\nvar_correct = 5.417425253731966e+10;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-4)\r\n\r\n%%\r\nfiletext = fileread('semiprimes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-08-02T01:42:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-02T01:34:03.000Z","updated_at":"2025-08-03T17:11:25.000Z","published_at":"2022-08-02T01:42:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"6 = 2x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6 = 2\\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"9 = 3x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e9 = 3 \\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are semiprimes, but \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"8 = 2x2x2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8 = 2\\\\times2 \\\\times 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"30 = 2x3x5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e30 = 2\\\\times 3 \\\\times 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52859\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52859\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52990\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52990\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53740\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e53740\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51466,"title":"List prime anagrams of a number","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.667px 7.91667px; transform-origin: 380.667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 172 is not prime, but its anagrams 127 and 271 are. Write a function that lists the unique prime anagrams of a number in increasing order. Leading zeros are allowed; for example, a prime anagram of 902 is 29. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = primeAnagrams(n)\r\n y = primes(n);\r\nend","test_suite":"%%\r\nn = 712;\r\ny = primeAnagrams(n);\r\ny_correct = [127 271];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 137;\r\ny = primeAnagrams(n);\r\ny_correct = [137 173 317];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 209;\r\ny = primeAnagrams(n);\r\ny_correct = 29;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 237;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 500;\r\ny = primeAnagrams(n);\r\ny_correct = 5;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 911;\r\ny = primeAnagrams(n);\r\ny_correct = [191 911];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1203;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 1913;\r\ny = primeAnagrams(n);\r\ny_correct = [1193 1319 1913 1931 3119 3191 3911 9311];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1973;\r\ny = primeAnagrams(n);\r\ny_correct = [1973 3719 3917 7193 9137 9173 9371];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 2648;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 5738;\r\ny = primeAnagrams(n);\r\ny_correct = [5387 5783 7583 7853 8537 8573 8753];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 11379;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 13379;\r\ny = primeAnagrams(n);\r\ny_correct = [13397 17393 19373 31379 31397 31793 31973 33179 33791 37139 39317 39371 71339 71933 79133 91373 91733 93371];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 13579;\r\ny = primeAnagrams(n);\r\ny_correct = [13597 13759 15739 15937 15973 17359 17539 19753 31957 37159 37591 37951 39157 51973 53197 53719 53791 53917 57139 57193 71359 71593 73951 75193 75391 75913 75931 79153 79531 91573 91753 95317 95713 95731];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 13779;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 13799;\r\ny = primeAnagrams(n);\r\ny_correct = [13799 13997 17939 19379 19739 19793 19937 19973 31799 37199 37991 39719 39791 39971 71399 71993 79139 79193 79319 91397 93179 93719 93971 97931 99137 99173 99317 99371 99713];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 54321;\r\ny = primeAnagrams(n);\r\nassert(isempty(y))\r\n\r\n%%\r\nn = 113377;\r\ny = primeAnagrams(n);\r\ny_correct = [117373 133717 137713 171733 173137 173713 311737 313717 317371 317731 373171 717133 717331 731173 731713 737131];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 113399;\r\ny = primeAnagrams(n);\r\ny_correct = [131939 133919 191339 193139 199313 313991 319391 319931 393191 399131 913139 919313 931193 931319 931913 991313];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 246803;\r\ny = primeAnagrams(n);\r\ny_correct = [24683 28463 28643 42683 42863 48623 62483 64283 82463 84263 86243 86423 206483 208463 246803 248063 260483 264083 268043 268403 280463 286043 402863 408263 408623 420683 486023 486203 604823 608423 624803 802463 802643 820643 824063 826403 842063 860423 864203];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1234567;\r\ny = primeAnagrams(n);\r\nlen_correct = 534;\r\nsum_correct = 2405142318;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nn = 3139793;\r\ny = primeAnagrams(n);\r\nlen_correct = 103;\r\nsum_correct = 544898129;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nn = 3917458;\r\ny = primeAnagrams(n);\r\nlen_correct = 708;\r\nsum_correct = 4185941334;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct))\r\n\r\n%%\r\nn = 13456789;\r\ny = primeAnagrams(n);\r\nlen_correct = 4192;\r\nsum_correct = 249146788612;\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(sum(y),sum_correct) \u0026\u0026 isequal(y(2096),59468713))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-18T14:18:17.000Z","updated_at":"2025-11-29T20:34:18.000Z","published_at":"2021-04-18T14:21:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 172 is not prime, but its anagrams 127 and 271 are. Write a function that lists the unique prime anagrams of a number in increasing order. Leading zeros are allowed; for example, a prime anagram of 902 is 29. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60988,"title":"List numbers that cannot be expressed as the sum of two primes","description":"The Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the other numbers, such as 1, 2, 3, and 11, which cannot? \r\nWrite a function that returns the nth number that cannot be expressed as the sum of two prime numbers.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 36px; transform-origin: 408px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the other numbers, such as 1, 2, 3, and 11, which cannot? \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the nth number that cannot be expressed as the sum of two prime numbers.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = notSum2Primes(n)\r\n y = x;\r\nend","test_suite":"%%\r\nassert(isequal(notSum2Primes(1),1))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(2),2))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(3),3))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(53),185))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(467),1365))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(3035),8101))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(25043),62663))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(453101),1073835))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(1200000),2807765))\r\n\r\n%%\r\nassert(isequal(notSum2Primes(notSum2Primes(4521)),30313))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-29T02:06:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-29T02:04:28.000Z","updated_at":"2026-04-03T11:25:30.000Z","published_at":"2025-07-29T02:06:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the other numbers, such as 1, 2, 3, and 11, which cannot? \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the nth number that cannot be expressed as the sum of two prime numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60969,"title":"Check p = 4n +/- 1, the generic formula for odd prime numbers","description":"Problem statement\r\n\r\nFor all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 :\r\n\r\n\r\n\r\nCheck this formula for some given odd primes in a vector by computing n for each p.\r\n\r\nExamples\r\n\r\np = 17 =\u003e n = 4;\r\n\r\np = 19 =\u003e n = 5;\r\n\r\n p = [3, 5, 7, 11, 13, 17, 19] =\u003e n = [1, 1, 2, 3, 3, 4, 5];\r\n\r\np = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]\r\n =\u003e n = [1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 15, 17, 18, 18, 20, 21, 22, 24];\r\n\r\n\r\nForbidden functions / expressions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\n\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 919.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 459.733px; transform-origin: 408px 459.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.1333px 8px; transform-origin: 80.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor all odd prime number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4583px 8px; transform-origin: 96.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, there exists a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3333px 8px; transform-origin: 30.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esuch that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep = 4n +/- 1 :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"231\" height=\"18\" style=\"width: 231px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 222.1px 8px; transform-origin: 222.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCheck this formula for some given odd primes in a vector by computing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.9417px 8px; transform-origin: 15.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eeach\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e p.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = 17 =\u0026gt; n = 4;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = 19 =\u0026gt; n = 5;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 164.367px 8px; transform-origin: 164.367px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [3, 5, 7, 11, 13, 17, 19] =\u0026gt; n = [1, 1, 2, 3, 3, 4, 5];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 280.842px 8px; transform-origin: 280.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 287.408px 8px; transform-origin: 287.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e =\u0026gt; n = [1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 15, 17, 18, 18, 20, 21, 22, 24];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = check_odd_primes_gen_formula(p)\r\n n = p;\r\nend","test_suite":"%%\r\np = 17;\r\nn_correct = 4;\r\nassert(isequal(check_odd_primes_gen_formula(p),n_correct))\r\n\r\n\r\n%%\r\np = 19;\r\nn_correct = 5;\r\nassert(isequal(check_odd_primes_gen_formula(p),n_correct))\r\n\r\n\r\n%%\r\np = [3, 5, 7, 11, 13, 17, 19];\r\nn_correct = [1, 1, 2, 3, 3, 4, 5];\r\nassert(isequal(check_odd_primes_gen_formula(p),n_correct))\r\n\r\n\r\n%%\r\np = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\r\nn_correct = [1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 15, 17, 18, 18, 20, 21, 22, 24];\r\nassert(isequal(check_odd_primes_gen_formula(p),n_correct))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('check_odd_primes_gen_formula.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-20T05:09:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-20T04:24:51.000Z","updated_at":"2026-02-12T07:13:21.000Z","published_at":"2025-07-20T05:09:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor all odd prime number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, there exists a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003esuch that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 4n +/- 1 :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall p \\\\in \\\\mathbb{P}, p \u0026gt; 2 \\\\Rightarrow \\\\exists n \\\\in \\\\mathbb{N}, p = 4n \\\\pm 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck this formula for some given odd primes in a vector by computing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eeach\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e p.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 17 =\u0026gt; n = 4;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 19 =\u0026gt; n = 5;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [3, 5, 7, 11, 13, 17, 19] =\u0026gt; n = [1, 1, 2, 3, 3, 4, 5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e =\u0026gt; n = [1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 15, 17, 18, 18, 20, 21, 22, 24];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ePrime numbers properties I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47798,"title":"Check if the input is a balanced prime","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 90.1425px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.491px 45.0712px; transform-origin: 406.497px 45.0712px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.5882px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10.2941px; text-align: left; transform-origin: 383.496px 10.2941px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMore about Balanced Primes on \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Balanced_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 59.5588px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.493px 29.7794px; transform-origin: 403.498px 29.7794px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisBalancedPrime(3) = false;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisBalancedPrime(7) = false;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 19.8529px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.99954px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.99954px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.99954px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.99954px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.493px 9.92647px; transform-origin: 403.498px 9.92647px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eisBalancedPrime(5) = true; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); \"\u003e% since (3+7)/2 = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = isBalancedPrime(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 1;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nlist = [5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103];\r\nfor idx = 1:50\r\n x = randi([10 1103]);\r\n if ismember(x,list)\r\n y_correct = 1;\r\n else\r\n y_correct = 0;\r\n end\r\n assert(isequal(isBalancedPrime(x),y_correct))\r\nend\r\n\r\n\r\n%%\r\nx = 81001;\r\ny_correct = 1;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 81402;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 177487;\r\ny_correct = 1;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 467101;\r\ny_correct = 1;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n\r\n%%\r\nx = 467102;\r\ny_correct = 0;\r\nassert(isequal(isBalancedPrime(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2020-12-04T16:29:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-04T16:26:34.000Z","updated_at":"2020-12-04T16:29:03.000Z","published_at":"2020-12-04T16:26:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore about Balanced Primes on \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Balanced_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[isBalancedPrime(3) = false;\\nisBalancedPrime(7) = false;\\nisBalancedPrime(5) = true; % since (3+7)/2 = 5]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":248,"title":"Twins in a Window","description":"\u003chttp://en.wikipedia.org/wiki/Twin_primes Twin primes\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\r\n\r\nExamples:\r\n\r\n Input lowVal = 10, highVal = 50\r\n Output p is [ 11 13\r\n 17 19\r\n 29 31\r\n 41 43 ]\r\n\r\n Input lowVal = 1000, highVal = 1050\r\n Output p is [ 1019 1021\r\n 1031 1033 ]\r\n","description_html":"\u003cp\u003e\u003ca href=\"http://en.wikipedia.org/wiki/Twin_primes\"\u003eTwin primes\u003c/a\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e Input lowVal = 10, highVal = 50\r\n Output p is [ 11 13\r\n 17 19\r\n 29 31\r\n 41 43 ]\u003c/pre\u003e\u003cpre\u003e Input lowVal = 1000, highVal = 1050\r\n Output p is [ 1019 1021\r\n 1031 1033 ]\u003c/pre\u003e","function_template":"function p = window_twins(lowVal,highVal)\r\n p = 0;\r\nend","test_suite":"%%\r\nlowVal = 10;\r\nhighVal = 50;\r\np = [11 13\r\n 17 19\r\n 29 31\r\n 41 43];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n\r\n%%\r\nlowVal = 1000;\r\nhighVal = 1050;\r\np = [1019 1021\r\n 1031 1033];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n\r\n%%\r\nlowVal = 3120;\r\nhighVal = 3300;\r\np = [ 3167 3169\r\n 3251 3253\r\n 3257 3259];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":161,"test_suite_updated_at":"2012-02-03T17:12:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-03T16:30:52.000Z","updated_at":"2025-12-17T11:07:45.000Z","published_at":"2012-02-03T17:12:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Twin_primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwin primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input lowVal = 10, highVal = 50\\n Output p is [ 11 13\\n 17 19\\n 29 31\\n 41 43 ]\\n\\n Input lowVal = 1000, highVal = 1050\\n Output p is [ 1019 1021\\n 1031 1033 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60970,"title":"Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3","description":"Problem statement\r\n\r\nFor all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 :\r\n\r\n\r\n\r\nCheck this formula for some given odd primes in a vector by computing n for each p.\r\n\r\nExamples\r\n\r\np = 17 =\u003e n = 3;\r\n\r\np = 19 =\u003e n = 3;\r\n\r\n p = [5, 7, 11, 13, 17, 19] =\u003e n = [1, 1, 2, 2, 3, 3];\r\n\r\np = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\r\n =\u003e n = [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16];\r\n\r\n\r\nForbidden functions / expressions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\n\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 919.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 459.733px; transform-origin: 408px 459.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.1333px 8px; transform-origin: 80.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor all odd prime number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.7333px 8px; transform-origin: 37.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003egreater than\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e 3\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4583px 8px; transform-origin: 96.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, there exists a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3333px 8px; transform-origin: 30.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esuch that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep = 6n +/- 1 :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAc4AAAAkCAYAAAAATtrgAAAN/UlEQVR4Xu2dW8h22xTHv31PTlcktLnYcs4xsi8kakeSHJO+2nIqyYUdknYSO4ckFw6x+1K2Q7GTUiSKiI3CJi4oJK6c4p7x861/jaa51ppjrTXX86z3HatG7+GZa605/3PM8R9zzDHnc8OVvBKBRCARSAQSgUSgGYEbmktmwUQgEUgEEoFEIBG4ksSZSpAIJAKJQCKQCAQQSOIMgJVFE4FEIBFIBBKBJM7UgUQgEUgEEoFEIIBAEmcArCyaCCQCiUAikAgkcaYOJAKJQCKQCJQIPNL+gTx3+OAO+/m3hOk6AiVx/tD+93STT5m8PgDSJ63s60x+ZPKMwH1HLfoBq/jbGiv/Fyt3r8ndJp9ovCeLXUfgeSa3mjzb5MEm/zb5gcm7TH58QUCijd8ItuWdVv79wXuOVvw/RYU/aH/f1tgI7Ng/TZ7fWD6LXUfggSbY/deY3M/keyafMfnmJQGIsfgek6/Oja+SON9gN3zcBGP/kABY/7Ky9zF5o8llIAeIk7a+ZMAIw4ez8eUKZpTBqcDogxMk8LsAtpe1qNfFPxoIDzOBPHW9wn754gUAJ4mz3okQp8YUztPLTCDCFiOexBkfGC+3Wz492PEv2U+cs8tip0SYTBq5Zh3TkjjxOP463NyqpAD+hYEYHm4/L8N0XsR53wErBvkY2DKM4IkBuMXksuAUH77X70CnPmLyMRM/swJLnBOctKhzt7Qu53SfIkKzA/ucKr2wLowpP8v8tf390Maxk8QZA10RQ5x7Jk6tM/vYW86vNHz39kGnHm8/bxqqODu+amucePF4d3gdGLC5K1p+7nlH+HwJcT7NGoYH90sTQiAt2B4Bix51xEgSLqqFY99h/3/f8FIw3SNkS0ThTpNTz3AvG3HSzY8axs1T7ee3TQjVz4VgkzjbR6VIkzsi4fD2N5xvSYiTi8mej/wsIk7NIHlgS/KQwrTnEjpjQRuP6QkmmnrPdV3UAC8lTow8hp+O0Wx1rm6n/hzS+PmA6R51QYGfbDK2hicFxzt+jskexCmjfWpv/FyIkzD6i00eZ+LD52P6QXh1juzKe7XG6SMLCt/PGbYkzraR6m39kj5qe8sxSq0mTpr552FAzJHh0jXRXlB67ynyjj2JUx0kTzpSz1OUlbE+lzCOBvtvDIxH7wiIyPPr9s5TRQtOTZxgQOJEC1n6rllilCFOol5l9EsRrqkxm8Q5PzCYbf3BhGUPxja5GC3rx/NP7lMCrrlq8l2THqHkTYhTBIS3R2LG2KWEjUgWLoOPqbEWnpX2/Hf735rZgwYUdSW799ow8Hqsua6ZcaqDomTdqo7gyaAQlvz+lOHmJQOD5xEaxYBxiUBPlZ5OP7NO/FqTvUOnchQh7WcNetzaL1uUOyVxynHQ+jLLDR9aOWanMFHeAGXQPyUeos/fN2G9cyxq05s4Nab8eGJcc/3kBHqxRLf8kscRdkNoJ8MSJ6wFn02Ik0FyT8vbBkM6FTKjQngzLzSRp0qo5VsmJH/4cOrS8Nvei9triBPjy1rCVqFaiI0UcvDV4jbK9UoTQosiPHXn0sznkkB5HjMCntfDOampH9i92+StJnuTJvXxyXNLdbVxWFWLjREnY+xGkyeZsESBQ/vYoV8Yy+81kWFf0v/0/c9MIE2M7JtN1ji5LRj4hDuWC6h/63pnD+JkzIOtcGRSAcYkl4Ap2OhqzQ9pwaFXGUUVeT72iMvbEPp5bFtGb32rtfkQxEnFSdDAEI+tJ8hjaQ2Z+TAqM9SbTW43wQD6WDsGKUIqDOrfDkjvtbi9hjgZ1Fxb73f1GDJw2fbCniR+f4CJDB/vXjPbPQWBQlisebKth2sNYUf24NYGcPm/ufW2lme0lqkRpzIDvVGXVy4n7S57watMZNxbchd8nRTNgSz22k7liZM2klTHpW1ysj81R6AHcfJu7zhBLOx1/JoJto2IGWH85i0NDmD1a6se1MpF7Ka3mTxLe83JZeB6tYkmOaV930Pfau07DHHOEaM8llbDocFHB//J5AUmfp+QiBrQIoZdgLYS+Brl1L1LiZNTOMCrx3qCwogaCFftFx9K8o5La59NYbUHgdbeoTqhR08sdKilb7cmTt65NtQVNZy1/vOhJsiE6y1unOkdmilFogRK1JnLeWjBv7VMucVLUTC/LFTORPXsXsTpCQf9I4Tsk9iWJttE+7+GYYQ4va6MrW/6pa9aeLSnvh2aOL2SlEQmJY4YLxHt2D1eeSIDVPftNdukUyPEqcGEcX2MCScO9Tgkwit6DT9PGJE16TlDtweBUgd07qUmPiy2p7NUwwHvW+HwNaHbqOGsEaf6V4bwmtXNzw41/qJhRJ/FvOf+49reaDnz0u/aTJR+6kWc3jmtjSFPJqfWzalx623BlD74cG6ZzNhL38bqfZgZJw2QR1cqiYx0q6ft10zHOsobj8iMszyaa87Q1z6PvG+MOKfeq6PiPmyFliTotLRJ24LGElf8YNlixlnWaYxAt04g8ett1CHady1YRsv4aEkPbFWfqeQgfUb/c91uonVgH2KMrnFuMUNfktAxdqgINumZJoo2yLZ4u9KLOGUPwbeWFe+Jc0mbo3q3tHyrLZiKUm2tbx67pe3ivqXjb5PkIFVcHlYZBoju3fQZXGMnEumZvCvi2Z4LceJc1I7cW5st3KJE3jEZm3n7Qd96KlTLu8sy/uguPiM0eNVkS4fBe/5LB8qSto3dI+LsvWVnjDg9MVLH0tH1eD3IPo+Eac+NODXL5CxabUcq1zt7Eads1NiEwdu5PSNgUV1uJc6x0HMPfbtQxEmHlCTpybSV4GS0x9ZXvOGPemoyWlFPOqpsvnwkVLvmPa33tpymo35cssbVUg8Un2QkJUcw8/msCV5rxFC3vMsP3FMSpw/V9nAQSizGiNMbuFr/RiNE/r169t5HHE4dYzm33vk5a8DWh7x7GzWmc945PYdIyNhYap1djc2ge+rbWJ0PFaqlERp0IrSx8O2UwdOscCxM69fnogpX1q/F8K4tc27E6cMmtf2FPWdoNcL8qAHcYx3X95t0Kjp73mIGVeoPY4PtP1s7CK3EObe+rbWqJbOgqVyHteNozmZMOUVyFtX/fiYKaW5NnF5vamFaj1PU+Y+ucddwiyQHtdbVE6ePYvTUtwtDnB48SO2eoWWtBsvfX0ta8SdYRBMXqIr3fqKku3TgnxtxikTGkn7miHUJDpAxeyp92voehEldNeNcMnvekjh7h2ZbiVPEWMPDz5SWjg9FdaKEsESvdM/UjFNl0GsS7hT56rnG6MeQQsS+fT5ZJnoU5N7ESb3Vp1NJTN62+oheb32r6c3hZpw0wgOFoYyEbbyhqq2vaAa75jQW1W+vTLYexImBY79ldC1wzjGRZ74m69Mr8ikJU/XQDHrJDGqNMfchYsbAi0x6HwTg61sL1c6tb6v/Rao8j037kWPLfMQikvG+BusW4pTT/St7kfZFTxlYnVK25HSfKefU98GeS0Zr8PV9OuZQeWdAzske+nZhiLP00iMGa8qz8XtFy32dEaXYOw18a+L0+EaTo3zmW+mY+G1Da/eOloQJwffIEqbOnChFqK32hdU6+s0by4iurCkrY0NyyC0mvUOzZV1rxDm3vq3xRzQHo85xdezvjDpofla0B3m2ECf4aOyXX0HGUaH+YPky+aQ1YsY7/MyrbLtCxEwoTrneHtVrX++xSEJtr/5e+la255AzznLjb2sownvo5WxQQBBe5Pe1X5rqPSjIp9d+STpUddfAZNa8ZtCUoZrIPku/FcITp7JbIZg1R6TxHL4bUyHZXoSpgeIHJv/D4PMt9Fx8awpt4bQWyu1JXCLsu+y9HHG41bUkm9Dr2lzERjMlbVMhYWvsm2em2qQzYm8aCqEHb9pg3I69s5U4/XgEl5+asGRQEmfp/EeiU9459cSJToAnJwid6hjINXrozx8ubY7WMcv/76VvZbt6E6fXj1n7Gzl6Swa6de8mDfeeGor6C5N/mDzC5PcmfOP4lqEuyBPP058b2aJY0bWf2jrZGuIst3C0riWVocN7rbEcm8Xxa+D8FRPt5WvBoVZGpN6bMPVuZaoyo1M/6ssGODsTIl3rZEWx0LeCQNhbkib1WEucc4l3MvpgSNbzmqQt+sYfK9eKY6s+++dFiJP7SuezfCfOPwfTywGMJNP47UY4onxDB6HL+5vcPejknk5cK+4t5XSEHufUcnA+7eMi4lOLKO2pb77+W30ZSIkJttyf0avP4Tn6+Q6T/+vbCHG2dEJZxmdfRfePLXkf96AIGDfWn7Q1Yu5ZUeKce96azzEAY4crl8/dY+0JxeJA/mhobw0G53YvevwdkzWkc25tWlMfyP5WE04mEhFNPW8Jca6p39y96DTOpQ/ljt3jo22zM5G5F+fnFwOB3sS5d9LO0XtF6w6tB2mfwjE5OsZZ/0QA55Tlh5ZozB7OafbIsshLDbc1kb/mfuhJnOmpNXfD/woqDHYtMLNJxySGcZZOBCBLljFaQ+7pnO6jM0uWLC4kcfokjz2y8Pbp3j5vgTQ/b3JnoxdMLXxaeIaQ+vRLPvViIcB6L2t3ka04/gzo2v7Ni4VQtqYJgZ4zTp/tWTtpo6mCWWgUAZ/pd5S9Y9mdicCRECi/45a/80oErvQgTiUOkHWmCy+PbM+Ip5fdU0eAEDg4ktzgLzLAINO9M06znxKBi4gACUQ3Fw3DhvFFDpc5Ue4i9nW4TT2IM1yJvCERSAQSgUQgETgKAkmcR+mprGcikAgkAonAWSCQxHkW3ZCVSAQSgUQgETgKAv8FXIhsYUfJqOoAAAAASUVORK5CYII=\" width=\"231\" height=\"18\" style=\"width: 231px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 222.1px 8px; transform-origin: 222.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCheck this formula for some given odd primes in a vector by computing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.9417px 8px; transform-origin: 15.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eeach\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e p.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = 17 =\u0026gt; n = 3;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = 19 =\u0026gt; n = 3;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 148.817px 8px; transform-origin: 148.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [5, 7, 11, 13, 17, 19] =\u0026gt; n = [1, 1, 2, 2, 3, 3];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.2167px; transform-origin: 392px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 275.4px 8px; transform-origin: 275.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 266.008px 8px; transform-origin: 266.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e =\u0026gt; n = [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = check_odd_primes_gen_formula3(p)\r\n n = p;\r\nend","test_suite":"%%\r\np = 17;\r\nn_correct = 3;\r\nassert(isequal(check_odd_primes_gen_formula3(p),n_correct))\r\n\r\n\r\n%%\r\np = 19;\r\nn_correct = 3;\r\nassert(isequal(check_odd_primes_gen_formula3(p),n_correct))\r\n\r\n\r\n%%\r\np = [5, 7, 11, 13, 17, 19];\r\nn_correct = [1, 1, 2, 2, 3, 3];\r\nassert(isequal(check_odd_primes_gen_formula3(p),n_correct))\r\n\r\n\r\n%%\r\np = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\r\nn_correct = [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16];\r\nassert(isequal(check_odd_primes_gen_formula3(p),n_correct))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('check_odd_primes_gen_formula3.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-20T05:22:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-20T04:25:50.000Z","updated_at":"2026-02-12T07:15:38.000Z","published_at":"2025-07-20T05:22:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor all odd prime number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003egreater than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, there exists a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esuch that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 6n +/- 1 :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall p \\\\in \\\\mathbb{P}, p \u0026gt; 3 \\\\Rightarrow \\\\exists n \\\\in \\\\mathbb{N}, p = 6n \\\\pm 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck this formula for some given odd primes in a vector by computing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eeach\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e p.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 17 =\u0026gt; n = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = 19 =\u0026gt; n = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [5, 7, 11, 13, 17, 19] =\u0026gt; n = [1, 1, 2, 2, 3, 3];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e =\u0026gt; n = [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1761,"title":"Primes Faster for Large N","description":"This Challenge is to improve the \"primes\" function for speed. This may be accomplished by fixing memory usage.\r\n\r\nThe Matlab function \"primes\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \"out of memory\", significant slow down, or Matlab freeze.\r\n\r\nCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\r\n\r\nThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\r\n\r\nThe reference solution can process N=2^33 on a 16GB machine in 284sec.\r\n\r\n*Input:* N (max of primes to find)\r\n\r\n*Output:* vector of primes (all primes less than or equal to N)\r\n\r\n*Scoring:* Time to find all primes \u003c 2^28\r\n\r\n*Hints:*\r\n\r\n 1) Doubles use 8 bytes; logicals use 1 byte\r\n 2) The method p = p(p\u003e0); is good but can be improved\r\n 3) The method p = 1:2:n; creates a double and is a little slow\r\n 4) Usage of profiler and Task Manager combined give performance insights\r\n\r\n*Related:* \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit Primes 2^30\u003e\r\n\r\n*Matlab 2014a incorporated the speed enhancement of logicals*","description_html":"\u003cp\u003eThis Challenge is to improve the \"primes\" function for speed. This may be accomplished by fixing memory usage.\u003c/p\u003e\u003cp\u003eThe Matlab function \"primes\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \"out of memory\", significant slow down, or Matlab freeze.\u003c/p\u003e\u003cp\u003eCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\u003c/p\u003e\u003cp\u003eThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\u003c/p\u003e\u003cp\u003eThe reference solution can process N=2^33 on a 16GB machine in 284sec.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e N (max of primes to find)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e vector of primes (all primes less than or equal to N)\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Time to find all primes \u0026lt; 2^28\u003c/p\u003e\u003cp\u003e\u003cb\u003eHints:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) Doubles use 8 bytes; logicals use 1 byte\r\n2) The method p = p(p\u0026gt;0); is good but can be improved\r\n3) The method p = 1:2:n; creates a double and is a little slow\r\n4) Usage of profiler and Task Manager combined give performance insights\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eRelated:\u003c/b\u003e \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit\"\u003ePrimes 2^30\u003c/a\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eMatlab 2014a incorporated the speed enhancement of logicals\u003c/b\u003e\u003c/p\u003e","function_template":"function p = primes_faster(n) % The mathworks primes function\r\n%PRIMES Generate list of prime numbers.\r\n% PRIMES(N) is a row vector of the prime numbers less than or \r\n% equal to N. A prime number is one that has no factors other\r\n% than 1 and itself.\r\n%\r\n% Class support for input N:\r\n% float: double, single\r\n%\r\n% See also FACTOR, ISPRIME.\r\n\r\n% Copyright 1984-2004 The MathWorks, Inc. \r\n% $Revision: 1.16.4.3 $ $Date: 2010/08/23 23:13:13 $\r\n\r\nif length(n)~=1 \r\n error(message('MATLAB:primes:InputNotScalar')); \r\nend\r\nif n \u003c 2, p = zeros(1,0,class(n)); return, end\r\np = 1:2:n;\r\nq = length(p);\r\np(1) = 2;\r\nfor k = 3:2:sqrt(n)\r\n if p((k+1)/2)\r\n p(((k*k+1)/2):k:q) = 0;\r\n end\r\nend\r\np = p(p\u003e0);\r\n\r\nend","test_suite":"feval(@assignin,'caller','score',30); %\r\n%%\r\ntic\r\nassert(isequal(primes_faster(1),primes(1)))\r\nassert(isequal(primes_faster(2),primes(2)))\r\nfor i=1:100\r\n n=randi(2000,1);\r\n assert(isequal(primes_faster(n),primes(n)))\r\nend\r\ntoc\r\n%%\r\ntic\r\nta=clock;\r\n p = primes_faster(2^28);\r\nt1=etime(clock,ta); % time in sec\r\n\r\nfprintf('P 2^28 %12i %10.3f\\n',length(p),t1)\r\n\r\nassert(isequal(size(unique(p),2),14630843))\r\n\r\nptr=randi(7603553,1,10); % small to avoid timeout\r\n\r\npchk=double(p(ptr));\r\n\r\nassert(all(isprime(pchk)))\r\n\r\nfeval( @assignin,'caller','score',floor(min(30,t1)) );\r\ntoc","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2013-08-07T00:21:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-30T02:37:44.000Z","updated_at":"2025-12-15T18:33:37.000Z","published_at":"2013-07-30T04:30:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to improve the \\\"primes\\\" function for speed. This may be accomplished by fixing memory usage.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Matlab function \\\"primes\\\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \\\"out of memory\\\", significant slow down, or Matlab freeze.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody appears to have 2GB of RAM based upon \\\"out of memory\\\" messages observed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution can process N=2^33 on a 16GB machine in 284sec.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e N (max of primes to find)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector of primes (all primes less than or equal to N)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Time to find all primes \u0026lt; 2^28\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1) Doubles use 8 bytes; logicals use 1 byte\\n2) The method p = p(p\u003e0); is good but can be improved\\n3) The method p = 1:2:n; creates a double and is a little slow\\n4) Usage of profiler and Task Manager combined give performance insights]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrimes 2^30\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMatlab 2014a incorporated the speed enhancement of logicals\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60972,"title":"Check Bertrand-Chebyshev's theorem about prime numbers","description":"Historical context\r\nBertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory stating that for every integer greater than 1, there always exists at least on prime number between it and its double : \r\n\r\n\r\n\r\nProblem statement\r\nFor a given input n, List the prime number(s) p in the interval ]n; 2n[.\r\n\r\nExamples\r\n\r\nn = 2 =\u003e p = 3;\r\nn = 3 =\u003e p = 5;\r\nn = 7 =\u003e p = [11, 13];\r\nn = 47 =\u003e p = [53, 59, 61, 67, 71, 73, 79, 83, 89];\r\n\r\nForbidden functions / expressions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 697.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 348.733px; transform-origin: 408px 348.733px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory stating that for every integer greater than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 223.658px 8px; transform-origin: 223.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethere always exists at least on prime number between it and its double : \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"223\" height=\"19.5\" style=\"width: 223px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.0667px 8px; transform-origin: 54.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.675px 8px; transform-origin: 81.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, List the prime number(s) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.8917px 8px; transform-origin: 66.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in the interval ]n; 2n[.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.6833px 8px; transform-origin: 46.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 2 =\u0026gt; p = 3;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 46.6833px 8px; transform-origin: 46.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 3 =\u0026gt; p = 5;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 68.3333px 8px; transform-origin: 68.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 7 =\u0026gt; p = [11, 13];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 152.467px 8px; transform-origin: 152.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en = 47 =\u0026gt; p = [53, 59, 61, 67, 71, 73, 79, 83, 89];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = check_Bertrand_Chebyshev_theorem(n)\r\n p = n;\r\nend","test_suite":"%%\r\nn = 2;\r\np_correct = 3;\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%%\r\nn = 3;\r\np_correct = 5;\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%%\r\nn = 7;\r\np_correct = [11, 13];\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%%\r\nn = 11;\r\np_correct = [13, 17, 19];\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%%\r\nn = 47;\r\np_correct = [53, 59, 61, 67, 71, 73, 79, 83, 89];\r\nassert(isequal(check_Bertrand_Chebyshev_theorem(n),p_correct))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('check_Bertrand_Chebyshev_theorem.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:03:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-20T04:28:51.000Z","updated_at":"2026-02-12T07:17:44.000Z","published_at":"2025-07-21T04:30:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory stating that for every integer greater than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethere always exists at least on prime number between it and its double : \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\forall n \\\\in \\\\mathbb{N}^* - \\\\{ 1 \\\\}, \\\\exists p \\\\in \\\\mathbb{P}, \\\\mathbf{n \u0026lt; p \u0026lt; 2n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, List the prime number(s) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the interval ]n; 2n[.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 2 =\u0026gt; p = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 3 =\u0026gt; p = 5;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 7 =\u0026gt; p = [11, 13];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en = 47 =\u0026gt; p = [53, 59, 61, 67, 71, 73, 79, 83, 89];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42749,"title":"Find the nearest prime","description":"Given a positive integer 'n', the task is to find a prime number greater than or equal to 'n'. \r\n\r\nExample 1\r\n\r\nIf given 'n' is 10, then the closest prime number greater than 10 is 11 at a distance of 1. So 11 must be returned. \r\n\r\nExample 2\r\n\r\nIf the given 'n' is 17, then the closest prime number is itself at a distance of 0. So 17 must be returned. \r\n\r\nThe returned prime number must be greater than or equal to 'n'. \r\n","description_html":"\u003cp\u003eGiven a positive integer 'n', the task is to find a prime number greater than or equal to 'n'.\u003c/p\u003e\u003cp\u003eExample 1\u003c/p\u003e\u003cp\u003eIf given 'n' is 10, then the closest prime number greater than 10 is 11 at a distance of 1. So 11 must be returned.\u003c/p\u003e\u003cp\u003eExample 2\u003c/p\u003e\u003cp\u003eIf the given 'n' is 17, then the closest prime number is itself at a distance of 0. So 17 must be returned.\u003c/p\u003e\u003cp\u003eThe returned prime number must be greater than or equal to 'n'.\u003c/p\u003e","function_template":"function y = closestPrime(n)\r\n y = 2; \r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 3;\r\nassert(isequal(closestPrime(n),y_correct))\r\n\r\n%%\r\nn = 20;\r\ny_correct = 23;\r\nassert(isequal(closestPrime(n),y_correct))\r\n\r\n%%\r\nn = 86;\r\ny_correct = 89;\r\nassert(isequal(closestPrime(n),y_correct))\r\n\r\n%%\r\nn = 250;\r\ny_correct = 251;\r\nassert(isequal(closestPrime(n),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":66083,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":104,"test_suite_updated_at":"2016-02-23T21:20:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-02-23T21:05:45.000Z","updated_at":"2025-12-11T05:21:59.000Z","published_at":"2016-02-23T21:20:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer 'n', the task is to find a prime number greater than or equal to 'n'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf given 'n' is 10, then the closest prime number greater than 10 is 11 at a distance of 1. So 11 must be returned.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the given 'n' is 17, then the closest prime number is itself at a distance of 0. So 17 must be returned.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe returned prime number must be greater than or equal to 'n'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60965,"title":"List the near-square primes, p = n² + 1 (Landau's 4th problem)","description":"Historical context\r\n\r\nAt the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as \"unattackable at the present state of mathematics\" and are now known as Landau's problems (source : Wiki)\r\n\r\nProblem statement\r\n\r\nThe 4th Landau's problem aalso known as the 'near square primes' asked whether there are infinitely many primes which are of the form . Your task here is to list such primes below a given input integer m.\r\n\r\nExamples\r\n\r\nm = 20 =\u003e p = [2, 5, 17] ;\r\nm = 200 =\u003e p = [2, 5, 17, 37, 101, 197] ;\r\nm = 2000 =\u003e p = [2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601] ;\r\n\r\nFobidden functions\r\nregexp\r\nstr2num\r\nassignin\r\necho\r\n\r\nSee also\r\n\r\nPrime numbers properties I","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 719.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 359.517px; transform-origin: 408px 359.517px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.375px 8px; transform-origin: 375.375px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAt the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as \"unattackable at the present state of mathematics\" and are now known as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.825px 8px; transform-origin: 65.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eLandau's problems \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.725px 8px; transform-origin: 44.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(source : Wiki)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.275px 8px; transform-origin: 376.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe 4th Landau's problem aalso known as the 'near square primes' asked whether there are infinitely many primes which are of the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN0AAAAmCAYAAABAkZ7AAAAHVUlEQVR4Xu1cS8huUxg+Z84AIxLC4Mi1XCMGBpQYyb10ilwGkgEh6SQhlGTgEjrJAAMlpRgYKHJJEWJAMWHkFnOep/ZTr2XtvW57r//f3/fuevu////Wevdez1rPe1tr/3v3+OUIOAJdEdjb9W5+M0fAEdjjpPNF4Ah0RsBJ1xlwv50j4KTzNeAIdEbASVcG+Nlo/jDkfMghkF8gd0FeL1PjrbcZASdd/uyTcG9BnoF8DrkScsvQ/Qn8vCdflbfcZgScdPmz/y6avhx4tfvw+yOQvyGH5qvyltuMgJMuf/Y/RtPLIL+ZLofj86/D70cE3+Vr9pZbhYCTrn26/4EK5nanrIR0l+A5H4IwVH60ffgbrYGG9lwzwk/w+bzMET+OdrfHIiAnXSaCI81OwN+/h7wHubRN1eK9RTYtovuddEnMSTpeD0LOhDCVyM3fnXRJeOsa3DZMwsX4+VmdisV7MQS+F3Is5DTIvuGOTro09CKdvNvz6MLiGQ0sDe3U5aRL41vV4mf0ehUyV+WSk3o65CnIXNsQJB0v5qL0diwI8XLSpadc4SXDxOcgxPJDyNGQVOHMSZfGt7gFQaX34ITY4kqxItNBk7wUITaJdBzLTRDrvaewr6kw25zuRCj/AcKto/chH0GmUgonXQsTIn2vwd+4KR5WM1tv46RLI0hv8w7EFjjSveq2dRReHjPc4KjhJ9OKZyFTxnE20rFwwEErf+Hns4YHScW4OcCsoQ0tHTfIbxgs35zP7KSbRlPhHfNSei56m3DvdO75+BMKH4B8CnkDQoPLi+H/1ZBzDB/svatJR5LdCrkCogSc5LoOQqbzpvZS7DvnwOfUJSPBStQZEIaHvJQoE9ADw1g5qWGBRKdSLsR3DDXsxUloDTXXTDpiczyE2F4EoXfYD+F6Ie5cL4wMeHzOLt6S+f12mJtex+84HyQdw0gdhMjN76pJJ0C4GF8bfiFgXHTc6+HnwyBfDGCyyRjzY+Byj6v1KinXc2FcBbFGRCECScNxvQ3R8S67L0MDxHF+A/kgeGgusi8hNFAt15pJx0V5nMFOe5fEjTkQQ0Kbf+VUAC2WCuloDG+GzFVompovSzq2YxGKuaTN70IPKH3NpNOAqZBg7ofYcFKlVH5fUgToTToLyN3DLwSQ+y+85Kn0XCK0DWvGJqnE2IzpWDPpNCZhR4P8JISb8FovXIjCvRQvYfMCdLQatymi2e9C0nEdfA2h9ztpaBh6wNlIp/iVCq+FhFbGgtkTlFzwwnaaQHqyg8OiUFFEG94iIUvFva61k85WR7lODgyi9aJ19B3+fgGkpOorMpd6yJa5C0lHXYyW6N3sOg89INs1e7q/oISx+BhYlnQlnq4FkJa+1pOdCkU2R7OhtMKIlnvZvhanFp2lXkL3WnrLQONTkeNH3Nh6JeVkpTmdfe5a3Gq3DJTT2fvKu8kByQOyjSqcTaQTs6lw7AiMmM42PS1RzQRYUrF/6LmtNVYIUXOfWJ9NJ51IxbEzirBbKjaCiEVLUxjvNtLxWbnm+V4lC3Lav7P5XRPpxGreaMzCyhOu4eCvzT9jRRieMjlywsDMRcCYnjWHl/aNi9hasYUQVo1LQkure+7oY2o+Y+Gl2qfyO1Zyqw88ayGMhZa2yFIaWu5EIUWkYrghKyUgrTXeCY+9ZtLZdRDL6xVBlJzUt4TQvJWusRYjOUU66lUUaCNAeUBWa+np/3dcLOctAxFjrECSIuXUoHuTzpIq5uXk1XfKY6+ZdLbYFouIFA3VkkYRSk1uVku8FOmoVymDjDQ94E8Q1kCiz5oiXViNCquW9s3p3XzSXqDbUDnmyZSbipAcP/che+wJ8Rl3G+k4/t8hOW9QiFQxT2brAiIkSVRS+rcGs1eFPId0mreT8UFhs3hTRTqb/4RvRgtIKub/C1nDMTCRKubJbN7AWJz/B+UVyOWQ8PRJreVM9dtNpNOz8JlTIaElVcyTaR0pReHpFHqD0rczem9N5ZJO3o0HJ+xrQNfXhJe2GmVJxwrgixDe5I5MS5hacD2+lzWOlaytV6cB4VbC/s7GZGnSlSzaMPSfqjjaCCJW6NC4tJXwB3CtPTJnw1iS+M4F5yiXdFy7Wj9cWy9B+AZEcU5nLT89w1cQHnXi+14E7U1Ir7BrDkJaUo2dEZWRoWXn28K9vfdSpCPZ7NE34clx8kjbY5Cwmhhub0zlYqm8Xts0JB29XOx+JXNsI7DcfjW5YAnp+BwhZsXhpa1Gle6r5ALh7f6LgF5iPYg/9zwJk5oHer3aDfmU7trvmeMxPOW5130ZSmpIl6G2vMlUIcW6cf9PV+XYbkoPRghPQ+Y+KLAp+BSPY4p02hdh3OyAF0O7ER1YIGEx6UZITgVzIwa99CDGSGerUb3Ks0uP1fWXIaB/Ic8XOJ1wZdhNth4jnU1Ux4oOMz6Gq3IEtgeBkHRKTlmhtBcrXCRir/2q7ZkBH+nWIZA6kbJ1gPiAHYGlEXDSLY2w63cEAgScdL4kHIHOCPwLWbz3NiLcL+4AAAAASUVORK5CYII=\" width=\"110.5\" height=\"19\" style=\"width: 110.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.775px 8px; transform-origin: 211.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eYour task here is to list such primes below a given input integer\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 78.575px 8px; transform-origin: 78.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 20 =\u0026gt; p = [2, 5, 17] ;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 125.25px 8px; transform-origin: 125.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 200 =\u0026gt; p = [2, 5, 17, 37, 101, 197] ;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 230.275px 8px; transform-origin: 230.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 2000 =\u0026gt; p = [2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601] ;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9167px 8px; transform-origin: 64.9167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFobidden functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95630\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e I\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = list_the_near_square_primes(m)\r\n p = m;\r\nend","test_suite":"%%\r\nm = 20;\r\np_correct = [2,5,17];\r\nassert(isequal(list_the_near_square_primes(m),p_correct))\r\n\r\n\r\n%%\r\nm = 200;\r\np_correct = [2,5,17,37,101,197];\r\nassert(isequal(list_the_near_square_primes(m),p_correct))\r\n\r\n\r\n%%\r\nm = 2000;\r\np_correct = [2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601];\r\nassert(isequal(list_the_near_square_primes(m),p_correct))\r\n\r\n\r\n%% Test forbidden functions\r\nfiletext = fileread('list_the_near_square_primes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:04:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":55,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-17T04:36:44.000Z","updated_at":"2026-02-13T13:18:04.000Z","published_at":"2025-07-17T05:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAt the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as \\\"unattackable at the present state of mathematics\\\" and are now known as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eLandau's problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(source : Wiki)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 4th Landau's problem aalso known as the 'near square primes' asked whether there are infinitely many primes which are of the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = n^2 + 1, n \\\\in \\\\mathbb{N}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYour task here is to list such primes below a given input integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 20 =\u0026gt; p = [2, 5, 17] ;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 200 =\u0026gt; p = [2, 5, 17, 37, 101, 197] ;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 2000 =\u0026gt; p = [2, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601] ;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFobidden functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95630\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52288,"title":"List Honaker primes","description":"The number 131 is the 32nd prime number. It is a Honaker prime because the sum of its digits (1+3+1) equals the sum of the digits of the index in the list of primes (3+2). \r\nWrite a function to list Honaker primes less than or equal to the input number.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.7417px 7.79167px; transform-origin: 79.7417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 131 is the 32\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003end\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 289px 7.79167px; transform-origin: 289px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e prime number. It is a Honaker prime because the sum of its digits (1+3+1) equals the sum of the digits of the index in the list of primes (3+2). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 239.083px 7.79167px; transform-origin: 239.083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list Honaker primes less than or equal to the input number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = HonakerPrimes(n)\r\n y = f(n);\r\nend","test_suite":"%%\r\nn = 1000;\r\ny_correct = [131 263 457];\r\nassert(isequal(HonakerPrimes(n),y_correct))\r\n\r\n%%\r\nn = 6500;\r\ny = HonakerPrimes(n);\r\ny40_45_correct = [5741 5801 5843 5927 6301 6311];\r\nassert(isequal(y(40:45),y40_45_correct))\r\n\r\n%%\r\nn = 100000;\r\ns = sum(HonakerPrimes(n));\r\nsum_correct = 18350014;\r\nassert(isequal(s,sum_correct))\r\n\r\n%%\r\nn = 250000;\r\ny = HonakerPrimes(n);\r\nz_correct = 62.432176393547657;\r\nz = prod(y(2:2:end)./y(1:2:end));\r\nassert(abs(z-z_correct)\u003c1e-13)\r\n\r\n%%\r\nn = 1.5e6;\r\ny = HonakerPrimes(n);\r\nz_correct = 147.5463941840111;\r\nz = prod(y(2:2:end)./y(1:2:end));\r\nassert(abs(z-z_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 5e6;\r\ny = HonakerPrimes(n);\r\nylast5_correct = [4991453 4991473 4991771 4993403 4998001];\r\nz_correct = 276.8019673660703;\r\nz = prod(y(2:2:end)./y(1:2:end-1));\r\nassert(isequal(y(end-4:end),ylast5_correct) \u0026\u0026 abs(z-z_correct)\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('HonakerPrimes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-14T03:41:59.000Z","updated_at":"2025-11-29T20:37:54.000Z","published_at":"2021-07-14T03:43:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 131 is the 32\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003end\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e prime number. It is a Honaker prime because the sum of its digits (1+3+1) equals the sum of the digits of the index in the list of primes (3+2). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list Honaker primes less than or equal to the input number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52293,"title":"Palindromic Primes","description":"A Palindromic Prime is a prime number that is also a palindromic number. (Wiki, OEIS) \r\n\r\nIf given a monotonic series (increment=1) or a single number, give the corresonding palindromic prime.\r\nElse, if given a random array of numbers, check if the numbers in the array are palindromic prime or not.\r\nTake base 10 as the reference.\r\n\r\nExample\r\ninput = 2:5;\r\noutput = [3 5 7 11];\r\n\r\ninput = 17;\r\noutput = 787;\r\n\r\ninput = [7 23 47 11 4 10];\r\noutput = [1 0 0 1 0 0];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 374.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 187.233px; transform-origin: 407px 187.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA Palindromic Prime is a prime number that is also a palindromic number. (\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Palindromic_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWiki\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002385\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOEIS\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 322.5px 8px; transform-origin: 322.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf given a monotonic series (increment=1) or a single number, give the corresonding palindromic prime.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 328px 8px; transform-origin: 328px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eElse, if given a random array of numbers, check if the numbers in the array are palindromic prime or not.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.5px 8px; transform-origin: 98.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTake base 10 as the reference.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.5px 8px; transform-origin: 26.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 163.467px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 81.7333px; transform-origin: 404px 81.7333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003einput = 2:5;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; tab-size: 4; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eoutput = [3 5 7 11];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; tab-size: 4; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003einput = 17;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eoutput = 787;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; 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tab-size: 4; transform-origin: 104px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003einput = [7 23 47 11 4 10];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eoutput = [1 0 0 1 0 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = palinprime(x)\r\n%{Enter your code here%}\r\n\r\n%Stay home, stay safe\r\n%Wear a mask and sanitize\r\n\r\nend","test_suite":"%%\r\nx = 17;\r\ny = 787;\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [101 111 121 131 141 151];\r\ny = [1 0 0 1 0 1];\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = 1:4;\r\ny = [2, 3, 5, 7];\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [22, 58, 84, 85, 94, 136, 160];\r\ny = zeros(1,7);\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\n%The only 2 digit palindromic prime\r\nx = 5;\r\ny = 11;\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [69 420 666];\r\ny = [0 0 0];\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = 11;\r\ny = 313;\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [363 373 383];\r\ny = [0 1 1];\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = 1;\r\ny = 2;\r\nassert(isequal(palinprime(x),y))\r\n\r\n%%\r\nx = [313, 323, 333, 343, 353];\r\ny = [1 0 0 0 1];\r\nassert(isequal(palinprime(x),y))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":223089,"edited_by":223089,"edited_at":"2022-06-04T20:18:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2021-07-15T05:24:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-14T10:18:02.000Z","updated_at":"2026-01-21T12:33:19.000Z","published_at":"2021-07-14T12:33:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Palindromic Prime is a prime number that is also a palindromic number. (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Palindromic_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWiki\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A002385\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf given a monotonic series (increment=1) or a single number, give the corresonding palindromic prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eElse, if given a random array of numbers, check if the numbers in the array are palindromic prime or not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTake base 10 as the reference.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[input = 2:5;\\noutput = [3 5 7 11];\\n\\ninput = 17;\\noutput = 787;\\n\\ninput = [7 23 47 11 4 10];\\noutput = [1 0 0 1 0 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60946,"title":"Fermat primes","description":"Historical context\r\n\r\n\r\nThe french mathematician Pierre de Fermat found the formula to find some prime numbers. He thought / conjectured all these numbers where primes, but P(5) is actually the first not prime Fermat number.\r\n\r\n\r\nProblem statement\r\n\r\nFor a given integer m, , list the Fermat prime numbers less or equal to m in a vector fp. Also compute their frequency / ratio f compare to all the primes in the same range. If , your function should return fp = [] and f = 0.\r\n\r\nExamples\r\n\r\nIf m = 10 then fp = [3, 5] and f = 2/3 since 3 = P(0), 5 = P(1), and there are in total three primes in the range [3; 10] ;\r\nIf m = 300 then fp = [3, 5, 17, 257] and f = 4/61 since 3 = P(0), 5 = P(1), 17 = P(2), 257 = P(3) and there are in total 61 prime numbers in the range [3; 300] ; \r\nIf m = 2 then fp = [] and f = 0;\r\n\r\n\r\nTip \r\n\r\n here.\r\n\r\n\r\nFobidden functions\r\n\r\nregexp\r\nassignin\r\nstr2num\r\n\r\n\r\nSee also\r\nProblem 60942. Euler primes\r\nPrime numbers properties II","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1001.03px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 500.517px; transform-origin: 408px 500.517px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 22.5px; text-align: left; transform-origin: 385px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 193.7px 8px; transform-origin: 193.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe french mathematician Pierre de Fermat found the formula \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"96\" height=\"23.5\" style=\"width: 96px; height: 23.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.625px 8px; transform-origin: 132.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to find some prime numbers. He thought / conjectured all these numbers where primes, but P(5) is actually the first not prime Fermat number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.2917px 8px; transform-origin: 60.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.225px 8px; transform-origin: 6.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 144.3px 8px; transform-origin: 144.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elist the Fermat prime numbers less or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.1083px 8px; transform-origin: 38.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a vector f\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.6167px 8px; transform-origin: 98.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Also compute their frequency / ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.242px 8px; transform-origin: 146.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecompare to all the primes in the same range. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8583px 8px; transform-origin: 82.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eyour function should return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.1333px 8px; transform-origin: 23.1333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e fp = [] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.0833px 8px; transform-origin: 18.0833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e f = 0.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.9833px 8px; transform-origin: 21.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e f\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 28.5833px 8px; transform-origin: 28.5833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [3, 5]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.975px 8px; transform-origin: 21.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 2/3 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 56.0083px 8px; transform-origin: 56.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3 = P(0), 5 = P(1),\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 169.192px 8px; transform-origin: 169.192px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and there are in total three primes in the range [3; 10] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.875px 8px; transform-origin: 25.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 300\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e f\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 55.8083px 8px; transform-origin: 55.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ep = [3, 5, 17, 257]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.8667px 8px; transform-origin: 25.8667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 4/61 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 86.9333px 8px; transform-origin: 86.9333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3 = P(0), 5 = P(1), 17 = P(2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 32.875px 8px; transform-origin: 32.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e257 = P(3)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 66.125px 8px; transform-origin: 66.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand there are in total 61\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 85.5833px 8px; transform-origin: 85.5833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eprime numbers in the range\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 31.1px 8px; transform-origin: 31.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e [3; 300] ; \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 20.0333px 8px; transform-origin: 20.0333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 2 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003efp = []\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 14.2px 8px; transform-origin: 14.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9167px 8px; transform-origin: 64.9167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFobidden functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/60942-euler-primes\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 60942. Euler primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95759\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties II\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [fp, f] = fermat_primes(n)\r\n fp = n;\r\n f = 1;\r\nend","test_suite":"%%\r\nm = 10;\r\nfp_correct = [3, 5];\r\nf_correct = 2/3;\r\n[fp,f] = fermat_primes(m);\r\nassert(isequal([fp,f],[fp_correct,f_correct]));\r\n\r\n%%\r\nm = 300;\r\nfp_correct = [3, 5, 17, 257];\r\nf_correct = 4/61;\r\n[fp,f] = fermat_primes(m);\r\nassert(isequal([fp,f],[fp_correct,f_correct]));\r\n\r\n%%\r\nm = 2;\r\nfp_correct = [];\r\nf_correct = 0;\r\n[fp,f] = fermat_primes(m);\r\nassert(isequal([fp,f],[fp_correct,f_correct]));\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('fermat_primes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T06:52:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2025-07-09T05:57:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-06-27T05:33:53.000Z","updated_at":"2026-03-16T20:10:35.000Z","published_at":"2025-06-27T06:14:34.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe french mathematician Pierre de Fermat found the formula \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbf{P(n) = 2^{2^n} + 1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to find some prime numbers. He thought / conjectured all these numbers where primes, but P(5) is actually the first not prime Fermat number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em \\\\geq 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003elist the Fermat prime numbers less or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in a vector f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Also compute their frequency / ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ecompare to all the primes in the same range. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em \u0026lt; 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eyour function should return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e fp = [] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e f = 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [3, 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 2/3 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3 = P(0), 5 = P(1),\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and there are in total three primes in the range [3; 10] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 300\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [3, 5, 17, 257]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 4/61 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3 = P(0), 5 = P(1), 17 = P(2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e257 = P(3)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand there are in total 61\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eprime numbers in the range\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e [3; 300] ; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 2 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efp = []\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \\\\leq 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e here.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFobidden functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/problems/60942-euler-primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 60942. Euler primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95759\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties II\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60561,"title":"Determine whether a number is a Blum integer","description":"A Blum integer is a semiprime—that is, the product of two distinct primes—whose factors have the form for some integer . The number 21 is a Blum integer because its two prime factors, 3 and 7, have the form with and . The number 123 is a semiprime because it is , but it is not a Blum integer because 41 is not 3 more than a multiple of 4. The number 1463 is not a Blum integer: although its prime factors are distinct and each 3 more than a multiple of 4, there are three of them, not two. \r\nWrite a function to determine whether the numbers in a matrix are Blum integers. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.60833px 8px; transform-origin: 6.60833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Blum_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eBlum integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.775px 8px; transform-origin: 14.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55275\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esemiprime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 228.683px 8px; transform-origin: 228.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—that is, the product of two distinct primes—whose factors have the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42\" height=\"18\" alt=\"4k+3\" style=\"width: 42px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1083px 8px; transform-origin: 31.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for some integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 273.808px 8px; transform-origin: 273.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The number 21 is a Blum integer because its two prime factors, 3 and 7, have the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42\" height=\"18\" alt=\"4k+3\" style=\"width: 42px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.3333px 8px; transform-origin: 16.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36\" height=\"18\" alt=\"k = 0\" style=\"width: 36px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36\" height=\"18\" alt=\"k = 1\" style=\"width: 36px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 145.083px 8px; transform-origin: 145.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The number 123 is a semiprime because it is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42\" height=\"18\" alt=\"3x41\" style=\"width: 42px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.633px 8px; transform-origin: 188.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but it is not a Blum integer because 41 is not 3 more than a multiple of 4. The number 1463 is not a Blum integer: although its prime factors are distinct and each 3 more than a multiple of 4, there are three of them, not two. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.917px 8px; transform-origin: 251.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether the numbers in a matrix are Blum integers. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isBlum(x)\r\n y = false;\r\nend","test_suite":"%%\r\nx = 21;\r\nassert(isBlum(x))\r\n\r\n%%\r\nx = 25;\r\nassert(~isBlum(x))\r\n\r\n%%\r\nx = 123;\r\nassert(~isBlum(x))\r\n\r\n%%\r\nx = 123;\r\nassert(~isBlum(x))\r\n\r\n%%\r\nx = 737;\r\nassert(isBlum(x))\r\n\r\n%%\r\nx = 1463;\r\nassert(~isBlum(x))\r\n\r\n%%\r\nx = [37533 37581 37601 37617 37641 37669 37709 37721 37749 37753 37769];\r\nassert(all(isBlum(x)))\r\n\r\n%%\r\nx = 4+[37533 37581 37601 37617 37641 37669 37709 37721 37749 37753 37769];\r\nassert(sum(isBlum(x))==1)\r\n\r\n%% \r\nx = [74089 74301 74401 74549 74669 74773 74881\r\n 74141 74309 74417 74553 74689 74801 74901\r\n 74213 74329 74429 74557 74701 74809 74913\r\n 74233 74369 74461 74569 74721 74813 74917\r\n 74249 74389 74473 74577 74741 74829 74937\r\n 74281 74393 74537 74621 74757 74833 74957\r\n 74289 74397 74541 74641 74769 74837 74977];\r\nassert(isequal(isBlum(x),true(7)))\r\n\r\n%% \r\nx = [74089 74301 74401 74549 74669 74773 74881\r\n 74141 74309 74417 74553 74689 74801 74901\r\n 74213 74329 74429 74557 74701 74809 74913\r\n 74233 74369 74461 74569 74721 74813 74917\r\n 74249 74389 74473 74577 74741 74829 74937\r\n 74281 74393 74537 74621 74757 74833 74957\r\n 74289 74397 74541 74641 74769 74837 74977];\r\nA = isBlum(x+16);\r\ny = A*2.^(6:-1:0)';\r\ny_correct = [16 9 0 66 4 20 17]';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = randi(1000);\r\nx = 2*randi(450000,1,n);\r\nassert(all(~isBlum(x)))\r\n\r\n%%\r\nx = reshape([97091 106789 109033 147703 186819 267349 345133 472647 480241 491283 510839 524249 87893 128567 185019 226173 273351 325969 377121 405283 440487 478509 506273 518377],[4 3 2]);\r\ny = isBlum(x);\r\ny_correct = reshape(logical([0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1]),[4 3 2]);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = [504737 539969 619369];\r\nassert(isequal(isBlum(x),logical([1 1 0])))\r\n\r\n%%\r\nf = 4*(1:200)+3;\r\nf1 = f(isprime(f));\r\nassert(isequal(isBlum(f1.*f1'),logical(~eye(length(f1)))))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-26T00:46:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-25T03:32:30.000Z","updated_at":"2025-07-31T19:37:37.000Z","published_at":"2024-06-25T03:33:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Blum_integer\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBlum integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55275\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esemiprime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—that is, the product of two distinct primes—whose factors have the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"4k+3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4k+3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for some integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\\n\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The number 21 is a Blum integer because its two prime factors, 3 and 7, have the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"4k+3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4k+3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The number 123 is a semiprime because it is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"3x41\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\\\\times41\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, but it is not a Blum integer because 41 is not 3 more than a multiple of 4. The number 1463 is not a Blum integer: although its prime factors are distinct and each 3 more than a multiple of 4, there are three of them, not two. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether the numbers in a matrix are Blum integers. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60942,"title":"Euler primes","description":"Historical context\r\n\r\n\r\nThe great swiss mathematician Leonhard Euler found the formula to give some prime numbers.\r\n\r\n\r\nProblem statement\r\n\r\nFor a given integer m, m \u003e= 41, list the Euler prime numbers less or equal to m in a vector ep. Also compute their frequency / ratio f compare to all the primes in the same range. If m is not a positive integer greater or equal to 41, your function should return ep = [] and f = 0.\r\n\r\nExamples (check the tests for more)\r\n\r\nIf m = 41 then ep = 41 and f = 1 since 41 = P(0) and it is the only prime number m greater or equal and less or equal to 41;\r\nIf m = 100 then ep = [41, 43, 47, 53, 61, 71, 83, 97] and f = 8/13 since 41 = P(0), 43 = P(1), 47 = P(2), 53 = P(3), 61 = P(4), 71 = P(5), 83 = P(6), and 97 = P(7), and in total there are 13 prime numbers in the range [41; 100] ; \r\nIf m = 19 then ep = [] and f = 0;\r\n\r\n\r\nTip \r\n\r\nn is less or equal to 107 here.\r\n\r\n\r\nFobidden functions\r\n\r\nregexp\r\nstr2num\r\nassignin\r\n\r\nSee also\r\nProblem 60944. Ulam primes first formula, Problem 60943. Ulam primes second formula\r\nPrime numbers properties II","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 988.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 494.233px; transform-origin: 408px 494.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHistorical context\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; 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\"\u003e\u003cspan style=\"\"\u003eThe great swiss mathematician Leonhard Euler found the formula \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"125\" height=\"19.5\" style=\"width: 125px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.1833px 8px; transform-origin: 92.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to give some prime numbers.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.2917px 8px; transform-origin: 60.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.225px 8px; transform-origin: 6.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.075px 8px; transform-origin: 26.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em \u0026gt;= 41\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.475px 8px; transform-origin: 138.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003elist the Euler prime numbers less or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.1667px 8px; transform-origin: 36.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.78333px 8px; transform-origin: 7.78333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.3833px 8px; transform-origin: 96.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Also compute their frequency / ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 286.658px 8px; transform-origin: 286.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecompare to all the primes in the same range. If m is not a positive integer greater or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.6667px 8px; transform-origin: 11.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e41, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.35px 8px; transform-origin: 63.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eyour function should return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.6917px 8px; transform-origin: 24.6917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e ep = [] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.0833px 8px; transform-origin: 18.0833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e f = 0.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.6167px 8px; transform-origin: 34.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3333px 8px; transform-origin: 79.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(check the tests for more)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 51.0833px; transform-origin: 392px 51.0833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.9833px 8px; transform-origin: 21.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 41\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 23.925px 8px; transform-origin: 23.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eep = 41\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 16.1417px 8px; transform-origin: 16.1417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 1 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 28.9833px 8px; transform-origin: 28.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e41 = P(0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 99.575px 8px; transform-origin: 99.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and it is the only prime number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 108.533px 8px; transform-origin: 108.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e greater or equal and less or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 10.1167px 8px; transform-origin: 10.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e41;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.875px 8px; transform-origin: 25.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 100\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 110.258px 8px; transform-origin: 110.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eep = [41, 43, 47, 53, 61, 71, 83, 97]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.8667px 8px; transform-origin: 25.8667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 8/13 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 18.2833px 8px; transform-origin: 18.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 141.192px 8px; transform-origin: 141.192px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e41 = P(0), 43 = P(1), 47 = P(2), 53 = P(3), 61 = P(4), 71 = P(5), 83 = P(6), and 97 = P(7), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand in total there are\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 11.6667px 8px; transform-origin: 11.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e 13 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 85.5833px 8px; transform-origin: 85.5833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eprime numbers in the range\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 34.9917px 8px; transform-origin: 34.9917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e [41; 100] ; \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 23.925px 8px; transform-origin: 23.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003em = 19 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 20.8083px 8px; transform-origin: 20.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eep = []\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 14.2px 8px; transform-origin: 14.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ef = 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is less or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e107\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9167px 8px; transform-origin: 64.9167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFobidden functions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 30.65px; transform-origin: 392px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/60944-ulam-primes-first-formula\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-style: italic; \"\u003eProblem 60944. Ulam primes first formula\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/problems/60943-ulam-primes-second-formula\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-style: italic; \"\u003eProblem 60943. Ulam primes second formula\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95759\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePrime numbers properties II\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [ep,f] = euler_primes(m)\r\n ep = m;\r\n f = 1;\r\nend","test_suite":"%%\r\nm = 41;\r\nep_correct = 41;\r\nf_correct = 1;\r\n[ep,f] = euler_primes(m);\r\nassert(isequal([ep,f],[ep_correct,f_correct]));\r\n\r\n%%\r\nm = 100;\r\nep_correct = [41, 43, 47, 53, 61, 71, 83, 97];\r\nf_correct = 8/13;\r\n[ep,f] = euler_primes(m);\r\nassert(isequal([ep,f],[ep_correct,f_correct]));\r\n\r\n%%\r\nm = 200;\r\nep_correct = [41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197];\r\nf_correct = 13/34;\r\n[ep,f] = euler_primes(m);\r\nassert(isequal([ep,f],[ep_correct,f_correct]));\r\n\r\n%%\r\nm = 19;\r\nep_correct = [];\r\nf_correct = 0;\r\n[ep,f] = euler_primes(m);\r\nassert(isequal([ep,f],[ep_correct,f_correct]));\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('euler_primes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T06:49:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2025-07-09T05:56:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-06-26T14:44:30.000Z","updated_at":"2026-03-16T19:16:06.000Z","published_at":"2025-06-26T15:44:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHistorical context\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe great swiss mathematician Leonhard Euler found the formula \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbf{P(n) = n^2 + n + 41}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to give some prime numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em \u0026gt;= 41\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003elist the Euler prime numbers less or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Also compute their frequency / ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ecompare to all the primes in the same range. If m is not a positive integer greater or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e41, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eyour function should return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e ep = [] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e f = 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(check the tests for more)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 41\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eep = 41\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 1 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e41 = P(0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and it is the only prime number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e greater or equal and less or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e41;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eep = [41, 43, 47, 53, 61, 71, 83, 97]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 8/13 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e41 = P(0), 43 = P(1), 47 = P(2), 53 = P(3), 61 = P(4), 71 = P(5), 83 = P(6), and 97 = P(7), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand in total there are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 13 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eprime numbers in the range\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e [41; 100] ; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em = 19 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethen \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eep = []\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is less or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e107\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFobidden functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/problems/60944-ulam-primes-first-formula\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 60944. Ulam primes first formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/problems/60943-ulam-primes-second-formula\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 60943. Ulam primes second formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95759\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrime numbers properties II\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50948,"title":"Identify prime words","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6083px 7.91667px; transform-origin: 13.6083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=9CcI5M1LfRs\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eNumberphile video on evil primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 236.375px 7.91667px; transform-origin: 236.375px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Tony Padilla introduced the “Jesus prime” 105,192,119, which is formed by concatenating the positions of the letters of ‘Jesus’ in the English alphabet: 10, 5, 19, 21, 19. In general, a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.625px 7.91667px; transform-origin: 34.625px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eprime word\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.91667px; transform-origin: 20.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e could be defined as a word such that the number formed by concatenating the positions of the letters in the alphabet is prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.425px 7.91667px; transform-origin: 368.425px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a string and identifies prime words. It should delete apostrophes and hyphens (e.g. “don’t” = “dont”, “un-ionized” = “unionized”) and treat other punctuation as spaces. The function should return an array of 0’s and 1’s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isPrimeWord(s)\r\n tf = isprime(s);\r\nend","test_suite":"%%\r\nassert(isPrimeWord('Croatia'))\r\n\r\n%%\r\nassert(~isPrimeWord('Serbia'))\r\n\r\n%%\r\nassert(isPrimeWord('frenetic'))\r\n\r\n%%\r\nassert(~isPrimeWord('frantic'))\r\n\r\n%%\r\nassert(isPrimeWord('smiling'))\r\n\r\n%%\r\nassert(~isPrimeWord('frowning'))\r\n\r\n%%\r\nassert(isPrimeWord('ziti'))\r\n\r\n%%\r\nassert(~isPrimeWord('spaghetti'))\r\n\r\n%%\r\nassert(isPrimeWord('tick'))\r\n\r\n%%\r\nassert(~isPrimeWord('tock'))\r\n\r\n%%\r\nassert(isPrimeWord('madam'))\r\n\r\n%%\r\nassert(~isPrimeWord('Adam')) \r\n\r\n%%\r\nassert(isPrimeWord('RFQ'))\r\n\r\n%%\r\nassert(~isPrimeWord('FAQ'))\r\n\r\n%%\r\nassert(isPrimeWord('Jesus'))\r\n\r\n%%\r\nassert(~isPrimeWord('Moses')) \r\n\r\n%%\r\nassert(isPrimeWord('adieu'))\r\n\r\n%%\r\nassert(~isPrimeWord('milieu'))\r\n\r\n%%\r\nassert(isPrimeWord('wallow'))\r\n\r\n%%\r\nassert(~isPrimeWord('swallow')) \r\n\r\n%%\r\ns = 'slim pickings';\r\nassert(all(isPrimeWord(s)))\r\n\r\n%%\r\ns = 'mellow fellow';\r\nassert(all(isPrimeWord(s)))\r\n\r\n%%\r\ns = 'Ms. Zadora stuck a cornucopia full of Bing cherries into her knapsack.';\r\ntf_correct = [1 1 1 0 1 0 0 1 0 0 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%%\r\ns = 'The dog and pig are going to India.';\r\ntf_correct = [0 1 0 1 0 1 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%%\r\ns = 'Liam, is Mauritius in Africa? I know that Mali and Libya are.';\r\ntf_correct = [1 1 1 0 1 0 0 0 1 0 1 0];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%% Maria Bamford\r\nq = char(39);\r\ns = ['I was in a lot of plays. We had a weird drama teacher in that he was incredibly enthusiastic about a high school drama program and would talk to all the kids for hours. He ended up marrying one of the kids, but that' q 's neither here nor there.'];\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[28 32 42]))\r\n\r\n%% Maria Bamford\r\nq = char(39);\r\ns = ['I do wanna get married. It just sounds great. You get to go grocery shopping together, rent videos, and the kissing and the hugging and the kissing and the hugging under the cozy covers. Mmmm! But sometimes I worry that I don' q 't wanna get married as much as I want to get dipped in a vat of warm, rising bread dough. That might feel pretty good, too.'];\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[3 15 34 43]))\r\n\r\n%% Monty Python\r\ns = 'I cut down trees, I eat my lunch, I go to the lavatory. On Wednesday I go shopping and have buttered scones for tea.';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[4 18]))\r\n\r\n%% Monty Python\r\ns = 'Strange women lying in ponds, distributing swords, is no basis for a system of government!';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[8 10]))\r\n\r\n%% Monty Python\r\ns = 'My hovercraft is full of eels.';\r\ntf_correct = [0 0 1 0 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n \r\n%% Basil Fawlty\r\ns = 'Well may I ask what you expected to see out of a Torquay hotel bedroom window? Sydney Opera House perhaps? The Hanging Gardens of Babylon? Herds of wildebeest sweeping majestically';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[18 23]))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-03-14T22:44:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-14T16:24:34.000Z","updated_at":"2026-01-20T19:15:07.000Z","published_at":"2021-03-14T16:29:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=9CcI5M1LfRs\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNumberphile video on evil primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, Tony Padilla introduced the “Jesus prime” 105,192,119, which is formed by concatenating the positions of the letters of ‘Jesus’ in the English alphabet: 10, 5, 19, 21, 19. In general, a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprime word\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e could be defined as a word such that the number formed by concatenating the positions of the letters in the alphabet is prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a string and identifies prime words. It should delete apostrophes and hyphens (e.g. “don’t” = “dont”, “un-ionized” = “unionized”) and treat other punctuation as spaces. The function should return an array of 0’s and 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