Problem 46594. Create a sequence of primes p such that p > n π(p)

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function to find the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>th term of a sequence of prime numbers </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p</w:t></w:r></w:customXml><w:r><w:t> such that </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p &gt; n \\pi(p)</w:t></w:r></w:customXml><w:r><w:t>, where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\pi(p)</w:t></w:r></w:customXml><w:r><w:t> is the prime counting function. The first three numbers in this sequence are 2, 11, and 37. For example, the second number is 11 because five primes are less than or equal to 11 (i.e., </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\pi(11) = 5</w:t></w:r></w:customXml><w:r><w:t>) and 11 &gt; </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2\\cdot5 = 10</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A related problem is </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/46117-test-approximations-of-the-prime-counting-function\"><w:r><w:t>Cody Problem 46117</w:t></w:r></w:hyperlink><w:r><w:t> Test approximations of the prime counting function. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div 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; "><div style="block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 46.5px; transform-origin: 407.5px 46.5px; vertical-align: baseline; "><div 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: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.1px 7.875px; transform-origin: 83.1px 7.875px; unicode-bidi: normal; ">Write a function to find the n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.017px 7.875px; transform-origin: 126.017px 7.875px; unicode-bidi: normal; ">th term of a sequence of prime numbers p<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.275px 7.875px; transform-origin: 32.275px 7.875px; unicode-bidi: normal; "> such that <img src="data:image/png;base64,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" style="width: 68px; height: 18.5px;" width="68" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 7.875px; transform-origin: 24.8917px 7.875px; unicode-bidi: normal; ">, where <img src="data:image/png;base64,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" style="width: 33px; height: 18.5px;" width="33" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0583px 7.875px; transform-origin: 40.0583px 7.875px; unicode-bidi: normal; "> is the prime counting function. The first three numbers in this sequence are 2, 11, and 37. For example, the second number is 11 because five primes are less than or equal to 11 (i.e., <img src="data:image/png;base64,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" style="width: 65px; height: 18.5px;" width="65" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.1333px 7.875px; transform-origin: 33.1333px 7.875px; unicode-bidi: normal; ">) and 11 &gt; <img src="data:image/png;base64,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" style="width: 62.5px; height: 18px;" width="62.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-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 7.875px; transform-origin: 3.88333px 7.875px; unicode-bidi: normal; ">. </div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 7.875px; transform-origin: 64.1833px 7.875px; unicode-bidi: normal; ">A related problem is <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46117-test-approximations-of-the-prime-counting-function">Cody Problem 46117</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161.808px 7.875px; transform-origin: 161.808px 7.875px; unicode-bidi: normal; "> Test approximations of the prime counting function. </div></div></div>

Solve

Solution Stats

20 Solutions
9 Solvers

Last Solution submitted on Jul 07, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers9

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 46594. Create a sequence of primes p such that p > n π(p)

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers9

Suggested Problems

More from this Author185

Problem Tags

Community Treasure Hunt

Problem 46594. Create a sequence of primes p such that p > n π(p)

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers9

Suggested Problems

More from this Author185

Problem Tags

Community Treasure Hunt

Players