Problem 2910. Mersenne Primes vs. All Primes

Created by goc3

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number.</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\"><w:r><w:t>Problem 525</w:t></w:r></w:hyperlink><w:r><w:t> asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

970 Solutions
357 Solvers

Last Solution submitted on Jan 17, 2023

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Jean-Marie Sainthillier on 16 May 2019

Hello Grant,
I don't know if it's a lot of work but it could be a good idea to add a Prime Numbers group 2 with more difficult problems. I think about beautiful Ned's problems (primes ladders, Longest prime diagonal, Twins in a window ...).

Solution Comments

Solution 6817490

1 Comment

1 Comment

Jan-Andrea Bard on 3 Nov 2021

Nice one. I found a solution of size 127. And I have the impression it's already quite condensed. It's a mystery to me how one can write a solution of size 26. Can anybody give me a hint on how to do so?

Solution 4370990

2 Comments

2 Comments

Ozer Eroglu on 20 Dec 2020

test cases are wrong.
please be more serious to accept problems.
it doesn't suit mathworks:(

Dyuman Joshi on 21 May 2021

@Ozer Eroglu
Test cases have been verified and they are indeed correct. What makes you think so that they are wrong?

Solution 1931803

1 Comment

1 Comment

Mayank Bajpai on 5 Oct 2020

Does all the leading solutions with the size below 10, use this ? Nice idea, but this doesn't improve the problem solving skills.

Solution 571313

6 Comments

6 Comments

Show 3 older comments

Anupam Agarwal on 1 Feb 2015

My logic is right but test cases are very hude numbers.... failed to evaluate...

Guillaume on 2 Feb 2015

You need to learn to avoid loops. You can use isprime on an array. In any case, your logic is wrong. You never test that b is prime.

goc3 on 2 Feb 2015

As Guillaume pointed out, this solution doesn't test if the numbers in b are Mersenne primes, simply if they're less than 2^n-1, which is not the right criterion. Further, you concatenate the index of the loop (j, which goes from 1 to 1...), rather than a Mersenne prime to b.

Also, this problem is designed, as many of James's problems are, to fail by timeout unless vectorized solutions are used.

Anupam Agarwal on 3 Feb 2015

i have corrected the logic but plz can u tell me smthing about vectorized solutions...
u can also mail me on anupamagarw@gmail.com

Jan Orwat on 3 Feb 2015

http://nl.mathworks.com/help/matlab/matlab_prog/vectorization.html

Jan Orwat on 3 Feb 2015

some tips: http://nl.mathworks.com/help/matlab/matlab_prog/techniques-for-improving-performance.html

Problem Recent Solvers357

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 2910. Mersenne Primes vs. All Primes

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers357

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Problem 2910. Mersenne Primes vs. All Primes

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers357

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players