Problem 42914. Counting the Grand Primes

Created by John D'Errico

Solve Later

{"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":"<?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:pPr><w:r><w:t>A grand prime pair is a pair of primes, p1 and p2=p1+1000, such that both numbers are prime. Like a twin prime pair, where the difference is 2, the members of a grand prime pair always have a difference of 1000. Some facts about grand prime pairs, so that you can test your code:</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>1. The smallest grand prime pair is [13,1013], the 100th such pair is [3229,4229].</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>2. There are 37 grand prime pairs such that the larger element of the pair is no larger than 2000.</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>3. There should be infinitely many grand prime pairs.</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>4. All such grand prime pairs must have the property that the smaller element of the pair is of the form 6*k+1, for some integer k.</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>Write a function that counts the number of grand prime pairs that exist, such that the larger element of the pair is no larger than N. I'll be nice and not ask you to compute that result for N too large, 1e8 seems a reasonable upper limit.</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

85 Solutions
40 Solvers

Last Solution submitted on May 25, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers40

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 42914. Counting the Grand Primes

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers40

Suggested Problems

More from this Author4

Problem Tags

Community Treasure Hunt

Problem 42914. Counting the Grand Primes

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers40

Suggested Problems

More from this Author4

Problem Tags

Community Treasure Hunt

Players