Talk:Legendre's conjecture

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 Field: Number theory

Related Conjectures[edit]

If any one of the following is proven true, then Legendre's is proven true too.

Andrica's: pn+11/2-pn1/2<1 for all n => 1.

Opperman's: pi(n2+n) > pi(n2) > pi(n2-n) for n > 1.

Brocard's: pi(pn+12) - pi(pn2) => 4 for n => 2.

Grimm's: if n+1, ..., n+k are consecutive composite numbers, then we can find distinct prime numbers pi so that pi divides n+i.

and Sierpinski: For every integer n > 1, let the n2 integers 1,2, ... ,n2 be written in an array with n rows, each with n integers, like an n x n matrix, then there exist a prime number in each row.

Reddwarf2956 (talk) 21:41, 15 July 2008 (UTC)


I've proven that Legendre's conjecture is true. Please visit... to see my solution; I've included a proof for Legendre's {stronger} conjecture as well. Enjoy! Bill (talk) 02:21, 26 February 2012 (UTC)

Thank you for posting this to the talk page and not the article. As you may know, Wikipedia has policies against original research and conflict of interest edits. If your work is published by a reliable source like a peer-reviewed journal then you can suggest addition to the article. PrimeHunter (talk) 03:03, 26 February 2012 (UTC)


When did this conjecture get first published? John W. Nicholson (talk) 00:48, 4 June 2014 (UTC)