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)

Proof[edit]

I've proven that Legendre's conjecture is true. Please visit... www.oddperfectnumbers.com to see my solution; I've included a proof for Legendre's {stronger} conjecture as well. Enjoy! Bill 99.118.131.124 (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[edit]

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

"Most historical accounts of the Prime Number Theorem mention Legendre's experimental conjecture (made in 1798 and again in 1808)...." http://www.mathpages.com/home/kmath032.htm 2601:18C:C601:7D90:C8BB:88CA:8966:7BAB (talk) 15:58, 1 February 2016 (UTC)

Unsolved ?[edit]

Is it correct to say that a statement is unsolved? Personally, I would say that only problems, questions, puzzles and the like can be unsolved. What I think is meant is that the statement is neither proven nor disproven. Can I change to that? --Ettrig (talk) 15:03, 27 August 2015 (UTC)

A conjecture is a question which has not been solved, so no don't change it. Yes, proving/disproving it will solve the question at hand, but the language is correct. John W. Nicholson (talk) 15:33, 27 August 2015 (UTC)
It is your personal view that A conjecture is a question. This view is not supported by the articles in Wikipedia or Wictionary on Conjecture. I think you are referring to a special meaning which is common among mathematicians (I can see why it is) but cannot be assumed in a Wikipedia article. --Ettrig (talk) 15:47, 27 August 2015 (UTC)
I will put it like this, you can state the conjecture, I will state the question that the author of the conjecture is asking. In this case it is Legendre asking 'is there a prime number between each natural square?' John W. Nicholson (talk) 20:11, 27 August 2015 (UTC)
I have no objection to the proposed alternative wording -- it seems at least as clear as the current wording. --JBL (talk) 23:07, 28 August 2015 (UTC)