Talk:Legendre's conjecture

message: 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)
replies: text: Not that it matters much, but the last conjecture is due to Schinzel, not Sierpinski, although the latter was a coauthor of the paper in which the result appeared. - CRGreathouse (t | c) 01:23, 30 July 2022 (UTC)
replies: text: Regardless, shouldn't these be added? Supyovalk (talk) 18:04, 14 November 2022 (UTC)
replies: text: Not without a reliable source. JBL (talk) 19:30, 14 November 2022 (UTC)
thread_title:  Related Conjectures 

message: 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)
replies: text: 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)

text: Oh, lovely, a SCIRP journal.  --JBL (talk) 19:12, 1 June 2023 (UTC)

text: It would be very unprofessional to publish high-quality mathematics with such a low-quality publisher, and force readers to sift through all of the other bad content from that publisher to figure out whether it's any good. Nobody has time for that. That would be a worse strategy for getting your work read and used than just putting up a preprint and leaving it at that. The purpose of a journal is to act as something of a filter so that readers can have some expectation of the reliability and significance of the published content. —David Eppstein (talk) 06:24, 2 June 2023 (UTC)
thread_title:  Proof 

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

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)

text: 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)
thread_title:  Unsolved ?  

message: I think that the conjecture is very close to proof, as I myself have proved it, Or probably have made it very close to proof. Sandeep Kumar Kandi (talk) 13:49, 12 June 2020 (UTC)
replies: text: And once it is published as a WP:RS, we could add something about it to the article.  But not before then (per WP:OR). --JBL (talk) 14:33, 12 June 2020 (UTC)
thread_title:  Proof of Legendre Conjecture 

message: (n²+1)² -minus- n² = equality = numer.
this is a prime number and the only one:
which, most likely, is exactly what he was talking about the "Legendre hypothesis" with an incomplete explanation of such words.
Nean Like 16:38, 20 November 2020 (UTC)
thread_title:   conjecture subject matter 

message: et the 
таким орбразом: (n+1)²-минус-n²=is a prime number between n² and (n + 1)² for every positive integer n.
that is, this number is their distance between these prime numbers in square multiplication.
Nean Like 14:04, 21 November 2020 (UTC)
thread_title: consistence

message: Is it really not trivial ? Make the Square Root of all terms. Then you get back that an Irrational (a Prime is never a square) is packed between two following integers... that is not trivial ?  — Preceding unsigned comment added by StefanoMaruelli (talk • contribs) 18:00, 24 November 2020 (UTC)
replies: text: It is trivial that every prime number lies between two consecutive squares, but that is not what Legendre's conjecture asserts.  This page is for discussing improvements to the article, not for discussion of the article subject; your question would be better placed at the reference desk. --JBL (talk) 18:06, 24 November 2020 (UTC)
thread_title: consistence 2

message: For 1<=n<=6, we'll have to check each one on its own: from 1 to 4 (n=1): 2 and 3.  from 4 to 9 (n=2): 5 and 7.  from 9 to 16 (n=3): 11 and 13  from 16 to 25 (n=4): 17, 19, and 23.  from 25 to 36 (n=5): 29 and 31.  from 36 to 49 (n=6): 37, 41, and 47.  Now for n>=7, since every n since have an entire set of 10s between n^2 and (n+1)^2, we can use Dirichlet's theorem to prove that for every m in N, there exists k in N cap [0,9] such that 10m+k is prime, so there is always a prime then as well. Serouj2000 (talk) 09:05, 21 June 2023 (UTC)
replies: text: It's unclear what you mean but Dirichlet's theorem on arithmetic progressions does not say anything about the size of primes, only their form. It cannot be used to prove Legendre's conjecture.  Also, Wikipedia content must be based on published reliable sources, not original research.  PrimeHunter (talk) 23:22, 21 June 2023 (UTC)
replies: text:  PrimeHunter is correct. Further, your statement is false (take m = 20; 201, 203, 207, and 209 are all composite). - CRGreathouse (t | c) 12:34, 27 June 2023 (UTC)
thread_title:  Here are my two cents