Talk:Landau's problems

4th problem
Does the 4th Landau problem have a "name", e.g. "Generalized Fermat primes Conjecture"? —The preceding unsigned comment was added by Special:Contributions/ (talk)
 * I don't think it's named. PrimeHunter 22:34, 19 August 2007 (UTC)


 * I have seen a very few authors who give the 4th Landau problem the name "Proth primes Conjecture". However, I have seen many more authors who follow convention, and leave the 4th Landau problem unnamed. PhiEaglesfan712 16:22, 21 August 2007 (UTC)


 * I have never seen that and it has zero Google hits. Proth primes are of another form. PrimeHunter 19:47, 21 August 2007 (UTC)

4th problem
It exists an infinity of squares of the form 6K (1/3 of the square of even number). It exists an infinity of prime number of the form 6k+1 (1/2 of Primes Numbers). So it exists necessary an infinity of primes of the form n2 + 1.

- Jérôme 02/08/2012 CET — Preceding unsigned comment added by 88.189.253.171 (talk) 17:41, 8 February 2012 (UTC)


 * There are also infinitely many composite numbers of the form 6k+1, so your argument doesn't work. PrimeHunter (talk) 00:07, 9 February 2012 (UTC)

Possible source
I haven't read this one yet, but if I can find a copy it might have something relevant to this article.
 * Glyn Harman, "On values of $$n^2 + 1$$ free of large prime factors", Archiv der Mathematik 90:3 (2008), pp. 239-245.

CRGreathouse (t | c) 19:36, 1 February 2009 (UTC)

Unresolved or proved
>> As of 2016, all four problems are unresolved.

Summary states that the problems are unresolved but the description says they are proved. E.g ChenPrime. Not clear why they are unresolved — Preceding unsigned comment added by 54.240.196.169 (talk) 03:21, 2 December 2016 (UTC)


 * None of them are proved. Weaker variants are proved, e.g. if we allow semiprimes (a product of two primes) instead of primes. PrimeHunter (talk) 10:04, 2 December 2016 (UTC)

conjecture?
Why are the first 3 called conjectures when they are posed as questions? Shouldn't they be written as statements?--Richardson mcphillips (talk) 12:32, 21 May 2018 (UTC) This is an article on Landau's Problems and so they are phased as problems whereas the conjectures themselves are written as statements that need to be proven. As an example Goldbach's conjecture is "Every even integer greater than 2 can be expressed as the sum of two primes." but Landau's first problem is "Can every even integer greater than 2 be written as the sum of two primes?"OrewaTel (talk) 06:23, 21 April 2020 (UTC)