20120727, 03:27  #1 
May 2004
2^{2}×79 Posts 
Infinitely many?
Are there infinitely many primes of the form x^2 + y^2 + 1 ?

20120730, 05:10  #4 
Romulan Interpreter
Jun 2011
Thailand
10010000110001_{2} Posts 
Not really. It may be that after a while, all primes of the form x^2+y^2+1 have x and y bigger than 0. I know the problem you mention is still open.
Last fiddled with by LaurV on 20120730 at 05:11 
20120730, 05:17  #5 
Aug 2006
5972_{10} Posts 
No, this is a much harder problem. We believe that there are infinitely many of that form, and Hardy & Littlewood have a conjecture giving the precise density of such primes, but there's no proof yet. I don't think it will come soon, either. Green & Tao have made great progress, it seems, on the linear case (Dickson's conjecture) but the higherdegree case remains open AFAICT.

20120731, 04:07  #6  
May 2004
2^{2}×79 Posts 
Infinitely many?
Quote:
tks 

20120731, 06:38  #7 
Aug 2006
2^{2}×1,493 Posts 
Link?

20120801, 04:23  #8 
May 2004
2^{2}·79 Posts 
Infinitely many?

20120801, 04:31  #9 
May 2004
2^{2}·79 Posts 
Infinitely many?

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Infinitely many primes of a form?  PawnProver44  Homework Help  1  20160315 22:39 
Article: First proof that infinitely many prime numbers come in pairs  Paulie  Twin Prime Search  46  20151117 09:22 
Are there infinitely many double Mersenne primes?  aketilander  Operazione Doppi Mersennes  1  20120919 22:24 
Infinitely many primes of form n^3 + 7 ?  devarajkandadai  Math  1  20120713 06:07 
infinitely many Mersenne primes???  LoKI.GuZ  Math  14  20031126 04:27 