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
"name field"
Jun 2011
Thailand
2×11×449 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
3·1,993 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
3·1,993 Posts 
Link?

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

20120801, 04:31  #9 
May 2004
316_{10} Posts 
Infinitely many?

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