mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2012-07-27, 03:27   #1
devarajkandadai
 
devarajkandadai's Avatar
 
May 2004

4748 Posts
Default Infinitely many?

Are there infinitely many primes of the form x^2 + y^2 + 1 ?
devarajkandadai is offline   Reply With Quote
Old 2012-07-27, 03:56   #2
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

3·52·79 Posts
Default

Yes. Bredihin (Б. М. Бредихин) first proved this in 1963. See A079545.

Last fiddled with by CRGreathouse on 2012-07-27 at 04:09
CRGreathouse is offline   Reply With Quote
Old 2012-07-30, 04:29   #3
devarajkandadai
 
devarajkandadai's Avatar
 
May 2004

13C16 Posts
Default Infinitely many?

Quote:
Originally Posted by CRGreathouse View Post
Yes. Bredihin (Б. М. Бредихин) first proved this in 1963. See A079545.
Does this imply the infinitude of x^2 + 1?
devarajkandadai is offline   Reply With Quote
Old 2012-07-30, 05:10   #4
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
Jun 2011
Thailand

22×11×199 Posts
Default

Quote:
Originally Posted by devarajkandadai View Post
Does this imply the infinitude of x^2 + 1?
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 2012-07-30 at 05:11
LaurV is online now   Reply With Quote
Old 2012-07-30, 05:17   #5
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

592510 Posts
Default

Quote:
Originally Posted by devarajkandadai View Post
Does this imply the infinitude of x^2 + 1?
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 higher-degree case remains open AFAICT.
CRGreathouse is offline   Reply With Quote
Old 2012-07-31, 04:07   #6
devarajkandadai
 
devarajkandadai's Avatar
 
May 2004

4748 Posts
Default Infinitely many?

Quote:
Originally Posted by CRGreathouse View Post
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 higher-degree case remains open AFAICT.
Would you care to have a look at my hueristic under the caption " draft proof" in PlanetMath?
tks
devarajkandadai is offline   Reply With Quote
Old 2012-07-31, 06:38   #7
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

10111001001012 Posts
Default

Link?
CRGreathouse is offline   Reply With Quote
Old 2012-08-01, 04:23   #8
devarajkandadai
 
devarajkandadai's Avatar
 
May 2004

4748 Posts
Default Infinitely many?

Quote:
Originally Posted by CRGreathouse View Post
Link?
Will try & provide.
tks
devarajkandadai is offline   Reply With Quote
Old 2012-08-01, 04:31   #9
devarajkandadai
 
devarajkandadai's Avatar
 
May 2004

22·79 Posts
Default Infinitely many?

Quote:
Originally Posted by devarajkandadai View Post
Will try & provide.
tks
PlanetMath.org - Forums- Research/postgraduate/Draft proof

Trust above is sufficient.
devarajkandadai is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Infinitely many primes of a form? PawnProver44 Homework Help 1 2016-03-15 22:39
Article: First proof that infinitely many prime numbers come in pairs Paulie Twin Prime Search 46 2015-11-17 09:22
Are there infinitely many double Mersenne primes? aketilander Operazione Doppi Mersennes 1 2012-09-19 22:24
Infinitely many primes of form n^3 + 7 ? devarajkandadai Math 1 2012-07-13 06:07
infinitely many Mersenne primes??? LoKI.GuZ Math 14 2003-11-26 04:27

All times are UTC. The time now is 02:54.

Wed Sep 30 02:54:39 UTC 2020 up 20 days, 5 mins, 0 users, load averages: 1.78, 1.53, 1.54

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.