Search for prime Gaussian-Mersenne norms (and G-M-cofactors) - Page 9

Thomas11 · 2014-03-02, 20:53

(2^792061-2^396031+1)/5 is 3-PRP! (238434 digits)

Cruelty · 2014-03-05, 09:17

Congratulations!

Citrix · 2014-03-09, 02:59

3.85M to 5M factored to 55 bits. Some numbers were done to 60 bits to make tests for efficiency.

(As mentioned above, I have unreserved this range). I hope this sieve file will be helpful to someone.

Batalov · 2014-03-13, 20:58

Quote:

Originally Posted by Batalov

I'll run the start of the slow range 3.85M-4.00M.

3.85M-4.00M is done, no primes.

Will continue to 4.3M now. (Sieved to 59 bits.)

Cruelty · 2014-03-14, 09:38

Code:

till 600k - completed by Jean Penné (GQ-only effort)
600k - 700k - completed by Cruelty (GQ-only effort)
700k - GM36 - reserved by Thomas11 (GQ-only effort, 1 GQ found so far)
GM36 - 1.95M - completed by Cruelty (2 GMs + 5 GQs found)
1.95M - 2M - reserved by Cruelty (currently @ 1.98M)
2M - 3.5M - completed by Batalov (1 GQ found)
3.5M - 3.85M - reserved by Citrix (prefactored to 55 bits)
3.85M - 4.3M - completed by Batalov
4.3M - 4.7M - reserved by Batalov

3.85M - 5M - pre-factored till 55 bits by Citrix
GM37-40M - pre-factored till 48 bits by Cruelty

pinhodecarlos · 2014-03-14, 12:22

Stupid question. Can the factoring be done with a 64-bit linux machine? If so how to do it? I can put a core into the effort and forget about it.

Cruelty · 2014-03-14, 20:20

Quote:

Originally Posted by pinhodecarlos

Stupid question. Can the factoring be done with a 64-bit linux machine? If so how to do it? I can put a core into the effort and forget about it.

Yes it can, simply use 32-bit executable

Batalov · 2014-03-17, 20:02

Quote:

Originally Posted by Batalov

Will continue to 4.3M now. (Sieved to 59 bits.)

4.0M-4.3M is done, no primes.

Will carry on to 4.7M.

Thomas11 · 2014-03-21, 10:17

I finished the range 700k-GM36 (GQ-only). 1 GQ found for n=792061 (already reported).

Cruelty · 2014-03-26, 09:11

Code:

till 600k - completed by Jean Penné (GQ-only effort)
600k - 700k - completed by Cruelty (GQ-only effort)
700k - GM36 - completed by Thomas11 (GQ-only effort, 1 GQ found)
GM36 - 1.95M - completed by Cruelty (2 GMs + 5 GQs found)
1.95M - 2M - reserved by Cruelty (currently @ 1.98M)
2M - 3.5M - completed by Batalov (1 GQ found)
3.5M - 3.85M - reserved by Citrix (prefactored to 55 bits)
3.85M - 4.3M - completed by Batalov
4.3M - 4.7M - reserved by Batalov

3.85M - 5M - pre-factored till 55 bits by Citrix
GM37-40M - pre-factored till 48 bits by Cruelty

Batalov · 2014-03-31, 02:30

Code:

(2^4533073+2^2266537+1)/5 is 11-PRP!  Time: 32517.456 sec.

Fancy that, an 11-PRP... where did this come from? ;-)

Well, apparently, from choosing the a for the N-1 test for the GM part (even though, per Berrizbeitia-Iskra 2010, a=5 is always the right choice for this class, but theirs is a different test); here, 3|GM-1, 5|GM-1, and 7|GM-1, so a=11 is chosen. The passenger PRP GQ test gets the same base "a".

But still, no GM.
_____________________

P.S. I did find an EM (and a few EQs), though. In some ways, the EM makes me much more proud: my own sieve, my own code (plus, of course, George's gwnum lib), -- and it is a Generalized Unique prime (GMs are not). It has to do with the nature of Eisenstein integers - they are based on ω, which is the cube root of unity, so the cyclotomic φ₃(x) arises naturally. Generalized Unique primes need some φ_n(x). All EMs are Generalized Unique primes.

2014-03-31, 02:30	#99
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2²×23×103 Posts	Another GQ Code: (2^4533073+2^2266537+1)/5 is 11-PRP! Time: 32517.456 sec. Fancy that, an 11-PRP... where did this come from? ;-) Well, apparently, from choosing the a for the N-1 test for the GM part (even though, per Berrizbeitia-Iskra 2010, a=5 is always the right choice for this class, but theirs is a different test); here, 3\|GM-1, 5\|GM-1, and 7\|GM-1, so a=11 is chosen. The passenger PRP GQ test gets the same base "a". But still, no GM. _____________________ P.S. I did find an EM (and a few EQs), though. In some ways, the EM makes me much more proud: my own sieve, my own code (plus, of course, George's gwnum lib), -- and it is a Generalized Unique prime (GMs are not). It has to do with the nature of Eisenstein integers - they are based on ω, which is the cube root of unity, so the cyclotomic φ₃(x) arises naturally. Generalized Unique primes need some φ_n(x). All EMs are Generalized Unique primes. Last fiddled with by Batalov on 2014-03-31 at 08:52 Reason: I didn't remember the B-I test properly, corrected

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2014-03-02, 20:53	#89
Thomas11 Feb 2003 2²×3²×53 Posts	(2^792061-2^396031+1)/5 is 3-PRP! (238434 digits)

2014-03-05, 09:17	#90
Cruelty May 2005 2³·7·29 Posts	Congratulations!

2014-03-14, 12:22	#94
pinhodecarlos "Carlos Pinho" Oct 2011 Milton Keynes, UK 3·17·97 Posts	Stupid question. Can the factoring be done with a 64-bit linux machine? If so how to do it? I can put a core into the effort and forget about it.

2014-03-21, 10:17	#97
Thomas11 Feb 2003 11101110100₂ Posts	I finished the range 700k-GM36 (GQ-only). 1 GQ found for n=792061 (already reported).