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 2021-03-20, 19:52 #551 GP2     Sep 2003 5·11·47 Posts The 351st fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M8233. The most recent factor (47 digits) was found by Bruno Victal on 2021-03-20 and the PRP test was done by user "mikr". FactorDB link Last fiddled with by GP2 on 2021-03-20 at 19:54
2021-03-21, 01:01   #552
Dr Sardonicus

Feb 2017
Nowhere

19·263 Posts

Quote:
 Originally Posted by GP2 The 351st fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M8233
Pardon my ignorance, but what is the "type" of a PRP test? I can't remember the last time I saw an exponent status page in which the type of a PRP test was anything but 1. I noticed that this one had a PRP test of "type" 5 rather than 1.

2021-03-21, 02:20   #553
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

3×1,933 Posts

Quote:
 Originally Posted by Dr Sardonicus what is the "type" of a PRP test? I can't remember the last time I saw an exponent status page in which the type of a PRP test was anything but 1. I noticed that this one had a PRP test of "type" 5 rather than 1.
From the undoc.txt of prime95 zip file:
Code:
PRP supports 5 types of residues for compatibility with other PRP programs.  If
a is the PRP base and N is the number being tested, then the residue types are:
1 = 64-bit residue of a^(N-1), a traditional Fermat PRP test used by most other programs
2 = 64-bit residue of a^((N-1)/2)
3 = 64-bit residue of a^(N+1), only available if b=2
4 = 64-bit residue of a^((N+1)/2), only available if b=2
5 = 64-bit residue of a^(N*known_factors-1), same as type 1 if there are no known factors
Gpuowl has implemented type 1 mostly, type 4 in some versions. In gpuowl V5.0, simultaneous P-1 and PRP was implemented IIRC as a "type 0" using a large base related to P-1 B1, IIRC.
https://www.mersenneforum.org/showpo...32&postcount=8
https://mersenneforum.org/showpost.p...postcount=1255
https://www.mersenneforum.org/showpo...3&postcount=15

I think Mlucas does type 1.

Type 1 is standard for PRP primality test of no-known-factor Mersenne numbers. Type 5 is standard for PRP-CF.

Last fiddled with by kriesel on 2021-03-21 at 02:44

2021-03-21, 13:49   #554
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

263B16 Posts

Quote:
 Originally Posted by GP2 The 351st fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M8233. The most recent factor (47 digits) was found by Bruno Victal on 2021-03-20 and the PRP test was done by user "mikr". FactorDB link
I've seen this one as I got it immediately assigned for DC (still in queue, it will be done tomorrow or the day after).
I could move it to the front, but as I have no doubt that is PRP, let it be.
Congrats to the finder(s) !

Last fiddled with by LaurV on 2021-03-21 at 13:53

2021-03-22, 14:10   #555
kruoli

"Oliver"
Sep 2017
Porta Westfalica, DE

10100110102 Posts

Quote:
 Originally Posted by GP2 The 351st fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M8233.
The cofactor is now certified prime: http://factordb.com/index.php?id=1100000002528023613.

 2021-03-26, 06:28 #556 GP2     Sep 2003 5·11·47 Posts The 352nd fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M7669. The most recent factor (47 digits) was found by Ryan Propper on 2021-03-26 and the PRP test was done by user "mikr". FactorDB link The cofactor is already certified prime.
 2021-03-27, 14:46 #557 GP2     Sep 2003 5×11×47 Posts The 353rd fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M7013. The most recent factor (49 digits) was found by Ryan Propper on 2021-03-27 and the PRP test was done by user "riccardo uberti". FactorDB link The cofactor is already certified prime. Last fiddled with by GP2 on 2021-03-27 at 14:46
 2021-03-27, 16:02 #558 axn     Jun 2003 3·17·101 Posts That's 3 in a week. Noice!
 2021-04-07, 16:33 #559 GP2     Sep 2003 5·11·47 Posts The 354th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M5393. The most recent factor (58 digits) was found by Ryan Propper on 2021-04-07 and the PRP test was done by user "mnd9". Ryan also found a 54-digit factor last October. The only other factor has 5 digits (32359). FactorDB link The cofactor is already certified prime.
 2021-04-18, 16:22 #560 GP2     Sep 2003 50318 Posts There are now 355 known Mersenne numbers with prime exponent that are composite and either fully factored or probably fully factored. The most recent is M4507. Its final factor (53 digits) was found by Ryan Propper on 2021-04-18 and the PRP test was done by user "ThomRuley". FactorDB link The cofactor is already certified prime.
 2021-04-28, 23:27 #561 ATH Einyen     Dec 2003 Denmark 2·7·227 Posts Ryan Propper found another factor and another PRP #356: M3917 Last fiddled with by ATH on 2021-04-28 at 23:29

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