20210320, 19:52  #551 
Sep 2003
5031_{8} Posts 
The 351st fullyfactored or probablyfullyfactored 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 20210320 and the PRP test was done by user "mikr". FactorDB link Last fiddled with by GP2 on 20210320 at 19:54 
20210321, 01:01  #552  
Feb 2017
Nowhere
5·1,153 Posts 
Quote:


20210321, 02:20  #553  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{6}×101 Posts 
Quote:
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 = 64bit residue of a^(N1), a traditional Fermat PRP test used by most other programs 2 = 64bit residue of a^((N1)/2) 3 = 64bit residue of a^(N+1), only available if b=2 4 = 64bit residue of a^((N+1)/2), only available if b=2 5 = 64bit residue of a^(N*known_factors1), same as type 1 if there are no known factors 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 noknownfactor Mersenne numbers. Type 5 is standard for PRPCF. Last fiddled with by kriesel on 20210321 at 02:44 

20210321, 13:49  #554  
Romulan Interpreter
"name field"
Jun 2011
Thailand
10011011101001_{2} Posts 
Quote:
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 20210321 at 13:53 

20210322, 14:10  #555  
"Oliver"
Sep 2017
Porta Westfalica, DE
1720_{8} Posts 
Quote:


20210326, 06:28  #556 
Sep 2003
5·11·47 Posts 
The 352nd fullyfactored or probablyfullyfactored 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 20210326 and the PRP test was done by user "mikr". FactorDB link The cofactor is already certified prime. 
20210327, 14:46  #557 
Sep 2003
A19_{16} Posts 
The 353rd fullyfactored or probablyfullyfactored 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 20210327 and the PRP test was done by user "riccardo uberti". FactorDB link The cofactor is already certified prime. Last fiddled with by GP2 on 20210327 at 14:46 
20210327, 16:02  #558 
Jun 2003
12357_{8} Posts 
That's 3 in a week. Noice!

20210407, 16:33  #559 
Sep 2003
5×11×47 Posts 
The 354th fullyfactored or probablyfullyfactored 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 20210407 and the PRP test was done by user "mnd9". Ryan also found a 54digit factor last October. The only other factor has 5 digits (32359). FactorDB link The cofactor is already certified prime. 
20210418, 16:22  #560 
Sep 2003
5×11×47 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 20210418 and the PRP test was done by user "ThomRuley". FactorDB link The cofactor is already certified prime. 
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