The 351st fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M8233[/M].
The most recent factor (47 digits) was found by Bruno Victal on 20210320 and the PRP test was done by user "mikr". [URL="http://factordb.com/index.php?id=1100000002528023613"]FactorDB link[/URL] 
[QUOTE=GP2;574238]The 351st fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M8233[/M][/QUOTE]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.

[QUOTE=Dr Sardonicus;574249]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.[/QUOTE]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 = 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 [/CODE]Gpuowl has implemented type 1 mostly, type 4 in some versions. In gpuowl V5.0, simultaneous P1 and PRP was implemented IIRC as a "type 0" using a large base related to P1 B1, IIRC. [URL]https://www.mersenneforum.org/showpost.php?p=510732&postcount=8[/URL] [URL]https://mersenneforum.org/showpost.php?p=519902&postcount=1255[/URL] [URL]https://www.mersenneforum.org/showpost.php?p=519603&postcount=15[/URL] I think Mlucas does type 1. Type 1 is standard for PRP primality test of noknownfactor Mersenne numbers. Type 5 is standard for PRPCF. 
[QUOTE=GP2;574238]The 351st fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M8233[/M].
The most recent factor (47 digits) was found by Bruno Victal on 20210320 and the PRP test was done by user "mikr". [URL="http://factordb.com/index.php?id=1100000002528023613"]FactorDB link[/URL][/QUOTE] I've seen this one as I got it immediately assigned for DC :lol: (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) ! 
[QUOTE=GP2;574238]The 351st fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M8233[/M].[/QUOTE]
The cofactor is now certified prime: [URL="http://factordb.com/index.php?id=1100000002528023613"]http://factordb.com/index.php?id=1100000002528023613[/URL]. 
The 352nd fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M7669[/M].
The most recent factor (47 digits) was found by Ryan Propper on 20210326 and the PRP test was done by user "mikr". [URL="http://factordb.com/index.php?id=1100000002531548425"]FactorDB link[/URL] The cofactor is already certified prime. 
The 353rd fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M7013[/M].
The most recent factor (49 digits) was found by Ryan Propper on 20210327 and the PRP test was done by user "riccardo uberti". [URL="http://factordb.com/index.php?id=1100000002534390416"]FactorDB link[/URL] The cofactor is already certified prime. 
That's 3 in a week. Noice!

The 354th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M5393[/M].
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). [URL="http://factordb.com/index.php?id=1100000002545348837"]FactorDB link[/URL] The cofactor is already certified prime. 
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 [M]M4507[/M]. Its final factor (53 digits) was found by Ryan Propper on 20210418 and the PRP test was done by user "ThomRuley". [URL="http://factordb.com/index.php?id=1100000002558891770"]FactorDB link[/URL] The cofactor is already certified prime. 
Ryan Propper found another factor and another PRP #356: M[M]3917[/M]

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