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 GP2 2021-03-20 19:52

The 351st fully-factored or probably-fully-factored 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 2021-03-20 and the PRP test was done by user "mikr".

 Dr Sardonicus 2021-03-21 01:01

[QUOTE=GP2;574238]The 351st fully-factored or probably-fully-factored 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.

 kriesel 2021-03-21 02:20

[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 = 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
[/CODE]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.
[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 no-known-factor Mersenne numbers. Type 5 is standard for PRP-CF.

 LaurV 2021-03-21 13:49

[QUOTE=GP2;574238]The 351st fully-factored or probably-fully-factored 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 2021-03-20 and the PRP test was done by user "mikr".

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) !

 kruoli 2021-03-22 14:10

[QUOTE=GP2;574238]The 351st fully-factored or probably-fully-factored 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].

 GP2 2021-03-26 06:28

The 352nd fully-factored or probably-fully-factored 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 2021-03-26 and the PRP test was done by user "mikr".

The cofactor is already certified prime.

 GP2 2021-03-27 14:46

The 353rd fully-factored or probably-fully-factored 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 2021-03-27 and the PRP test was done by user "riccardo uberti".

The cofactor is already certified prime.

 axn 2021-03-27 16:02

That's 3 in a week. Noice!

 GP2 2021-04-07 16:33

The 354th fully-factored or probably-fully-factored 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 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).

The cofactor is already certified prime.

 GP2 2021-04-18 16:22

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 2021-04-18 and the PRP test was done by user "ThomRuley".