New Mersenne Prime

[James Wanless]

Congratulations to the Great Internet Mersenne Prime Search, who today released their latest Mersenne Prime discovery, M136279841

localhost:~/math/M+2$ time ./mpptf16 -P136279841 -S1 -T100000000

99900000

real     17m 41.63s

user    17m 40.97s

sys     0m 0.00s

[James Wanless]

With thanks to Batalov [on mersenneforum]

[Tue Oct 15 23:56:56 2024]

P-1 found a factor in stage #2, B1=10000000, B2=5000714880.

(2^136279841+1)/3 has a factor: 7827576937344589790262450890609 (P-1, B1=10000000, B2=5000714880)

{"status":"F", "k":1, "b":2, "n":136279841, "c":1, "worktype":"P-1", "factors":["7827576937344589790262450890609"], "b1":10000000, "b2":5000714880, "d":3990, "poly1-size":432, "poly2-size":1489, "stage2-fft-length":8601600, "fft-length":7864320, "security-code":"EF22E7BD", "program":{"name":"Prime95", "version":"30.19", "build":20, "port":8}, "timestamp":"2024-10-16 06:56:56", "known-factors":["3"]}

[Tue Oct 15 23:56:56 2024]

P-1 found a factor in stage #2, B1=10000000, B2=5000714880.

(2^136279841+1)/3 has a factor: 7827576937344589790262450890609 (P-1, B1=10000000, B2=5000714880)

{"status":"F", "k":1, "b":2, "n":136279841, "c":1, "worktype":"P-1", "factors":["7827576937344589790262450890609"], "b1":10000000, "b2":5000714880, "d":3990, "poly1-size":432, "poly2-size":1489, "stage2-fft-length":8601600, "fft-length":7864320, "security-code":"EF22E7BD", "program":{"name":"Prime95", "version":"30.19", "build":20, "port":8}, "timestamp":"2024-10-16 06:56:56", "known-factors":["3"]}

[James Wanless]

? factor(7827576937344589790262450890608)
%2 =
[         2 4]

[    324223 1]

[   7349413 1]

[ 136279841 1]

[1506535157 1]

[James Wanless]

localhost:~$ time atkin251 -q
random seed = 1729949665
error_shift = 1000
precision = 10000
7827576937344589790262450890609
Bmax = 2000
Dmax = 20
N[0] = 7827576937344589790262450890609
a = 7827576937344589790262450890608
b = 0
m = 7827576937344595039531505072704
q = 70763962199684734069
P = (3461315182, 6639964524204630972734543345751)
P1 = (0, 1)
P2 = (6673501791997247171198614852600, 5645130563016943576817995337059)
Bmax = 2000
Dmax = 20
N[1] = 70763962199684734069
a = 0
b = 54500773635066940251
m = 70763962214382157552
q = 1420346586397
P = (1104911237, 68652199275077988218)
P1 = (0, 1)
P2 = (44107554638943367203, 2620228389356018706)
Bmax = 2000
Dmax = 20
N[2] = 1420346586397
a = 0
b = 1420346586396
m = 1420348742928
q = 9863532937
P = (528961408, 467680073052)
P1 = (0, 1)
P2 = (971389233820, 650033685520)
Bmax = 2000
Dmax = 20
N[3] = 9863532937
a = 0
b = 4255225546
m = 9863353227
q = 5161357
P = (658975216, 5565726632)
P1 = (0, 1)
P2 = (5467568085, 4734755752)
proven prime
real    1m 43.03s
user    1m 42.95s
sys     0m 0.00s

[James Wanless]

Thanks to Batalov again:

{"status":"C", "k":1, "b":2, "n":136279841, "c":1, "worktype":"PRP-3", "res64":"C8BB13406BB989EE", "residue-type":5, "res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fft-length":7864320, "error-code":"00000000", "security-code":"7C9A877C", "program":{"name":"Prime95", "version":"30.19", "build":20, "port":8}, "timestamp":"2024-11-03 04:42:57", "errors":{"gerbicz":0}, "proof":{"version":2, "power":8, "hashsize":64, "md5":"ad79f04343d0a73b97c34662a64b9417"}, "known-factors":["3","7827576937344589790262450890609"]}