52. and 53. mersennes :)
 

hello;

i recognised that i have already found 51 mersenne prime by using my model now, i would like to give you next number 2^137438953471 -1, another is 2^2199023255551 -1 and i know the other one, i will be happy if you control them, then i will share the my model. Acording to my model we can find all numbers.

regards..

The exponent of a Mersenne Prime must be prime too.

137438953471 = 223 * 616318177
2199023255551 = 13367 * 164511353

M[M]164511353[/M] already has 1 completed LL test which indicated it was a composite number.
M[M]616318177[/M] is quiet a large prime exponent for someone to run a PRP test even with AMD Threadripper 5970X and Nvidia Geforce 3080 Ti.

:davar55::reality-check::bs meter::barbie:


Your model whatever it is has issues.

[URL]https://www.alpertron.com.ar/ECM.HTM:[/URL]
137438953471 = 2[SUP]37[/SUP]-1 = 223 × 616318177
2199023255551 = 2[SUP]41[/SUP]-1 = 13367 × 164511353
Therefore both claimed primes are easily shown to actually have factors, in seconds. See
[URL]https://www.mersenneforum.org/showpost.php?p=512813&postcount=4[/URL]
Such large exponents would otherwise be impractical to primality test, P-1 factor, or adequately trial factor. Current primality testing state of the art is ~5 months for exponent ~10[SUP]9[/SUP] on a Radeon VII GPU with Gpuowl. Runtime scaling extrapolates at p[SUP]2.1[/SUP] to primality test duration ~12,000 years for 137438953471, ~4.2 MILLION years for 2199023255551 at ~1 minute per iteration. (And 16 GiB of GPU ram would be inadequate.) So P-1 runtime would be ~300 years and ~100,000 years. And also need more memory.

See also [URL]https://primes.utm.edu/notes/crackpot.html[/URL]

I'd enjoy a trivia such as: Prove 3,945,487,217,704,212,192,966,311 to be a factor of M28,326,058,902,171,529

I guess I'll know whether M13,910,929,897,510,559 is a Semiprime or not soon.

you are certainly right, thanks

[QUOTE=tuckerkao;583095]I'd enjoy a trivia such as: Prove 3,945,487,217,704,212,192,966,311 to be a factor of M28,326,058,902,171,529

I guess I'll know whether M13,910,929,897,510,559 is a Semiprime or not soon.[/QUOTE]

82589933 × 168433723

[QUOTE=tuckerkao;583095]I'd enjoy a trivia such as: Prove 3,945,487,217,704,212,192,966,311 to be a factor of M28,326,058,902,171,529[/QUOTE]

It is. Pari/gp:

[code]Mod(2,3945487217704212192966311)^28326058902171529
%2 = Mod(1, 3945487217704212192966311)[/code]

[QUOTE=Stargate38;583480]It is. Pari/gp:

[code]gp> Mod(2,3945487217704212192966311)^28326058902171529
%2 = Mod(1, 3945487217704212192966311)
gp> [COLOR=Red]##
*** last result computed in [B]0 ms[/B].[/COLOR]
gp >

[/code][/QUOTE]
You missed the most important part. Fixed that for you :razz: