52. and 53. mersennes :)

[aasteroyis]

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..

[tuckerkao]

The exponent of a Mersenne Prime must be prime too.

137438953471 = 223 * 616318177
2199023255551 = 13367 * 164511353

M164511353 already has 1 completed LL test which indicated it was a composite number.
M616318177 is quiet a large prime exponent for someone to run a PRP test even with AMD Threadripper 5970X and Nvidia Geforce 3080 Ti.

[kriesel]

Your model whatever it is has issues.

https://www.alpertron.com.ar/ECM.HTM:
137438953471 = 2³⁷-1 = 223 × 616318177
2199023255551 = 2⁴¹-1 = 13367 × 164511353
Therefore both claimed primes are easily shown to actually have factors, in seconds. See
https://www.mersenneforum.org/showpo...13&postcount=4
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 ~10⁹ on a Radeon VII GPU with Gpuowl. Runtime scaling extrapolates at p^2.1 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 https://primes.utm.edu/notes/crackpot.html

[tuckerkao]

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.

[aasteroyis]

you are certainly right, thanks

[aasteroyis]

Originally Posted by tuckerkao

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.

82589933 × 168433723

[Stargate38]

Originally Posted by tuckerkao

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

It is. Pari/gp:

Mod(2,3945487217704212192966311)^28326058902171529
%2 = Mod(1, 3945487217704212192966311)

[LaurV]

Originally Posted by Stargate38

It is. Pari/gp:

gp> Mod(2,3945487217704212192966311)^28326058902171529
 %2 = Mod(1, 3945487217704212192966311)
gp> ##
  ***   last result computed in 0 ms.
gp >

You missed the most important part. Fixed that for you