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 2021-07-13, 08:51 #1 aasteroyis   Jul 2021 3 Posts 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..
 2021-07-13, 09:20 #2 tuckerkao   "Tucker Kao" Jan 2020 Head Base M168202123 22×3×47 Posts 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. Last fiddled with by tuckerkao on 2021-07-13 at 09:26
 2021-07-13, 09:29 #3 kriesel     "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 592410 Posts 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 p2.1 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 Last fiddled with by kriesel on 2021-07-13 at 09:58
 2021-07-13, 09:52 #4 tuckerkao   "Tucker Kao" Jan 2020 Head Base M168202123 22·3·47 Posts 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. Last fiddled with by tuckerkao on 2021-07-13 at 10:31
 2021-07-16, 13:21 #5 aasteroyis   Jul 2021 3 Posts you are certainly right, thanks
2021-07-16, 13:23   #6
aasteroyis

Jul 2021

112 Posts

Quote:
 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

2021-07-18, 17:07   #7
Stargate38

"Daniel Jackson"
May 2011
14285714285714285714

677 Posts

Quote:
 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:

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

Last fiddled with by Stargate38 on 2021-07-18 at 17:08 Reason: forgot code tags

2021-07-19, 03:54   #8
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

100110010100002 Posts

Quote:
 Originally Posted by Stargate38 It is. Pari/gp: Code: 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

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