20210713, 08:51  #1 
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.. 
20210713, 09:20  #2 
"Tucker Kao"
Jan 2020
Head Base M168202123
2·389 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 20210713 at 09:26 
20210713, 09:29  #3 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3^{2}·761 Posts 
Your model whatever it is has issues. https://www.alpertron.com.ar/ECM.HTM: 137438953471 = 2^{37}1 = 223 × 616318177 2199023255551 = 2^{41}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, P1 factor, or adequately trial factor. Current primality testing state of the art is ~5 months for exponent ~10^{9} 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 P1 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 20210713 at 09:58 
20210713, 09:52  #4 
"Tucker Kao"
Jan 2020
Head Base M168202123
1100001010_{2} 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 20210713 at 10:31 
20210716, 13:21  #5 
Jul 2021
3_{10} Posts 
you are certainly right, thanks

20210716, 13:23  #6 
Jul 2021
11_{2} Posts 

20210718, 17:07  #7  
"Daniel Jackson"
May 2011
14285714285714285714
727 Posts 
Quote:
Code:
Mod(2,3945487217704212192966311)^28326058902171529 %2 = Mod(1, 3945487217704212192966311) Last fiddled with by Stargate38 on 20210718 at 17:08 Reason: forgot code tags 

20210719, 03:54  #8 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×5,059 Posts 

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