20200705, 16:22  #1 
Oct 2019
5×19 Posts 
MM127+2 has a nontrivial factor
MM127+2 (aka 2^(2^1271)+1) has a nontrivial factor: 886407410000361345663448535540258622490179142922169401.
It seems either New Mersenne (Wagstaff) conjecture will be false(if MM127 is prime) or M127 will be the last prime in the CatalanMersenne sequence(if MM127 is not prime). 
20200705, 16:51  #2  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{2}×3^{2}×281 Posts 
Quote:
Ernst, I believe you have software attempting to factor this number. Can you confirm 

20200705, 17:56  #3 
"Robert Gerbicz"
Oct 2005
Hungary
2·3·5·47 Posts 
Yes, that is a divisor:
Code:
? d=886407410000361345663448535540258622490179142922169401; ? Mod(2,d)^(2^1271)+1 %2 = Mod(0, 886407410000361345663448535540258622490179142922169401) ? ## *** last result computed in 0 ms. ? Last fiddled with by R. Gerbicz on 20200705 at 17:56 
20200706, 15:23  #4  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2×3^{3}×5×17 Posts 
Quote:
MM127, a 127 bit exponent, p=170141183460469231731687303715884105727, no factor in TF to ~184.818 bits by various contributors. See http://www.doublemersennes.org/mm127.php, and results and reservations threads in https://mersenneforum.org/forumdisplay.php?f=99 Last fiddled with by kriesel on 20200706 at 15:26 

20200706, 18:53  #5  
Mar 2019
2^{2}·5^{2} Posts 
Quote:


20200706, 19:41  #6 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{2}×3^{2}×281 Posts 

20200706, 20:27  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9124_{10} Posts 
All potential factors (of interest) are of form 2*k*M_{127}+1 and prime,  so the same program that checks for MM_{127} divisors with minor changes could have been used. (Perhaps on GPU).
Only a fraction of 10^15 k values to test (after prime sieve). f = 2604917257456100 * 2 * M_{127}+1 
20200706, 20:31  #8 
"Jeppe"
Jan 2016
Denmark
2^{5}×5 Posts 
Nice factor!
The New Mersenne conjecture is rather silly, but it holds for small numbers, and it is maybe unlikely that large numbers will satisfy just two of the three criteria. It would be fun if MM127 were a counterexample, of course, but nobody thinks so. /JeppeSN 
20200707, 03:49  #9 
Oct 2019
5×19 Posts 
Yes, it's found by trial division. I modified the original mmff (with minor change) to factor this kind of "Mersenne plus two"("Wagstaff Mersenne") number. (WM31, WM61, WM89, WM107, WM127)
Here is the source file. The usage is just like that of mmff, but change the format of "MMFactor" in worktodo.txt to "WMFactor". Example: Code:
WMFactor=89,1e15,1.5e15 Last fiddled with by Fan Ming on 20200707 at 03:52 
20200707, 03:51  #10  
Oct 2019
5×19 Posts 
Quote:


20200707, 18:24  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,281 Posts 
Offtopic messages were moved to their own thread (in the blogorrhea area)

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