20200705, 16:22  #1 
Oct 2019
51_{16} 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!
May 2003
Down not across
17×593 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
10101010011_{2} 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
FDE_{16} 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
67 Posts 
Quote:


20200706, 19:41  #6 
Bamboozled!
May 2003
Down not across
10081_{10} Posts 

20200706, 20:27  #7 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
3·3,019 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
7·17 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
3^{4} 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
3^{4} Posts 
Quote:


20200707, 18:24  #11 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
3×3,019 Posts 
Offtopic messages were moved to their own thread (in the blogorrhea area)

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
MM127  Stan  Miscellaneous Math  34  20150619 03:24 
Is MM127 a PRP?  aketilander  Operazione Doppi Mersennes  6  20121031 16:02 
MM127  antimath  Lone Mersenne Hunters  12  20120111 03:46 
MM127  Dougal  LMH > 100M  26  20091213 09:57 
MM127 Checkout Page  clowns789  Lone Mersenne Hunters  44  20040930 08:06 