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 2020-07-05, 16:22 #1 Fan Ming   Oct 2019 9510 Posts MM127+2 has a non-trivial factor MM127+2 (aka 2^(2^127-1)+1) has a non-trivial 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 Catalan-Mersenne sequence(if MM127 is not prime).
2020-07-05, 16:51   #2
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

101000000000102 Posts

Quote:
 Originally Posted by Fan Ming MM127+2 (aka 2^(2^127-1)+1) has a non-trivial 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 Catalan-Mersenne sequence(if MM127 is not prime).
Interesting!

Ernst, I believe you have software attempting to factor this number. Can you confirm

 2020-07-05, 17:56 #3 R. Gerbicz     "Robert Gerbicz" Oct 2005 Hungary 7·199 Posts Yes, that is a divisor: Code: ? d=886407410000361345663448535540258622490179142922169401; ? Mod(2,d)^(2^127-1)+1 %2 = Mod(0, 886407410000361345663448535540258622490179142922169401) ? ## *** last result computed in 0 ms. ? Last fiddled with by R. Gerbicz on 2020-07-05 at 17:56
2020-07-06, 15:23   #4
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

3·13·113 Posts

Quote:
 Originally Posted by xilman Interesting! Ernst, I believe you have software attempting to factor this number. Can you confirm
If you're asking about MM127, it's faster to use a good gpu program than Ernst's mfactor program for that. I'm slogging away on getting MM127 up to 185 bits TF using George Woltman's mmff program on a gtx1650 gpu. There's about 9 weeks to go. Going from there to 186 bits I estimate would be 2.4 years. That's more than I'm willing to spend for a 0.54% chance of a factor found.

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 2020-07-06 at 15:26

2020-07-06, 18:53   #5
mathwiz

Mar 2019

3×29 Posts

Quote:
 Originally Posted by Fan Ming MM127+2 (aka 2^(2^127-1)+1) has a non-trivial 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 Catalan-Mersenne sequence(if MM127 is not prime).

2020-07-06, 19:41   #6
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

2·32·569 Posts

Quote:
 Originally Posted by mathwiz Cool! How was this factor found?
My guess is trial division.

 2020-07-06, 20:27 #7 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22×2,281 Posts All potential factors (of interest) are of form 2*k*M127+1 and prime, -- so the same program that checks for MM127 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 * M127+1
 2020-07-06, 20:31 #8 JeppeSN     "Jeppe" Jan 2016 Denmark 2328 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
2020-07-07, 03:49   #9
Fan Ming

Oct 2019

5×19 Posts

Quote:
 Originally Posted by mathwiz Cool! How was this factor found?
Quote:
 Originally Posted by xilman My guess is trial division.
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
Note: The code was modified by myself. It looks OK(from my view) and works well, but without single-step track & observation. It's not guarateed that there were no deep bugs in the modified code.
Attached Files
 wmff.zip (174.6 KB, 9 views)

Last fiddled with by Fan Ming on 2020-07-07 at 03:52

2020-07-07, 03:51   #10
Fan Ming

Oct 2019

5·19 Posts

Quote:
 Originally Posted by JeppeSN 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
I agree with that. Most likely MM127 is not prime, thus primes in Catalan-Mersenne sequence end at M127.

 2020-07-07, 18:24 #11 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22·2,281 Posts Off-topic messages were moved to their own thread (in the blogorrhea area)

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