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Old 2020-07-05, 16:22   #1
Fan Ming
 
Oct 2019

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Default 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).
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Old 2020-07-05, 16:51   #2
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Quote:
Originally Posted by Fan Ming View Post
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
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Old 2020-07-05, 17:56   #3
R. Gerbicz
 
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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
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Old 2020-07-06, 15:23   #4
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Quote:
Originally Posted by xilman View Post
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
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Old 2020-07-06, 18:53   #5
mathwiz
 
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Quote:
Originally Posted by Fan Ming View Post
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).
Cool! How was this factor found?
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Old 2020-07-06, 19:41   #6
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Quote:
Originally Posted by mathwiz View Post
Cool! How was this factor found?
My guess is trial division.
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Old 2020-07-06, 20:27   #7
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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
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Old 2020-07-06, 20:31   #8
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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
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Old 2020-07-07, 03:49   #9
Fan Ming
 
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Quote:
Originally Posted by mathwiz View Post
Cool! How was this factor found?
Quote:
Originally Posted by xilman View Post
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
File Type: zip wmff.zip (174.6 KB, 9 views)

Last fiddled with by Fan Ming on 2020-07-07 at 03:52
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Old 2020-07-07, 03:51   #10
Fan Ming
 
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Quote:
Originally Posted by JeppeSN View Post
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.
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Old 2020-07-07, 18:24   #11
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Off-topic messages were moved to their own thread (in the blogorrhea area)
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