MM127+2 has a non-trivial factor

[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).

[xilman]

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

[R. Gerbicz]

Yes, that is a divisor:

? d=886407410000361345663448535540258622490179142922169401;
? Mod(2,d)^(2^127-1)+1
%2 = Mod(0, 886407410000361345663448535540258622490179142922169401)
? ##
  ***   last result computed in 0 ms.
?

[kriesel]

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

[mathwiz]

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).

Cool! How was this factor found?

[xilman]

Originally Posted by mathwiz

Cool! How was this factor found?

My guess is trial division.

[Batalov]

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

[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

[Fan Ming]

Originally Posted by mathwiz

Cool! How was this factor found?

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:

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.

[Fan Ming]

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.

[Batalov]

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