Is MM127 Prime? Just a Poll

jinydu · 2004-05-27, 02:42

Uncwilly · 2006-03-21, 23:28

Someone please find a factor for this number.

philmoore · 2006-03-22, 00:41

Quote:

Originally Posted by Uncwilly

Someone please find a factor for this number.

Ernst, please? Isn't there someone who can help us?

jasong · 2006-03-22, 01:12

I'd be happy to run a few curves on this number. Maybe someone would be willing to email me the decimal expansion? Then I could work on my Prime95 skills a little bit.

Citrix · 2006-03-22, 01:23

Quote:

Originally Posted by jasong

I'd be happy to run a few curves on this number. Maybe someone would be willing to email me the decimal expansion? Then I could work on my Prime95 skills a little bit.

Good luck

ewmayer · 2006-03-22, 01:32

Quote:

Originally Posted by philmoore

Ernst, please? Isn't there someone who can help us?

Patience - getting Mlucas v3.0 released is by necessity higher on my list of priorities, but OTOH most of the code needed to trial-factor numbers like this is already in place - I just need to do some tuning of the PowerPC client and figure out the best way to organize the search, i.e. hand out ranges and verify work done. Here - by way of a self-kick-in-the-pants, I'll go on record and promise to have this rolling by my birthday (May 15th) - roughly 8 weeks from now.

Just to keep people's expectations reasonable, I estimate the odds of this number having a factor that a decent-sized distributed search (say on the order of a couple hundred CPUs) could find in the next couple of years at roughly 10%. But what a coup it would be to find one...

clowns789 · 2006-03-22, 01:41

Quote:

Originally Posted by jasong

I'd be happy to run a few curves on this number. Maybe someone would be willing to email me the decimal expansion? Then I could work on my Prime95 skills a little bit.

170141183460469231731687303715884105727

Uncwilly · 2006-03-22, 01:52

Quote:

Originally Posted by clowns789

170141183460469231731687303715884105727

That's 2^^{170141183460469231731687303715884105727}-1

R.D. Silverman · 2006-03-22, 12:11

Such a poll is ridiculous. We have no basis, other than the
prime number theorem on which to make an assessment.

For M < x < (1 + epsilon)M, x chosen uniformly at random, the
probability that x is prime is 1/log M.

For MM127, the "probability" that it is prime (assuming that it just
another random integer selected from other integers near the same size)
is 1/( M127 * log(2)). This is small indeed.

Unless we are VERY lucky and find a small factor, the true answer is
computationally out of reach.

I don't regard the question as interesting. We already know that that
MMp isn't always prime.

Uncwilly · 2006-03-22, 14:32

Quote:

Originally Posted by R.D. Silverman

Such a poll is ridiculous. We have no basis, other than the prime number theorem on which to make an assessment.
.......
I don't regard the question as interesting. We already know that that MMp isn't always prime.

The whole idea is not to devine truth from this. Rather to take the temperature of the group. Notice the title of the thread, 'Just a Poll'.

xilman · 2006-03-22, 18:21

Quote:

Originally Posted by R.D. Silverman

Such a poll is ridiculous. We have no basis, other than the
prime number theorem on which to make an assessment.

Of course it's ridiculous. It's supposed to be ridiculous, as I read it anyway.

Seems to be no more ridiculous than the interminable discussion about some cultural activity called "march madness". At least I can follow what's going on here.

To be fair, the other thread isn't in the Math subforum.

Paul

View Poll Results: Is MM127 Prime?
Yes	16	19.75%
No	43	53.09%
Really Don't Know	22	27.16%
Voters: 81. You may not vote on this poll

2004-05-27, 02:42	#1
jinydu Dec 2003 Hopefully Near M48 2·3·293 Posts	Is MM127 Prime? Just a Poll

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2006-03-21, 23:28	#2
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 23D9₁₆ Posts	Someone please find a factor for this number.

2006-03-22, 01:12	#4
jasong "Jason Goatcher" Mar 2005 5×701 Posts	I'd be happy to run a few curves on this number. Maybe someone would be willing to email me the decimal expansion? Then I could work on my Prime95 skills a little bit.

2006-03-22, 12:11	#9
R.D. Silverman Nov 2003 2²×5×373 Posts	Such a poll is ridiculous. We have no basis, other than the prime number theorem on which to make an assessment. For M < x < (1 + epsilon)M, x chosen uniformly at random, the probability that x is prime is 1/log M. For MM127, the "probability" that it is prime (assuming that it just another random integer selected from other integers near the same size) is 1/( M127 * log(2)). This is small indeed. Unless we are VERY lucky and find a small factor, the true answer is computationally out of reach. I don't regard the question as interesting. We already know that that MMp isn't always prime.