20090106, 21:33  #1 
Jan 2009
Ireland
2×3×31 Posts 
MM127
Since there seems to be a large chance that this number is prime compared to other numbers,has anyone tried trial factoring it to a high bit depth?im new enough to this,so is there any way that you can stop in the middle of factoring and pick up where you started later on?

20090106, 22:34  #2  
Banned
"Luigi"
Aug 2002
Team Italia
3×5×17×19 Posts 
Quote:
Check Will Edgington page: http://www.garlic.com/~wedgingt/MMPstats.txt MathWorld page http://mathworld.wolfram.com/DoubleMersenneNumber.html and if you still want to check them, you have the choice of Ernst Mayer's mfactor (if there is a version that can handle large exponents) ready to restart from any k in factors like 2kp+1, and my Factor5 multithread aware. Luigi 

20090106, 23:41  #3 
∂^{2}ω=0
Sep 2002
República de California
2^{4}·733 Posts 
FYI, I have tested MM127 up to 175 bits (k = 2^47 = 140737488355328, a few bits higher than the limits listed for Tony Forbes` search on the MMPstats.txt page) with no factors found. Once I finish work on my current updates to Mlucas I plan to revisit the doubleMersenne factoring code, perhaps release a multithreaded binary (the current version allows the factoring to be split into up to 16 independent passes, but that requires 16 executable images running separately) and see if we can't organize a search at least up to 180odd bits.
And the fact that MM127 has no known factors only makes it roughly twice as likely to be prime as a randomly chosen Mersenne number in that size range, which  if we extrapolate the known plausible heuristics regarding the statistical distribution of Mprime exponents  still makes it exceedingly unlikely to be prime. But it sure would be nice to settle the question once and for all, just to shut up the cranks. [Who would then surely proceed to some other equallyunfounded speculation  but one would hope that at least the cranks would lose enough "credibility" thereby that they would have trouble wasting other folks' times in their future crankish endeavors.] 
20090106, 23:50  #4  
"Mark"
Apr 2003
Between here and the
6603_{10} Posts 
Quote:


20090107, 00:21  #5  
Aug 2006
3·1,993 Posts 
Quote:


20090107, 00:34  #6  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
4277_{10} Posts 
Quote:
Quote:


20090107, 07:00  #7 
Aug 2006
1011101011011_{2} Posts 
Great, I combined that source with Chris Caldwell's simplified Wagstaff proof to come up with a reasonable heuristic. There is a funny bit about constants (wanting to be e^gamma at one end at 2 at the other), but I'll probably just interpolate smoothly.
This gives the odds that MM127 is prime as 1.8 x 10^36, given that M127 is prime and it has no factors up to 175 bits. 
20090108, 18:02  #8 
Jan 2009
Ireland
BA_{16} Posts 
MM127
luigi, i have tried your factoring programs before and they are very good,but there seems to be a problem with the cygwin files so it wont open,could you help me with this problem?
with prime95 are you supposed to create your own work to do file?because my download doesnt have one,it also doesnt have a help file. MM127 is MMMMM2,isnt it?i know essentialy this doesnt make it more likely to be prime but it would be important if it was proved that it doesnt have a factor,wouldnt it? what other trial factoring programs are there that can be stopprd and restarted where it left off? i dont know a lot about this subject but im looking to learn,does anyone have links to web sites with dumbed down explanations of,lets say, the lucas lehmer test? thanks for all your help. Don 
20090108, 18:31  #9  
∂^{2}ω=0
Sep 2002
República de California
10110111010000_{2} Posts 
Quote:
Be happy to do some comparative timings, though, to see where each of us in the speed ballpark. 

20090108, 19:35  #10 
Nov 2008
4422_{8} Posts 

20090108, 20:26  #11 
"Ben"
Feb 2007
3,617 Posts 
Proving that it doesn't have a factor by trial division up to some bound is essentially meaningless, as CR Greathouse showed (you could raise the trial factoring bit level several levels and it would still have only an infinitesimal chance of being prime). The hope is to prove that it *does* have a factor. Then the MM127 zealots can go pick a different number to rally around.

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