20130828, 07:29  #1 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
2·283 Posts 
MMM127
This thread is intended for any discussion of any aspect of MMM127
The TF for MM127 is now at k=70*10^15. The probability of finding a factor is decreasing rapidly as the k:s grow bigger. The TFwork is enormous now just for the probability of 1% of finding a factor. Another way of proving that the CatalanMersenneseries does not generate an infinite number of primes would be to TF MMM127 = MM170141183460469231731687303715884105727. Well, if it is difficult to TF any of the double mersennes that presently, at this moment, are included in the project it would be so much more difficult with MMM127 of course. My question is though at which k for MM127 would it be equally probable of finding a factor of MMM127 for the smallest reasonable k to TF if the same amount of work is done? That is if we want to prove that the CatalanMersenneseries does not generate infinitely many primes at which point (k) would it be easier doing so by starting TF MMM127 instead of continuing TF MM127? Is it possible to estimate this? Another question: If both MM127 and MMM127 are composite is there any relation between the k:s of the smallest factor, that is must the k for the smallest factor of MM127 be smaller then the k for the smallest factor of MMM127? Last fiddled with by aketilander on 20130828 at 07:32 
20130828, 10:46  #2  
Romulan Interpreter
Jun 2011
Thailand
2^{2}×7×11×29 Posts 
Quote:
But these numbers are so big that are intangible... For a good comparison look to, for example, M1081, and find the k of all known factors (yes, I mean 1081=23*47). For the C251 remaining factor of it, all factors must be 2*23*47*k+1. (Remember my request to Oliver to allow nonprime exponents in mfaktc, just to ask for confirmation, and not to exit with error, this will allow a guy who knows what is doing, to try to TF cases like this). Last fiddled with by LaurV on 20130828 at 10:55 Reason: links 

20130828, 20:16  #3 
Bemusing Prompter
"Danny"
Dec 2002
California
2×19×61 Posts 
I may be wrong, but I believe a single trial division of MMM127 would require roughly the same computational complexity as an LL test of MM127.
Last fiddled with by ixfd64 on 20130828 at 20:25 
20130831, 17:20  #4  
"Åke Tilander"
Apr 2011
Sandviken, Sweden
566_{10} Posts 
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So the couclusion is that it will not be any reason doing one single TF of MMM127 until we have LLed MM127. And the breakevenpoint for that is around: Quote:
Last fiddled with by aketilander on 20130831 at 17:20 

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