20130207, 22:07  #1 
Feb 2013
1_{8} Posts 
Factoring details
I am wondering what the following means:
"Trial factoring M82611773 to 2^68 is 82.77% complete. Time:374.213 sec." M82611773 must be 2^826117731, the number being tested for primality? Is the program checking all factors n < 2^68? Is the time a cumulative time, or since the last message? Thanks for any help. 
20130207, 22:23  #2 
Apr 2010
Over the rainbow
2^{2}×641 Posts 
primality?
no, just factors (at this point). fator n<2^68? not exactly.. All mersenne factor are of the form 2*k*p+1 where p is 82611773 in your case. what is tested is the value of k wich make 2*k*p+1 <2^68... k being an integer, equal or above 1. as for the time it is since the last message. Last fiddled with by firejuggler on 20130207 at 22:24 
20130207, 23:28  #3 
Jun 2003
7×167 Posts 
To clarify, the number will eventually be tested for primality (by you or someone else), if no factor is found.
To find out whether the person who will do the primality test will be you or someone else, look in your worktodo.txt file. If the line with that exponent begins with "Test=" or "Doublecheck=", they you will do the primality test. If it begins with "Factor=", then you're only doing the factoring stage. 
20130208, 01:33  #4  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10010101010111_{2} Posts 
Quote:
The factors of Mersenne numbers can only be in the form 2*k*p+1 Your machine is testing for numbers in the range between 2^67 and 2^68. The report is stating that you are 82.77% of the way through that. 374.213 seconds (wall clock time) have elapsed since the last status update. The trial factoring that you are doing is the fastest way to eliminate as many candidates as possible. The starting list of candidates is all prime numbers for the exponent. About 50% are quickly eliminated by trial factoring to low bit levels. Then about 1015% more are eliminated by more trial factoring and 'P1' testing. Those numbers that remain are then tested for primality. This test takes much longer, but will not find any factors. 

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