20030530, 13:48  #1 
May 2003
291_{10} Posts 
How does trialfactoring work?
I had a quick question about how the trialfactoring in Prime95 works. Does the program trialdivide by prime numbers in order or does it try them randomly until one works? :?

20030530, 14:00  #2 
May 2003
2^{5}·3 Posts 
Trial factoring tries all possible dividers up to a certain limit, which depends on the exponent you are testing (or which you set yourself with the FactorOverride option).
However, not all prime numbers are tried, because there is a theorem that if a number divides a Mersenne number, it MUST be of the form 2*k*p+1 where p is the exponent of the number you are testing. So it only tries to devide the Mersenne by these kind of numbers. How the program tries to divide it exactly, I don't know myself. I don't know the exact algorithm for it, but I know that it is waaaay faster than just trying to numerically divide it. Axel Fox. 
20030530, 14:54  #3 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Prime95 trialfactoring is orderly. It's designed to ensure that once it reports that there's no factor up to 2^m, it really does mean that no potential factor below 2^m divides the Mnumber it tested, so any factor of that Mnumber must be greater than 2^m.

20030530, 17:51  #4  
"Sander"
Oct 2002
52.345322,5.52471
29·41 Posts 
Quote:
The program does however try all numbers below a bit length before moving to the next though. Below is a message from George to the mersenne mailing list on 08 may 1996 Quote:


20030530, 18:30  #5  
Aug 2002
Richland, WA
2^{2}×3×11 Posts 
Quote:


20030530, 20:34  #6  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Quote:
And if no factor is found, then the progress as measured at the standard powersof2 breakpoints is sequential. 

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