20030530, 13:48  #1 
May 2003
443_{8} 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
1111000001100_{2} Posts 
Quote:
And if no factor is found, then the progress as measured at the standard powersof2 breakpoints is sequential. 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Automatic fetch of Trial Factoring work for GPU mfakt*  LaurV  GPU to 72  81  20201202 05:17 
Simple Script to get Trial Factoring Work  jfamestad  PrimeNet  3  20161106 20:32 
Why trial factoring work chopped into chunks?  lidocorc  PrimeNet  4  20081106 18:48 
over trial factoring  JFB  Software  23  20040822 05:37 
How does the trial factoring work with 15K*2^n1  jocelynl  15k Search  0  20030711 14:23 