G W Reynolds wrote: >I am using mprime 22.12 on a pentium 166 MMX to do trial >factoring. For the exponents currently being assigned from >primenet it takes this machine about 12 minutes to factor >from 2^57 to 2^58. > >I thought I would try factoring some small exponents (under >1,000,000) from the nofactors.zip file. I put >FactorOverride=64 into prime.ini and started mprime as usual >but progress is _much_ slower, it will take about 8 hours to >factor from 2^57 to 2^58. > >Can someone tell me why the time difference is so great?
The number of potential factors and time required to attempt to trial-factor exponents are inversely proportional to the exponent... and proportional to the bit-depth... All potential factors are in the form 2kp+1... The smaller the p (the exponent)... the more potential factors in any given bit-depth... Basically... If you cut the exponent in 1/2... you will have approximately TWICE as many potential factors to test... and therefore it will also take approx. TWICE the time to trial- factor that exponent... (assuming trial-factoring to the same bit-depth for each exponent)... But... If you increase the bit-depth... you will DOUBLE the number of potential factors to test... for each bit-depth you increase by... (ie: 2x for 2^57 to 2^58... 4x for 2^57 to 2^59... 8x for 2^57 to 2^60)... To keep the approx. same number of potential factors to test... for any given trial-factoring attempt... you could DOUBLE the exponent AND increase the bit-depth by ONE... (ie: go from p=20M to p=40M and factor from 2^57 to 2^58 instead of from 2^56 to 2^57...) FYI... Trial-factoring the range 70M-75M... from 2^60 to 2^62... is taking approx. 1.25 hours/exponent on a P2-266... which is approx. 2x as fast as a P166-MMX... (Thankfully I have more than one machine working on this range :-) ) Eric Hahn P.S. By factoring exponents around 1M instead of 20M... and factoring to 2^64... instead of from 2^57 to 2^58... you are increasing the number of potential factors (and hence the time required)... by an approx. 2048x... That reduces down to instead of 12 MINS from 2^57 to 2^58 at p=20M to 17 DAYS for p=1M from 2^57 to 2^64... :-( _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
