On Thursday 07 December 2006 14:20, david eddy wrote: > Andy Messier wrote: > > I can answer question 2. Given the probability of finding a factor using > > P-1 and the times required to factor vs. primality testing, Prime95 will > > only P-1 factor to the extent that it minimizes the total CPU time > > required to test primality. > > This is sensible and explains what "optimal" means. > However I have looked at the file "how much P-1 factoring" and there was no > consistency in the values of the two bounds as far as I could discern.
1) The "optimal" bounds calculated for double checking are a lot lower than for first tests - since the time saved by finding a factor is less after investing in the first L-L test run. (I'm not sure that sufficient allowance is made for the fact that more than two L-L tests are sometimes required before a pair with matching residues is found.) 2) Systems with small memory simply cannot run P-1 phase 2, so the phase 1 limit is raised and phase 2 omitted in this case. There is still an inefficiency as it would be more efficient to run P-1 halfway through trial factoring (i.e. before increasing the trial factoring limit by 1 bit for the last time). This has been discussed before. Regards Brian Beesley _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
