On 3 Dec 2001, at 20:45, Daran wrote: > Shouldn't that be 1.015 for double-checking assignments?
I think 1.03. However you do have a point. P-1 limits do depend on the trial factoring depth, and are much smaller for DC assignments than for first tests, so there is already something "built in". > > Also does the cost part of the calculation recognise the increased cost of > trial-factorisation after 2^64? Yes. The trial factoring depth is constant at 64 bits from ~8.5 million to ~13 million. Don't forget that the number of candidates which need to be checked is _inversely_ proportional to the exponent. > > I've noticed on occasion that I've had to do an extra round of trial > factoring before proceeding with an doublecheck. This indicates that > previous factorisation has been non-optimal, or have the estimates for the > relative costs of factoring vs. LL testing changed with the introduction of > new hardware? I think the latter has something to do with it - PPro is about twice as efficient at factoring compared with LL testing as a plain Pentium. This is because of much improved pipeline organization including the provision of spare registers enabling speculative execution, which greatly increased the throughput of the floating point unit in particular. Another factor is that early versions of the program were unable to factor as deep as current versions. > > Finally if P-1 factorisation were to be spun off into a separate work unit, > then the optimal arangement would be to trial factor while > cost_of_trial_factoring * chance_of_P-1_factoring is less than > cost_of_P-1_factoring * chance_of_trial_factoring. Then P-1 factorise. > Then complete trial factorisation according to the above formula. Interesting - but I think the effect would be small. What about factoring to a "fractional" depth? With a roughly logarithmic distribution of factors, surely about half the factors between 2^n and 2^(n+1) would be smaller than 2^(n+0.5), whilst searching to 2^(n+0.5) would take only about 41% of the time taken to search the whole interval. Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
