P-1 coordination thread - discussion

[Nuri]

1 out of 22 is a very lucky shot... You should expect 1-2% success rate, unless the limits you're using are on the extremes.

[vjs]

yup one out of 22 is pretty lucky. I believe the first time I tried P-1 factoing I found one on the second or third number. Then not again for quite some time.

[jasong]

I gave Prime95 an 800MB maximum which, unless I totally misunderstood something I read about that, should be more than enough.

Question: If you run p-1 more than once, it does the problem slightly differently each time because of randomization, right? So, would that make it possible that another p-1 could find a factor that the previous one missed? Even with exactly the same parameters?

[Nuri]

Question: If you run p-1 more than once, it does the problem slightly differently each time because of randomization, right? So, would that make it possible that another p-1 could find a factor that the previous one missed? Even with exactly the same parameters?

to the best of my knowledge, this is not how it works. it's true for ECM though and this is why we run many curves (trials) in ECM at each boundary.

[hhh]

Consider a prime factor p of your number k*2^n-1. p-1 is not prime, and has a factorisation p=p_1*p_2*p_3*...*q*r, where q and r are the two largest factors.
If r<B1, the factor p will be found in stage 1, if r<B2 AND q<B1, it will be found in stage 2. No random parameters.
In other words: if all prime factors of p-1 are below B1, it's a stage-1-hit, if the largest (and only the largest) is between B1 and B2, it's a stage-2-hit.
Yours H.