Re: sufficient test for primes with certificate
- --- In email@example.com, "paulunderwooduk" <paulunderwood@...> wrote:
> Please see my draft paper at:I should say that the program by Jen K. Andersen is a "psp-sieve" -- it generates a list of pseudoprimes for a given base and range, where gcd(base,n)==1. For instance, I can pre-screen my test
> (Ignore the the mix up I made with the comparison between FFT multiplication and FFT squaring timings.)
> The 2.X selfridge composite test I have there has been tested to 4*10^12. I am planning to get to 10^14 in a core year, with the help of a prp-sieve written by Jens K. Anderson. I would go to 10^15 if my resources were not elsewhere employed.
(2+L)^(n+1)==5 (mod n, L^2+1) with output from Jens program for base 5:
5^(n+1)==25 (mod n).
This takes care of about half the throughput.
I then repeat the process for odd bases 7,...,29. This greatly reduces the amount of work my program has to do; It can then ignore the case where x<(31-5)/2 and gcd(base,n)==1
--- In firstname.lastname@example.org, "paulunderwooduk" <paulunderwood@...> wrote:
> I ran various "minimal \lambda+2" tests on Gilbert Mozzo's 20,000 digit PRP, 5890*10^19996+2^66422-3 (x=1), using a 2.4GHz core:
> 0m32.374s pfgw64 (3-prp)
> 1m9.876s pfgw64 -t
> 1m53.535s pfgw64 -tp
> 3m0.483s pfgw64 -tc
> 5m12.972s pfgw64 scriptify
> 4m4.811s gmp (-O3/no pgo)
> 4m9.148 pari-gp
> 1m15s theoretical Woltman implementation
I compiled a better version of my code with gmp 5.0.5, on a different box running at 3.6GHz and got some better timings
17.505s pfgw (3-prp)
1m1.986s pfgw -tp
1m13.789s gmp (-O3/no pgo)