Re: sufficient test for primes with certificate
- --- In email@example.com,
"djbroadhurst" <d.broadhurst@...> wrote:
> Indeed there seems to be little obstacle to manufacturingSo far, it took about 6 minutes to find a 354-digit counterexample.
> "Fermat plus Lucas" pseudoprimes that are much larger,
> given Bernhard's unwise choice of a positive Kronecker symbol.
Going titanic, with more than 1000 decimal digits, seems possible,
but rather hard, with only Pari-GP. Help from OpenPFGW may be needed.
David (per proxy the positive-Kronecker pseudoprime gremlins)
--- 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)