Re: sufficient test for primes with certificate
- Dear David,
thanks a lot that you reveal a hole in the proof and in the algorithm.
You will surely remark that both counterexample are of the form
a=16 and a=121 and that they are squares.
I have to exclude the case that a is a square, because otherwise
the proof and the criteria do not work.
> This nullifies the false claim ofDo not be so fast in nullifying my theory.
Do you find one counterexample where a is not a square ?
I thank you for your engagement and your work.
Nice greetings from the primes.
--- 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)