Re: sufficient test for primes with certificate
- In firstname.lastname@example.org,
"bhelmes_1" <bhelmes@...> asked:
> Is the mathematical proof rightNo.
Your test uses the kronecker symbol:
> a is a number with jacobi (a,p)=1Your attempted "proof" wrongly assumes
that a positive kronecker implies
a quadratic residue:
> Now, let P be composite = p1^k1 * p2^k2 * ....Let P = 15.
> Let A be a square residue mod P.Let A = 2. Then your test would record that
kronecker(2,15) = 1
> there exist x such that x^2 = A mod P.False. There is no x such that x^2 = 2 mod 15.
Moreover, you have been told this before.
--- In email@example.com, "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)