## Re: sufficient test for primes with certificate

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• In primenumbers@yahoogroups.com, ... No. ... Your attempted proof wrongly assumes that a positive kronecker implies ... Let P = 15. ... Let A = 2. Then your
Message 1 of 33 , Jul 14, 2012
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> Is the mathematical proof right

No.

Your test uses the kronecker symbol:

> a is a number with jacobi (a,p)=1

that a positive kronecker implies

> 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.

David
• ... 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
Message 33 of 33 , Sep 21, 2012
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--- In primenumbers@yahoogroups.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)
}

Paul
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