Browse Groups

• ## Re: sufficient test for primes with certificate

(33)
• NextPrevious
• {g = 582; a = 121; p = 703; if(p%4 == 3 && kronecker(a,p) == 1 && Mod(a,p)^((p-1)/2) == 1 && Mod((1+x)*Mod(1,p),x^2-a)^((p-1)/2) == g*x && Mod(g,p)^2*a == 1 &&
Message 1 of 33 , Jul 15, 2012
View Source
{g = 582; a = 121; p = 703;
if(p%4 == 3 &&
kronecker(a,p) == 1 &&
Mod(a,p)^((p-1)/2) == 1 &&
Mod((1+x)*Mod(1,p),x^2-a)^((p-1)/2) == g*x &&
Mod(g,p)^2*a == 1 &&
!isprime(p), print("Counterexample!"));}

Counterexample!

This nullifies the false claim of
http://109.90.3.58/devalco/suf_helmes.htm

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
View Source
--- 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
Your message has been successfully submitted and would be delivered to recipients shortly.
• Changes have not been saved
Press OK to abandon changes or Cancel to continue editing
• Your browser is not supported
Kindly note that Groups does not support 7.0 or earlier versions of Internet Explorer. We recommend upgrading to the latest Internet Explorer, Google Chrome, or Firefox. If you are using IE 9 or later, make sure you turn off Compatibility View.