## Re: sufficient test for primes with certificate

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• 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
Message 1 of 33 , Jul 16, 2012
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 of
> http://109.90.3.58/devalco/suf_helmes.htm

Do not be so fast in nullifying my theory.

Do you find one counterexample where a is not a square ?

Nice greetings from the primes.
Bernhard
• ... 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
--- 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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