## 25328Re: 4 Fermat and 1 Lucas [freely admitted by its author to be hopeless]

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• Aug 1, 2013
"paulunderwooduk" <paulunderwood@...> wrote:

> Breaking my Trappist vow...

Why, Paul? You have freely admitted that there is no point:

> one parameter Lucas plus N Fermat/Euler/M-R PRP test
> can be counterexampled

Here are 10 counterexamples to your latest vain idea:

{tst(n,x)=local(P=x^8-1,Q=1-x^8);
kronecker(P^2-4*Q,n)==-1&&gcd(x,n)==1&&
Mod(x-1,n)^(n-1)==1&&
Mod(x+1,n)^(n-1)==1&&
Mod(x^2+1,n)^(n-1)==1&&
Mod(x^4+1,n)^(n-1)==1&&
Mod(Mod(1,n)*L,L^2-P*L+Q)^(n+1)==Q;}

{F=[
[7750135694869, 822096191222],
[23723039862349, 1323013054084],
[90273119893069, 5862741794270],
[264256506403909, 38817437399213],
[8955652979403079, 1851456656424086],
[4574665869143389, 885331489130492],
[5266652551034509, 988874992567097],
[8618233825140949, 584166437019905],
[9541864502273629, 720345160544763],
[10245855908959669, 226701623305716]];

c=0;for(k=1,#F,n=F[k][1];x=F[k][2];if(!isprime(n)&&tst(n,x),c++));
print(" fooled "c" times");}

fooled 10 times

NB: Please, Paul, no more wriggles, sign tests, gcds, extra Fermats,
new choices of [P,Q], this August. The Gremlins are sunning
themselves and find it irkesome to tool up for such vain tests.

David (their overheated minder)
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