--- In

primenumbers@yahoogroups.com,

"paulunderwooduk" <paulunderwood@...> wrote:

> n=228241=181*(13*97)

Here the kronecker is (-1)^3 = -1 and we are into Arnault territory:

{pu3(n,x)=gcd(x^3-x,n)==1&&kronecker(x^2-4,n)==-1&&

Mod(x,n)^(n-1)==1&&Mod((x+s)/Mod(2,n),s^2+4-x^2)^(n+1)==1;}

{pu6(n,x,y)=gcd(x^2-y^2,n)==1&&pu3(n,x)&&pu3(n,y);}

{n=13*97*181; x=218; y=824; if(pu6(n,x,y),print("refuted"));}

refuted

Note that there are no "matrices" above: a double mod is enough.

Congratulations again, Paul, on testing your ideas to destruction.

Best regards

David