--- In

primenumbers@yahoogroups.com,

"mikeoakes2" <mikeoakes2@...> wrote:

> I have a cunning script which found these first

> 7 non-Carmichaels in 9313 msecs.

It can be done a shade faster than that:

{ncarm(n)=local(F=factor(n),f=F[,1],m=#f,p,t,d);if(m>3&&

sum(j=1,m,F[j,2])==m,t=1;for(j=1,m,p=f[j];if((n-1)%(p-1),

if((n-1)%(p+1)==0&&(n+1)%(p-1)==0,d++,t=0;break()))));t&&d;}

{forstep(n=1,4638985,2,if(n%3&&ncarm(n),print1(n",")));

print("took "gettime" ms");}

507529,1080905,1739089,1992641,2110159,4013569,4638985,took 7187 ms

Is the above, in essence, your conjectural method?

David