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## Re: Lucas super-pseudoprimes for Q <> 1

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• ... 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),
Message 1 of 46 , Nov 6, 2010
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"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
• ... http://physics.open.ac.uk/~dbroadhu/cert/dbmo116.out gives my 116, in the format [n, factors, number of solutions] With n
Message 46 of 46 , Nov 9, 2010
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"mikeoakes2" <mikeoakes2@...> wrote:

> > My revised count up to 2*10^10 is 116.
> My (original) count up to 2*10^10 was 105.
> So it must have missed 11, i.e. a bigger proportion.