> > Eg, how would you
> > interpret the docs for PrimeQ?
> >http://reference.wolfram.com/mathematica/ref/PrimeQ.html
>
> I would interpret that as Mathematica's PrimeQ[] tests with 100%
> certainty if the number is prime or not.

Mma probably uses the fast "psuedo-primality tests" in the range where
they are known to be correct (less than about 2^64, though they can go
higher.)  After that, sieving or AKS is necessary.

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