On Fri, Dec 4, 2009 at 2:34 PM, Bill Hart <goodwillh...@googlemail.com> wrote:

> No, I meant, was trial factoring done before testing for base 2
> pseudoprimality. I guess not. I guess that you have a list of *all*
> base 2 pseudoprimes up to 2^64 and worked with that, i.e. base 2
> pseudoprime test followed by BPSW is unconditional primality test to
> 2^64, and it is not necessary to do trial factor to 1000, then base 2,
> then BPSW (though it may be more efficient to do so). In other words,
> I can tune my own trial factoring cutoff to whatever limit I like and
> the result is still guaranteed. It is only an efficiency thing.

Right, we did not trial factor before base 2 psp so we would get the
entire list to ensure BPSW will guarantee.  So yes when you are
actually testing you can figure out a good trial factoring cutoff and
it will still be guaranteed.

Jeff.

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