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ZachB 2004-08-26 06:36

LL question
Just wondering, when Prime95 is testing a number for primality, is it possible for it to discover that it's not prime partway through its testing, or does it have to test the number all the way to the end before it can be called a prime or not?

S80780 2004-08-26 10:28

As for the LL-Test, yes, it has to be passed completely, before you can say anything about the tested number being prime or not.
As for Trial-Factoring, no, each candidate can be a factor thus stopping the test nearly instantly (as far as I know, the actual bit-level will be finished before).
As for P-1, no, the test can stop at any time a GCD is computed. Prime95 computes (up to) two GCDs, one for each stage of the P-1-Test.

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