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Re: Prime numbers and primality tests
Posted:
Jan 20, 2013 1:25 AM


I wouldn't use the Lucas pseudoprime test by itself. The key is to use a regular pseudoprime test a^(N1) = 1 (mod N) (like MillerRabin) AND a Lucas test.
The types of pseudoprimes that pass a regular test tend to have differ characteristics than those that pass a Lucas test. In other words, if you make a list of regular pseudoprimes (say, base 2) and another list of Lucas pseudoprimes, then the two lists tend to avoid each other and there is very little overlap, that is, few numbers that can survive both tests.
This is explained in a paper, "Lucas Pseudoprimes", which you can find at http://mpqs.free.fr/LucasPseudoprimes.pdf
Robert Baillie



