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Math Forum » Discussions » Software » comp.soft-sys.math.mathematica

Topic: Prime numbers and primality tests
Replies: 4   Last Post: Jan 22, 2013 11:18 PM

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bobbaillie@frii.com

Posts: 16
Registered: 11/27/06
Re: Prime numbers and primality tests
Posted: Jan 20, 2013 1:25 AM
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I wouldn't use the Lucas pseudoprime test by itself. The key is to
use a regular pseudoprime test a^(N-1) = 1 (mod N) (like Miller-Rabin)
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

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