Re: Prime numbers and primality tests

*To*: mathgroup at smc.vnet.net*Subject*: [mg129522] Re: Prime numbers and primality tests*From*: RBaillie <bobbaillie at frii.com>*Date*: Sun, 20 Jan 2013 01:21:27 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <kd2lt4$co5$1@smc.vnet.net>

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