  We use Experimental Mathematics and Symbolic Computation (with Maple), to
search for lots and lots of Perrin- and Lucas- style primality tests, and try
to sort the wheat from the chaff. More impressively, we find quite a few such
primality tests for which we can explicitly construct infinite families of
pseudo-primes, rather, like in the cases of Perrin pseudo-primes and the famous
Carmichael primes, only proving the mere existence of infinitely many of them.
