  We provide a new algorithm for tabulating composite numbers which are
pseudoprimes to both a Fermat test and a Lucas test. Our algorithm is optimized
for parameter choices that minimize the occurrence of pseudoprimes, and for
pseudoprimes with a fixed number of prime factors. Using this, we have
confirmed that there are no PSW challenge pseudoprimes with two or three prime
factors up to $2^{80}$. In the case where one is tabulating challenge
pseudoprimes with a fixed number of prime factors, we prove our algorithm gives
an unconditional asymptotic improvement over previous methods.
