Physical Sciences and Mathematics | Open Access Articles

This paper explores the asymptotic complexity of two problems related

to the Miller-Rabin-Selfridge primality test. The first problem is to

tabulate strong pseudoprimes to a single fixed base $a$. It is now proven

that tabulating up to $x$ requires $O(x)$ arithmetic operations and $O(x\log{x})$ bits of space.

The second problem is to find all strong liars and witnesses, given a fixed odd composite $n$.

This appears to be unstudied, and a randomized algorithm is presented that requires an

expected $O((\log{n})^2 + |S(n)|)$ operations (here $S(n)$ is the set of strong liars).

Although interesting in their own right, a notable application …

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