Mathematics of Computation

Abstract

For each prime p, let p# be the product of the primes less than or equal to p. We have greatly extended the range for which the primality of n! ± 1 and p# ± 1 are known and have found two new primes of the first form (6380! + 1, 6917! − 1) and one of the second (42209# + 1). We supply heuristic estimates on the expected number of such primes and compare these estimates to the number actually found.