A prime number sieve is an algorithm that lists all prime numbers up to a given bound n. Two parallel prime number sieves for an algebraic EREW PRAM model of computation are presented and analyzed. The first sieve runs in O(log n) time using O(n/(log n log log n)) processors, and the second sieve runs in O(root n) time using O(root n) processors. The first sieve is optimal in the sense that it performs work O(n/log log n), which is within a constant factor of the number of arithmetic operations used by the fastest known sequential prime number sieves. However, when both sieves are analyzed on the Block PRAM model as defined by Aggarwal, Chandra, and Snir, it is found that the second sieve is more work-efficient when communication latency is significant.
