Trading time for space in prime number sieves

Abstract

A prime number sieve is an algorithm that finds the primes up to a bound n. We present four new prime number sieves. Each of these sieves gives new space complexity bounds for certain ranges of running times. In particular, we give a linear time sieve that uses only O(√n/(log log n)2) bits of space, an O1(n/log log n) time sieve that uses O(n/((log n)t log log n)) bits of space, where l > 1 is constant, and two super-linear time sieves that use very little space.