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We introduce an algorithm that computes the prime numbers up to N N using O (N / log log N) O (N/ N) additions and N 1 / 2 + o (1) N^1/2+o (1) bits of memory. The algorithm enumerates representations of integers by certain binary quadratic forms. We present implementation results for this algorithm and one of the best previous algorithms.
Atkin et al. (Fri,) studied this question.