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Communications of the ACM

Communications of the ACM

Some new upper bounds on the generation of prime numbers

Given an integer N, what is the computational complexity of finding all the primes less than N? A modified sieve of Eratosthenes using doubly linked lists yields an algorithm of OA(N) arithmetic complexity. This upper bound is shown to be equivalent to the theoretical lower bound for sieve methods without preprocessing. Use of preprocessing techniques involving space-time and additive-multiplicative tradeoffs reduces this upper bound to OA(N/log logN) and the bit complexity to OB(N logN log log logN). A storage requirement is described using OB(N logN/log logN) bits as well.

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