2927	 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 O 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 O N log logN and the bit complexity to O N logN log log logN . A storage requirement is described using O N logN log logN bits as well. computational complexity sieve prime number generation number theory linked list preprocessing balancing
