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.
CACM September, 1977
Mairson, H. G.
