The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Algorithm 356: a prime number generator using the treesort principle [A1]
Communications of the ACM
Algorithm 310: Prime number generator 1
Communications of the ACM
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A practical sieve algorithm finding prime numbers
Communications of the ACM
A sublinear additive sieve for finding prime number
Communications of the ACM
A linear sieve algorithm for finding prime numbers
Communications of the ACM
Linear time algorithms for Abelian group isomorphism and related problems
Journal of Computer and System Sciences
| Hi-index | 48.27 |
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.