A Distributed Wheel Sieve Algorithm

Abstract

This paper presents a new distributed approach for generating all prime numbers in a given interval of integers. From Eratosthenes, who elaborated the first prime sieve (more than 2000 years ago), to the current generation of parallel computers, which have permitted to reach larger bounds on the interval or to obtain previous results in a shorter time, prime numbers generation still represents an attractive domain of research and plays a central role in cryptography. We propose a fully distributed algorithm for finding all primes in the interval [2; n], based on the wheel sieve and the SMER (Scheduling by Multiple Edge Reversal) multigraph dynamics which runs in O(√(n)) computational complexity, close to the theoretical lower bound on sieve methods, that is O(n), without making use of preprocessing techniques.