Exploration of the Conjecture of Bateman Using Particle Swarm Optimisation and Grid Computing

Abstract

The Particle Swarm Optimisation concept is an evolutionary computation technique employed to find optimal solutions in problems with immense solution space. In this article, an application of Particle Swarm Optimisation technique to the survey of the Conjecture of Bateman is presented. The Conjecture of Bateman requests how many coincidences of sums of powers of prime numbers are. Up today, only one coincidence has been proved. Neither previous exploration of the Conjecture has been published in the scientific literature, nor analytical demonstration has proved the existence of a finite or infinite number of coincidences. In a previous and systematic exploration, not new coincidences have appeared. Unfortunately, the size of the Conjecture makes impossible to go on this brute-force and systematic survey. In order to support the exploration, a gLite grid computing infrastructure has been used, providing seamless access to computational resources.