Predicting Prime Numbers Using Cartesian Genetic Programming

Abstract

Prime generating polynomial functions are known that can produce sequences of prime numbers (e.g. Euler polynomials). However, polynomials which produce consecutive prime numbers are much more difficult to obtain. In this paper, we propose approaches for both these problems. The first uses Cartesian Genetic Programming (CGP) to directly evolve integer based prime-prediction mathematical formulae. The second uses multi-chromosome CGP to evolve a digital circuit, which represents a polynomial. We evolved polynomials that can generate 43 primes in a row. We also found functions capable of producing the first 40 consecutive prime numbers, and a number of digital circuits capable of predicting up to 208 consecutive prime numbers, given consecutive input values. Many of the formulae have been previously unknown.