Prime number generation using memetic programming

Abstract

For centuries, the study of prime numbers has been regarded as a subject of pure mathematics in number theory. Recently, this vision has changed and the importance of prime numbers has increased rapidly, especially in information technology, e.g., public key cryptography algorithms, hash tables, and pseudo-random number generators. One of the most popular topics to attract attention is to find a formula that maps the set of natural numbers into the set of prime numbers. However, to date there is no known formula that produces all primes. In this article, we use a hybrid evolutionary algorithm, called the memetic programming (MP) algorithm, to generate mathematical formulas that produce distinct primes. Using the MP algorithm, we succeeded in discovering an interesting set of formulas that produce sets of distinct primes.