A New Deterministic Algorithm for Testing Primality Based on a New Property of Prime Numbers

Abstract

Although they have been being intensely studied, there remain numerous open questions around prime numbers. For example, no known formula exists that yields all of the prime numbers and no composites. Due to this uncertainty surrounding the theory of prime numbers, popular algorithms proposed in literature till date, rely heavily on probabilistic methods to determine primality. The paper proposes a new theory on the nature of prime numbers. In particular the paper proposes new theorems by which any prime number can be calculated from the knowledge of any other prime number of lower value in a simple way. It is shown in the paper that, in so doing, the theorems prove to be a common thread through which all the prime numbers of a number system can be related. Based on the theorems, a new prime number generating algorithm and a new purely deterministic method to test primality is explained and illustrated with the help of examples.