Using patterns to generate prime numbers

Abstract

A new deterministic method to determine primality of any given number is presented in this paper. The underlying principle involves the use of a special series that generates lesser prime numbers till the root of the number under scrutiny. Subsequently, divisibility is performed to check whether the number is prime or not. Such a series characteristically produces all the successive prime numbers along with a few composite numbers as well, the proportion of latter increasing as one moves to higher numbers. This technique is provably more efficient than other deterministic methods that employ division by primes till the root of the number, either by generating those smaller primes or storing them or by simply taking all odd numbers till the square root. © Springer-Verlag Berlin Heidelberg 2005.