Primality testing and prime constellations

Author:

Larry ERICKSEN

AMS Classification:

11A51, 11B39, 11B50, 11N13

Keywords:

congruence, factorization, Lucas sequence, primality test, prime constellation, recurrence

Abstract:

Extending the deterministic approach of the Lucas-Lehmer test for Mersenne numbers, we present primality tests for numbers of a more general form. Building on the idea that Pascal-type triangles can be used to verify the existence of primes and twin primes, we create generalized number triangles to identify arbitrary prime constellations. Along the way, we provide techniques for finding probable primes and we develop methods for factoring composite numbers. For each primality test strategy, we give efficient recursive algorithms to establish the primality of very large numbers.

Download paper:

ericksen-08.pdf

Vol. 3 (11), 2008