A probabilistic primality test based on the properties of certain generalized lucas numbers

Abstract

After defining a class of generalized Fibonacci numbers and Lucas numbers, we characterize the Fibonacci pseudoprimes of the m th kind. In virtue of the apparent paucity of the composite numbers which are Fibonacci pseudoprimes of the m th kind for distinct values of the integral parameter m, a method, which we believe to be new, for finding large probable primes is proposed. An efficient computational algorithm is outlined.