Full period of a multiple recursive random number generator with generalized Mersenne prime number

Abstract

An interesting special case of efficiently checking the full period conditions of a k thorder multiple recursive generator (MRG) is that of a prime order k, a prime modulus m and a prime , which is called a Generalized Mersenne prime (GMP). A MRG with either Mersenne prime modulus or Sophie Germain prime modulus is a way of improving on computational efficiency and full period, respectively. Computational experiments are conducted to search a prime order k, for a given prime modulus m, such that is a prime number. We find a GMP for k = 4217 and m = 231−69 . The largest period of a 4217th–order MRG with Sophie Germain prime modulus 231−69 is 1039352.7485 .