Random Number Generators with Period Divisible by a Mersenne Prime

Pseudo-random numbers with long periods and good statistical properties are often required for applications in computational nance, numerical integration, physics, simulation, etc. We consider the requirements for good uniform random number generators, and describe a class of generators whose period is a Mersenne prime or a small multiple of a Mersenne prime. These generators are based on primitive or "almost primitive" trinomials, that is trinomials having a large primitive factor. They enable very fast vector/parallel implementations with excellent statistical properties