Mersenne prime random number generators

211. R. P. Brent and P. Zimmermann, Random number generators with period divisible by a Mersenne prime, Computational Science and its Applications - ICCSA 2003 (invited paper). Lecture Notes in Computer Science, Vol. 2667, Springer-Verlag, 2003, 1-10.

Preprint: dvi (21K), pdf (182K), ps (70K).

Overhead Transparencies (for a related talk): dvi (19K), pdf (240K), ps (152K).


Pseudo-random numbers with long periods and good statistical properties are often required for applications in computational finance. 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 "almost primitive" trinomials, that is trinomials having a large primitive factor. They have very fast vector/parallel implementations and excellent statistical properties.


This paper concentrates on the application of almost primitive trinomials to random number generators [185].
The algorithm for finding almost primitive trinomials is described in [212].

See the online description for the current status of the search for almost primitive trinomials.

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