## 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).

## Abstract

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.

## Comments

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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