  We present results of an extensive test program of a group of pseudorandom
number generators which are commonly used in the applications of physics, in
particular in Monte Carlo simulations. The generators include public domain
programs, manufacturer installed routines and a random number sequence produced
from physical noise. We start by traditional statistical tests, followed by
detailed bit level and visual tests. The computational speed of various
algorithms is also scrutinized. Our results allow direct comparisons between
the properties of different generators, as well as an assessment of the
efficiency of the various test methods. This information provides the best
available criterion to choose the best possible generator for a given problem.
However, in light of recent problems reported with some of these generators, we
also discuss the importance of developing more refined physical tests to find
possible correlations not revealed by the present test methods.
