The specific standard RNG is a multiplicative linear congruential generator with a = 16807 and m = 2147483647.

T1a: if the RNG is a multiplicative linear congruential generator (MLCG), it should have full period (m - 1); else it should have a period at least as long as the "equivalent" MLCG, is a sense to be made clear later.

In a recent study L'Ecuyer presented an efficient way of combining Multiplicative Linear Congruential Generators. I would like to make a few comments and corrections on this article.

For reasons discussed later, this minimal standard is a multiplicative linear congruential generator with multiplier 16807 and prime modulus 2.sup.31 - 1.

A random number generator based on this algorithm is known formally as a prime modulus multiplicative linear congruential generator (PMMLCG).

In general, any multiplicative linear congruential generator with modulus m = 2.sup.b is flawed in the sense that it can not have a full period; instead the maximum possible period is only 2.sup.b-2 = m/4.

The result of this emphasis on speed was a generation of computationally efficient but highly non-portable and statistically flawed multiplicative linear congruential generators, the most notorious being the now infamous IBM SYSTEM/360 product RANDU.

One usually chooses c = 0, in which case the generator is called

multiplicative linear congruential generator (MLCG) and its state space is S = [1, 2, .

With the example of the Bernoulli shift, we observe that prime modulus

multiplicative linear congruential generators are implementations of deterministic chaotic processes.