For a given prime m, whether a MLCG has full period or not depends only on the characteristic polynomial of its matrix.
The ACORN generator proposed recently in  is in fact equivalent to a MLCG with matrix A such that [a.
It turns out [61, 97] that there exists a MLCG with modulus m = *=[sub.
Its "approximating" MLCG has m = 4611685301167870637 and a = 1968402271571654650 (see Table I) [61, 97].
For example, my laptop computer needs less than 6 hours to loop around the whole period of a MLCG with modulus m = [2.
For that reason, MLCGs with moduli of this form are used abundantly in practice, despite their serious drawbacks.
2] have proposed a very efficient way to implement a portable MLCG with modulus m using only [log.
Fishman and Moore  made an exhaustive search of all multipliers for a MLCG with modulus m = 2.
Now we consider the case where each individual generator j is a maximal-period MLCG with moduls m.
2], inspired by Wichmann and Hill , propose an efficient way to implement a portable MLCG with modulus m and multiplier a using only integers from -m to +m, when a.
The above technique can be used for each individual MLCG in the implementing of a combined generator as proposed in Section 2, when each of the individual generators satisfies a.
For a simple and easily implementable MLCG on a 32-bit computer, we suggest m = 2147483399 and a = 40692.