A system of high-dimensional, efficient, long-cycle and portable uniform random number generators

We propose a system of multiple recursive generators of modulus p and order k where all nonzero coefficients of the recurrence are equal. The advantage of this property is that a single multiplication is needed to compute the recurrence, so the generator would run faster than the general case. For p = 2 31 − 1, the most popular modulus used, we provide tables of specific parameter values yielding maximum period for recurrence of order k = 102 and 120. For p = 2 31 − 55719 and k = 1511, we have found generators with a period length approximately 10 14100.5 .