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

We propose a system of multiple recursive generators of modulus <i>p</i> and order <i>k</i> 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 <i>p</i> = 2<sup>31</sup> − 1, the most popular modulus used, we provide tables of specific parameter values yielding maximum period for recurrence of order <i>k</i> = 102 and 120. For <i>p</i> = 2<sup>31</sup> − 55719 and <i>k</i> = 1511, we have found generators with a period length approximately 10<sup>14100.5</sup>.

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