Abstract. Linear congruential generators (LCGs) remain the most popular method of pseudorandom number generation on digital computers. Ease of implementation has favored implementing LCGs with power-of-two moduli. However, prime modulus LCGs are superior in quality to power-of-two modulus LCGs, and the use of a Mersenne prime minimizes the computational cost of generation. When implemented for parallel computation, quality becomes an even more compelling issue. We use a full-period exponential sum as the measure of stream independence and present a method for producing provably independent streams of LCGs in parallel by utilizing an explicit parameterization of all of the primitive elements modulo a given prime. The minimization of this measure of independence further motivates an algorithm required in the explicit parameterization. We describe and analyze this algorithm and describe its use in a parallel LCG package. 1. Introduction. Perhaps the oldest generator still in use for the generation of uniformly distributed integers is the linear congruential generator (LCG). This generator is sometime
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