In searching for statistically sound multipliers for the prime modulus multiplicative congruential random number generator, both theoretical and empirical tests are conducted extensively over one hundred thousand primitive roots of the ten largest primes in 215. Sixty-two multipliers pass all the tests to possess good global and local statistical properties. It is worthwhile to note that the empirically tested multipliers recommended in some previous studies are not on this list. The conclusion is that both theoretical and empirical tests are mandatory to sieve out good multipliers.
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