The Lehmer random number generator[1] (named after D. H. Lehmer), sometimes also referred to as the Park–Miller random number generator (after Stephen K. Park and Keith W. Miller), is a type of linear congruential generator (LCG) that operates in multiplicative group of integers modulo n. The general formula is
where the modulus m is a prime number or a power of a prime number, the multiplier a is an element of high multiplicative order modulo m (e.g., a primitive root modulo n), and the seed X0 is coprime to m.
Other names are multiplicative linear congruential generator (MLCG)[2] and multiplicative congruential generator (MCG).
^W. H. Payne; J. R. Rabung; T. P. Bogyo (1969). "Coding the Lehmer pseudo-random number generator" (PDF). Communications of the ACM. 12 (2): 85–86. doi:10.1145/362848.362860. S2CID 2749316.[1]
^L'Ecuyer, Pierre (June 1988). "Efficient and Portable Combined Random Number Generators" (PDF). Communications of the ACM. 31 (6): 742–774. doi:10.1145/62959.62969. S2CID 9593394.
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