Lehmer random number generator

The Lehmer random number generator (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

${\displaystyle X_{k+1}=a\cdot X_{k}{\bmod {m}},}$

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) and multiplicative congruential generator (MCG).