Parameters in Common Use
In 1988, Park and Miller suggested a Lehmer RNG with particular parameters n = 231 − 1 = 2,147,483,647 (a Mersenne prime M31) and g = 75 = 16,807 (a primitive root modulo M31), now known as MINSTD. Although MINSTD was later criticized by Marsaglia and Sullivan, it is still in use today (in particular, in CarbonLib).
ZX Spectrum uses the Lehmer RNG with parameters n = 216 + 1 = 65,537 (a Fermat prime F4) and g = 75 (a primitive root modulo F4). The CRAY random number generator RANF is a Lehmer RNG with n = 248 and g = 44,485,709,377,909. Another popular pair of parameters is n = 232 − 5 = 4,294,967,291 and g = 279,470,273.
LC53 in Forth uses parameters n = 232 − 5 = 4,294,967,291 and g = 232 − 333333333 = 3,961,633,963.
The GNU Scientific Library includes several random number generators of the Lehmer form, including MINSTD, RANF, and the infamous IBM random number generator RANDU.
Read more about this topic: Lehmer Random Number Generator
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