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| The '''prime modulus multiplicative linear congruential generator''' is a special type of
| | <math>y_{n+1}\equiv ay_n + b~~~(\mod ~m),</math> |
| [[linear congruential generator]], given by:
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| :<math>y_{n+1}\equiv ay_n + b \qquad({\mathrm {mod}} ~m),</math>
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| The parameter <math>m</math> | | The parameter <math>m</math> |
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| then the logical choice of <math>m</math> is the Mersenne prime | | then the logical choice of <math>m</math> is the Mersenne prime |
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| :<math>\left.m\right.=2^{31} -1=2147483647</math>,
| | <math>m=2^{31} -1=2147483647</math>, |
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| with <math>a=7^5</math> (a positive primitive root of <math>m</math> see Ref.s 1 and 2), | | with <math>a=7^5</math> (a positive primitive root of <math>m</math> see Ref.s 1 and 2), |
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| ==References== | | ==References== |
| #[http://dx.doi.org/10.1145/365696.365712 D. W. Hutchinson, "A New Uniform Pesudorandom Number Generator", Communications of the ACM, '''9''' pp. 432-433 (1966)] | | #[CACM_1966_09_0432] |
| #[http://www.research.ibm.com/journal/sj/082/ibmsj0802D.pdf P. A. W. Lewis and A. S. Goodman and J. M. Miller, "A pseudo-random number generator for the System/360", IBM Systems Journal '''2''' pp. 136 (1969)] | | #[IBM_1969_02_0136] |
| #[http://dx.doi.org/10.1145/769800.769827 G. Marsaglia, "Seeds for Random Number Generators",Communications of the ACM, '''46''' pp. 90-93 (2003)] | | #[CACM_2003_46_0090] |
| #[http://dx.doi.org/10.1090/S0025-5718-99-00996-5 Pierre L'Ecuyer, "Tables of linear congruential generators of different sizes and good lattice structure", Mathematics of Computation, '''68''' pp. 249 - 260 (1999)] | | #[MC_1999_68_249] |
| #[http://dx.doi.org/10.1016/S0010-4655(97)00052-0 Iosif G. Dyadkin and Kenneth G. Hamilton "A study of 64-bit multipliers for Lehmer pseudorandom number generators", Computer Physics Communications, '''103''' pp. 103-130 (1997)] | | #[CPC_1997_103_0103] |
| #[http://dx.doi.org/10.1016/S0010-4655(99)00467-1 Iosif G. Dyadkin and Kenneth G. Hamilton "A study of 128-bit multipliers for congruential pseudorandom number generators", Computer Physics Communications, '''125''' pp. 239-258 (2000)]
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| [[Category: Random numbers]]
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