Summary
In DeMatteis and Pagnutti [1] multiplicative congruential pseudo random number generators with composite moduli are analysed and it is proved that there are strong correlations between terms located far apart in the generated sequences. In this note the same result is obtained for multiplicative congruential generators with prime moduli.
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References
DeMatteis, A., Pagnutti, S.: Parallelization of random number generators and long-range correlations. Numer. Math.53, 595–608 (1988)
Knuth, D.E.: The art of the computer programming, Vol. 2, 2nd Ed. Reading (Mass.): Addison-Wesley 1981
Ripley, B.D.: The lattice structure of pseudo-random number generator. Proc. R. Soc. Lond. A389, 197–204 (1983)
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Eichenauer-Herrmann, J., Grothe, H. A remark on long-range correlations in multiplicative congruential pseudo random number generators. Numer. Math. 56, 609–611 (1989). https://doi.org/10.1007/BF01396346
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DOI: https://doi.org/10.1007/BF01396346