Computation of critical distances within multiplicative congruential pseudorandom number sequences

Abstract Multiplicative congruential pseudorandom number generators with prime moduli are considered. Recently, it has been shown by two of the authors (Eichenauer-Herrmann and Grothe (1989)) that terms located far apart in the generated sequences are strongly correlated. However, the critical distances between the terms were not obtained explicitly. Since a straight approach for computing them through tabulations cannot be used for large values of the modulus, an efficient method has been developed and is described in the present note. The resulting algorithm has been applied to several generators and tables of the most critical distances for two generators with large moduli are included.