Critical distances in pseudorandom sequences generated with composite moduli

Abstract
In periodic sequences of pseudorandom numbers generated by multiplicative congruential schemes, terms at certain critical distances are strongly correlated. For powers of two moduli a fast arithmetic method for computing these distances is given and applied to several generators. For all of them the length of the sequence that can be safely used turns out to be much shorter than the period. These correlations should be taken into account in parallel computations when a single pseudorandom sequence is partitioned among concurrent processors.