1691	 A Comparison of the Correlational Behavior of Random Number Generators for the IBM	 Hutchinson states that the new prime modulo multiplicative congruential pseudorandom generator attributed to D. H. Lehmer has passed the usual statistical tests for random number generators. It is here empirically shown that generators of this type can produce sequences whose autocorrelation functions up to lag exhibit evidence of nonrandomness for many multiplicative constants. An alternative generator proposed by Tausworthe which uses irreducible polynomials over the field of characteristic two is shown to be free from this defect. The applicability of these two generators to the IBM is then discussed. Since computer word size can affect a generator s statistical behavior the older mixed and simple congruential generators although extensively tested on computers having or more bits per word may not be optimum generators for the IBM . random numbers pseudorandom number generators autocorrelation function serial correlation digital shift-register generators linear recurrence modulo two irreducible polynomials primitive trinomials modulo two congruential generators prime numbers statistical tests for randomness IBM -bit versus -bit word size
