Coding the Lehmer Pseudo-random Number Generator An algorithm and coding technique is presented for quick evaluation of the Lehmer pseudo-random number generator modulo 2**31 - 1, a prime Mersenne number with produces 2**31 - 2 numbers, on a p-bit (greater than 31) computer. The computation method is extendible to limited problems in modular arithmetic. Prime factorization for 2**61 - 2 and a primitive root for 2**61 - 1, the next largest prime Mersenne number, are given for possible construction of a pseudo-random number generator of increased cycle length. CACM February, 1969 Payne, W. H. Rabung, J. R. Bogyo, T. P. pseudo-random number, random number, modular arithmetic, uniform probability density, uniform frequency function, simulation, prime factorization, primitive roots CA690205 JB February 20, 1978 11:07 AM 1933 5 1933 1933 5 1933 1933 5 1933