The behavior of pseudo-random sequences generated on computers by the multiplicative congruential method

Introduction. The use of pseudo-random elements in Monte Carlo work is essential when the scale of this work is such that the calculations involved are too extensive for hand calculating machines and it is necessary to employ an electronic computer. Although the ability of modern digital computers to perform simple binary operations at very high speed makes their use in this work particularly relevant, the limited extent of the computer memory, the relatively slow input speeds and speeds of access to the memory, and the very large number of random elements required (often of the order of 106) combine to make it unfeasible to prepare the elements beforehand in the required form for input to the computer (e.g., on tape or cards), and we must resort to some means of generation of the random elements within the computer. Mechanical means of generation on peripheral equipment, e.g., by radioactive decay, thermal noise in electronic valves, etc., are undesirable because of the irreproducibility of the numbers obtained, which enables no check to be kept on their quality. It is therefore natural to employ some deterministic method of generation of the random elements by recurrence relationships. One such technique which has attracted much attention is the multiplicative congruential method (see for exam