MULTIPLICATIVE, CONGRUENTIAL RANDOM-NUMBER GENERATORS WITH MULTIPLIER+ -2(K1)+/-2(K2) AND MODULUS 2(P)-1/

The demand for random numbers in scientific applications is increasing . However, the most widely used multiplicative, congruential random-nu mber generators with modulus 2(31) - 1 have a cycle length of about 2. 1 X 10(9). Moreover, developing portable and efficient generators with a larger modulus such as 2(61) - 1 is more difficult than those with modulus 2(31) - 1. This article presents the development of multiplica tive, congruential generators with modulus m = 2(p) - 1 and four forms of multipliers: 2(k1) - 2(k2), 2(k1) + 2(k2), m - 2(k1) + 2(k2), and m - 2(k1) - 2(k2), k1 > k2. The multipliers for modulus 2(31) - 1 and 2(61) - 1 are measured by spectral tests, and the best ones are presen ted. The generators with these multipliers are portable and very fast. They have also passed several empirical tests, including the frequenc y test, the run test, and the maximum-of-t test.