The MWC multiplier formula_28 and lag formula_19 determine the modulus formula_30. In practice, formula_28 is chosen so the modulus is prime and the sequence has long period. If the modulus is prime, The period of a lag-formula_19 MWC generator is the order of formula_5 in the multiplicative group of numbers modulo formula_4. While it is theoretically possible to choose a non-prime modulus, a prime modulus eliminates the possibility of the initial seed sharing a common divisor with the modulus, which would reduce the generator's period.