A popular form of random-number generator uses the recurrencesk= (ASk−1mod 2ewithAands0odd to produce a pseudo-random sequence of integers in the range 0 to 2e− 1. We give a simple modification which increases the guaranteed period by an enormous factor with only a small computational overhead. The recurrence is changed tosk= (Ask−1+ Sk−nmod 2ewherenis such thatxn+ x + 1 is a primitive binary polynomial. The period is increased from 2e−2to (2n−1)2e−1. The overhead is an extra addition and the inclusion of a circular buffer of lengthn.