FERMAT AND MERSENNE NUMBERS

Fermat numbers (F-n = 2(2n) + 1)and Mersenne numbers (M-m = 2(m) - 1) m odd are compared on the basis of integer structure, using the modular rings Z(4) and Z(6). The two numbers fall in different classes and this results in different composite row structures and different potentials for the formation of primes. The constraints on 2(n) and the right end digits for F-n result in fewer numbers over a given range than those for M-m. This is shown with two functions which link the two numbers and show that F-n = (2(x2+y2-1) + 1): for primes y = n, but when n>4, y not equal n.