(bn − 1)/(b − 1) is divisible by n itself. Cunningham numbers of the form bn − 1 can only be prime if b = 2 and n is prime, assuming that n ≥ 2; these are the Mersenne numbers. Numbers of the form bn + 1 can only be prime if b is even and n is a power of 2, again assuming n ≥ 2; these are the generalized Fermat numbers, which are Fermat numbers when b = 2. Any factor of a Fermat number 22n + 1 is of the form k2n+2 + 1. Notation bn − 1 is denoted as b,n−. Similarly, bn + 1 is denoted as b,n+. When dealing with numbers of the form required for Aurifeuillian factorisation, b,nL and b,nM are used to denote L and M in the products above. References to b,n− and b,n+ are to the number with all algebraic and Aurifeuillian factors removed. For example, Mersenne numbers are of the form 2,n− and Fermat numbers are of the form 2,2n+; the number Aurifeuille factored in 1871 was the product of 2,58L and 2,58M. See also Cunningham number ECMNET and NFS@Home, two collaborations working for the Cunningham project References External links Cunningham project homepage Brent-Montgomery-te Riele table (Cunningham tables for higher bases) Cunningham tables on Prime Wiki Number theory