
Glossary: Prime Pages: Top 5000: 
The numbers F_{b,n}
= (with n and b integers, b greater than one)
are called the generalized Fermat numbers
because they are
Fermat numbers in the special case b=2.
When b is even, these numbers share many properties with the regular Fermat numbers. For example, they have no algebraic factors; for a fixed base b they are all pairwise relatively prime; and all of the prime divisors have the form k^{.}2^{m}+1 with k odd and m > n. (When b is even, many of these properties are are shared by the numbers F_{b,n}/2.) On the rare occasion that these generalized Fermat numbers are prime, they are call generalized Fermat primes.
See Also: Fermats, GeneralizedFermatPrime, Cullens, Mersennes Related pages (outside of this work)
References:
Chris K. Caldwell © 19992017 (all rights reserved)
