Any prime generalized Fermat number Fb,n = (with b an integer greater than one) is called a generalized Fermat prime (because they are
Fermat primes in the special case b=2).
Why is the exponent a power of two?
Because if m is an odd divisor of n, then bn/m+1 divides bn+1, so for the latter to be
prime, m must be one. Because the exponent is a power of two, it seems reasonable to conjecture that
the number of Generalized Fermat primes is finite for
every fixed base b.
See Also: Fermats, Mersennes, Cullens
Related pages (outside of this work)
- A. Björn and H. Riesel, "Factors of generalized Fermat numbers," Math. Comp., 67 (1998) 441--446. MR 98e:11008 (Abstract available)
- H. Dubner and W. Keller, "Factors of generalized Fermat numbers," Math. Comp., 64 (1995) 397--405. MR 95c:11010