generalized Fermat primeAny 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.
Related pages (outside of this work)
- Generalized Fermat Prime Search by Yves Gallot
- The top twenty which lists the top 20 Generalized Fermat divisor for several choices of b
- Smallest base values yielding Generalized Fermat Primes by Yves Gallot