generalized Fermat number (another Prime Pages' Glossary entries)
 Glossary: Prime Pages: Top 5000: The numbers Fb,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.2m+1 with k odd and m > n. (When b is even, many of these properties are are shared by the numbers Fb,n/2.) On the rare occasion that these generalized Fermat numbers are prime, they are call generalized Fermat primes. See Also: Fermats, GeneralizedFermatPrime, Cullens, MersennesRelated pages (outside of this work) The generalized Fermats on the list of 5000 largest known primesReferences: BR98 A. Björn and H. Riesel, "Factors of generalized Fermat numbers," Math. Comp., 67 (1998) 441--446.  MR 98e:11008 (Abstract available) DG2000 H. Dubner and Y. Gallot, "Distribution of generalized Fermat prime numbers," Math. Comp., 71 (2002) 825--832.  MR 2002j:11156 (Abstract available) DK95 H. Dubner and W. Keller, "Factors of generalized Fermat numbers," Math. Comp., 64 (1995) 397--405.  MR 95c:11010 Dubner86 H. Dubner, "Generalized Fermat primes," J. Recreational Math., 18 (1985-86) 279--280.  MR 2002j:11156 RB94 H. Riesel and A. Börn, Generalized Fermat numbers.  In "Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics," W. Gautschi editor, Proc. Symp. Appl. Math. Vol, 48, Amer. Math. Soc., 1994.  Providence, RI, pp. 583-587, MR 95j:11006 Chris K. Caldwell © 1999-2018 (all rights reserved)