H. Dubner, Y. Gallot
Apr 1, 2002
Numbers of the form Fb,n = b2n ±1 are called Generalized Fermat Numbers (GFN). A computational method for testing the probable primality of a GFN is described which is as fast as testing a number of the form 2m - 1. The theoretical distributions of GFN primes, for fixed n, are derived and compared to the actual distributions. The predictions are surprisingly accurate and can be used to support Bateman and Horn's quantitative form of "Hypothesis H" of Schinzel and Sierpinski. A list of the current largest known GFN primes is included.