Home
Search Site
Largest
Finding
How Many?
Mersenne
Glossary
Prime Curios!
email list
FAQ
Prime Lists
Titans
Submit primes

This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 DG2000
 H. Dubner and Y. Gallot, "Distribution of generalized Fermat prime numbers," Math. Comp., 71 (2002) 825832. MR 2002j:11156
Abstract:
Numbers of the form F_{b,n}=b^{2n}+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 2^{m}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.
