Distribution of generalized Fermat prime numbers
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- by Harvey Dubner and Yves Gallot PDF
- Math. Comp. 71 (2002), 825-832 Request permission
Abstract:
Numbers of the form $F_{b,n}=b^{2^n}+1$ 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 Sierpiński. A list of the current largest known GFN primes is included.References
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Additional Information
- Harvey Dubner
- Affiliation: 449 Beverly Road, Ridgewood, New Jersey 07450
- Email: hdubner1@compuserve.com
- Yves Gallot
- Affiliation: 12 bis rue Perrey, 31400 Toulouse, France
- Email: galloty@wanadoo.fr
- Received by editor(s): October 13, 1999
- Received by editor(s) in revised form: July 10, 2000
- Published electronically: May 17, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 825-832
- MSC (2000): Primary 11Y11; Secondary 11A41
- DOI: https://doi.org/10.1090/S0025-5718-01-01350-3
- MathSciNet review: 1885631