New Fibonacci and Lucas primes

Authors:
Harvey Dubner and Wilfrid Keller

Journal:
Math. Comp. **68** (1999), 417-427

MSC (1991):
Primary 11A51; Secondary 11B39, 11--04

Supplement:
Additional information related to this article.

MathSciNet review:
1484896

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Abstract | References | Similar Articles | Additional Information

Abstract: Extending previous searches for prime Fibonacci and Lucas numbers, all probable prime Fibonacci numbers have been determined for and all probable prime Lucas numbers have been determined for . A rigorous proof of primality is given for and for numbers with , , , , , , , , the prime having 3020 digits. Primitive parts and of composite numbers and have also been tested for probable primality. Actual primality has been established for many of them, including 22 with more than 1000 digits. In a Supplement to the paper, factorizations of numbers and are given for as far as they have been completed, adding information to existing factor tables covering .

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Additional Information

**Harvey Dubner**

Affiliation:
449 Beverly Road, Ridgewood, New Jersey 07450

Email:
70327.1170@compuserve.com

**Wilfrid Keller**

Affiliation:
Regionales Rechenzentrum der Universität Hamburg, 20146 Hamburg, Germany

Email:
keller@rrz.uni-hamburg.de

DOI:
http://dx.doi.org/10.1090/S0025-5718-99-00981-3

Keywords:
Fibonacci numbers,
Lucas numbers,
primality testing,
large primes,
prime primitive parts,
factor tables

Received by editor(s):
March 29, 1996

Received by editor(s) in revised form:
April 10, 1997

Article copyright:
© Copyright 1999
American Mathematical Society