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