Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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: Extending previous searches for prime Fibonacci and Lucas numbers, all probable prime Fibonacci numbers $F_{n}$ have been determined for $6000 < n \le 50000$ and all probable prime Lucas numbers $L_{n}$ have been determined for $1000 < n \le 50000$. A rigorous proof of primality is given for $F_{9311}$ and for numbers $L_{n}$ with $n = 1097$, $1361$, $4787$, $4793$, $5851$, $7741$, $10691$, $14449$, the prime $L_{14449}$ having 3020 digits. Primitive parts $F^{*}_{n}$ and $L^{*}_{n}$ of composite numbers $F_{n}$ and $L_{n}$ 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 $F_{n}$ and $L_{n}$ are given for $n > 1000$ as far as they have been completed, adding information to existing factor tables covering $n \le 1000$.

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Additional Information

Harvey Dubner
Affiliation: 449 Beverly Road, Ridgewood, New Jersey 07450

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

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