New Fibonacci and Lucas primes
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- by Harvey Dubner and Wilfrid Keller PDF
- Math. Comp. 68 (1999), 417-427 Request permission
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 $n \le 1000$.References
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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
- Received by editor(s): March 29, 1996
- Received by editor(s) in revised form: April 10, 1997
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1484896