New Fibonacci and Lucas primes

被引:10
作者
Dubner, H [1 ]
Keller, W [1 ]
机构
[1] Univ Hamburg, Reg Rechenzentrum, D-20146 Hamburg, Germany
关键词
Fibonacci numbers; Lucas numbers; primality testing; large primes; prime primitive parts; factor tables;
D O I
10.1090/S0025-5718-99-00981-3
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Extending previous searches for prime Fibonacci and Lucas numbers, all probable prime Fibonacci numbers F-n have been determined for 6000 < n less than or equal to 50000 and all probable prime Lucas numbers L-n have been determined for 1000 < n less than or equal to 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 less than or equal to 1000.
引用
收藏
页码:417 / 427
页数:11
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