Results

**1 - 1**of**1**### On the primality of F 4723 and F 5387

, 1999

"... Introduction We follow the notations of both [2] and [3]. Let F n (resp. L n ) be the n-th Fibonacci number (resp. Lucas number). The aim of this informal note is to describe a short proof of primality for both F 4723 and F 5387 . See the paper [5] for more on this topic. 2 F 4723 From [3, (4.1)], ..."

Abstract
- Add to MetaCart

Introduction We follow the notations of both [2] and [3]. Let F n (resp. L n ) be the n-th Fibonacci number (resp. Lucas number). The aim of this informal note is to describe a short proof of primality for both F 4723 and F 5387 . See the paper [5] for more on this topic. 2 F 4723 From [3, (4.1)], one has F 4k+3 \Gamma 1 = F k+1 L k+1 L 2k+1 : (1) Here k = 1180, k + 1 = 1181 and 2k + 1 = 2361 = 3 \Theta 787. From [3] and with the help of factors found by Montgomery and Silverman [7, 8, 9], we get F 1181 = 5453857 \Theta C 240 ; L 1181 = 59051 \Theta<F27.43