New Fibonacci and Lucas primes

Abstract

Abstract. Extending previous searches for prime Fibonacci and Lucas num-

Primes in Elliptic Divisibility Sequences

“…So far, there is a shortage of proofs for prime appearance in linear recurrence sequences, but there are some heuristic arguments and some compelling data. See [18] for heuristic arguments concerning the Mersenne sequence, and [5] for recent work on other classical sequences. The heuristics agree with the data, although there is not a lot of data for the Mersenne sequence, only 38 Mersenne primes being known.…”

Algebraic Divisibility Sequences Over Function Fields

“…More generally, most integer Lucas sequences are expected to have infinitely many prime terms [8,17,25]. The only obvious exceptions occur with a type of generic factorization [13].…”

The Little Book of Bigger Primes

“…From the published work I mention Jarden's book of 1958, its third edition, revised and enlarged by Brillhart (1973), and the papers by , and by Dubner & Keller (1999). The current state of our knowledge is as follows.…”

“…On the other hand, it was proved by Sellers & Williams (2002) that the sequence (W n ) n≥0 (and many other similar sequences) contain infinitely many composite numbers. In 1999, H. Dubner determined that in the interval 2000 < p < 80000, S p is a probable prime (PRP) for p = 6689, 8087, 9679, 28953, 79043, and for no other prime p in that interval. The following values of p < 2000 yield prime NSW numbers S p : p = 3, 5, 7, 19, 29, 47, 59, 163, 257, 421, 937, 947, 1493, 1901. F. Morain has shown in 1989 that the last two values in fact yielded primes.…”