ON PRIMES IN THE FIBONACCI SEQUENCE
It is well known that primes can occur in the Fibonacci sequence only for prime indices, the
only exception being F4 = 3. This follows from the fact that for any two positive integers k and n,
Fn divides Fkn. I could not locate the earliest reference to that result, but page 111 in [1] contains
several proofs of this. Of course, if/? is a prime, Fp may very well be composite; the first example
of this is F19 =4181 = 37-113. Here isthe list of the next few terms Fp that are composite: