# finding $n$ consecutive composite Fibonacci numbers.

For each $n$, How can we find $n$ consecutive composite Fibonacci numbers?

• Know any sufficient conditions for $F_n$ to be composite? – Erick Wong May 31 '14 at 10:15
• @ErickWong No, I don't know. – user118535 May 31 '14 at 10:18
• Now you do, after DenisMath's answer :). – Erick Wong May 31 '14 at 10:19
• For $F_n$ if $n$ is composite, $F_n$ is composite. Except $n = 4$ and $n = 1$ – Dane Bouchie Jun 21 '14 at 2:13

$F_{kn}$ is divisible by $F_n$, so, apart from $F_4 = 3$, any Fibonacci prime must have a prime index.