finding $n$ consecutive composite Fibonacci numbers.

Question

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

Answer 1

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

http://en.wikipedia.org/wiki/Fibonacci_number

So you should simply take n consecutive composite indexes.