# Definition:Primitive Prime Factor of Fibonacci Number

## Definition

Let $F_n$ denote the $n$th Fibonacci number.

A primitive prime factor of $F_n$ is a prime number $p$ of $F_n$ such that:

$p \divides F_n$
$\nexists k \in \Z_{>0}: k < n: p \divides F_k$

where $a \divides b$ denotes that $a$ is a divisor of $b$.

That is, a prime factor of $F_n$ but of no smaller Fibonacci numbers.