# Definition:Primitive Prime Factor

## Definition

Let $\left\langle{a_n}\right\rangle$ be an integer sequence.

A primitive prime factor for a term $a_n$ is a prime number $p$ of $a_n$ such that:

$p \divides a_n$
$\nexists k \in \Z_{>0}: k < n: p \divides a_k$

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

That is, a prime factor of $a_n$ but of no preceding terms.