Proof Writing & Problem Solving · Superchallenge problem

The numbers $31$, $331$, $3331$, $33331$, $333331$, $3333331$ and $33333331$ are all prime, which suggests that every number written as some $3$s followed by a $1$ is prime. The next one, $333333331$ (eight $3$s and then a $1$), is not. What is its smallest prime factor?