Australian AMC 2014 - Senior Question 28

Let $a_1=2$ and $a_{n+1}=a_n+p_n$ for every positive integer $n$, where $p_n$ is the largest prime factor of $a_n$. The first terms are $2,4,6,9,12,15,20$. What is the largest $n$ for which $a_n$ has four digits?