Question 3
Suppose $\overline{a_1a_2\ldots a_{2009}}$ is a $2009$-digit integer such that for each $i=1,2,\ldots,2007$, the $2$-digit integer $\overline{a_i a_{i+1}}$ contains $3$ distinct prime factors. Find $a_{2008}$.
(Note: $\overline{xyz\ldots}$ denotes an integer whose digits are $x,y,z,\ldots$.)
(Note: $\overline{xyz\ldots}$ denotes an integer whose digits are $x,y,z,\ldots$.)