3. Suppose $\overline{a_{1} a_{2} \ldots a_{2009}}$ is a 2009-digit integer such that for each $\dot{i}=1,2, \ldots, 2007$, the 2-digit integer $\overline{a_{i} a_{i+1}}$ contains 3 distinct prime factors. Find $a_{2008}$. (Note: $x y z \ldots$ denotes an integer whose digits are $x, y, z, \ldots$ )
3. Two-digit numbers which contain three distinct prime factors are:
$$
30=2 \cdot 3 \cdot 5,42=2 \cdot 3 \cdot 7,60=4 \cdot 3 \cdot 5,66=2 \cdot 3 \cdot 11,70=2 \cdot 5 \cdot 7,78=2 \cdot 3 \cdot 13,84=4 \cdot 3 \cdot 7
$$

From here, we conclude that $a_{i}=6$ for $i=1,2, \ldots, 2007$ and $a_{2008}$ is either 6 or 0 .