8. Given that $S$ is an infinite subset of the set of positive integers, satisfying that for any $a, b, c \in S, a b c \in S$, the elements of $S$ are arranged in ascending order to form the sequence $\left\{a_{n}\right\}$, and it is known that $a_{1}=2, a_{2031}=2^{4061}$, then $a_{2017}=$ $\qquad$ .
According to the problem, $a_{2}=a_{1}^{3}=2^{3}, a_{3}=a_{1}^{2} \cdot a_{2}=2^{5}, a_{4}=a_{1}^{2} \cdots a_{3}=2^{7}, \cdots, a_{n}=2^{2 n-1}$.
Verification shows that $a_{2031}=2^{4061}$ meets the conditions. Therefore, $a_{2017}=2^{4033}$.