Can $2^s+3^s+\cdots +q^s$ , $q$ odd prime , $s\ge 2$ be a perfect power?

Question

Let $q$ be an odd prime and $s\ge 2$ be an integer. Define the sum

$$S(q,s):=\sum_{p\ prime,p\le q} p^s=2^s+3^s+\cdots +q^s$$

Can $S(q,s)$ be a perfect power ? Among other searches, I searched for $s\le 1000$ and $q\le1000$ and did not find an example.