7. $p$ is a prime number greater than 5, the remainder when $p^{2}$ is divided by 30 is
7. 1 or 19 Hint: It is easy to know $p \equiv 1,7,11,13,17,19,23$ or $29(\bmod 30)$.

So $p^{2} \equiv 1$ or $19(\bmod 30)$.
When $p=31$, $p^{2} \equiv 1(\bmod 30)$,
When $p=67$, $p^{2} \equiv 19(\bmod 30)$.