* Find all prime numbers $p$ such that $4 p^{2}+1$ and $6 p^{2}+1$ are also prime.
When $p \equiv \pm 1(\bmod 5)$, $5 \mid 4 p^{2}+1$. When $p \equiv \pm 2(\bmod 5)$, $5 \mid 6 p^{2}+1$. Therefore, the only solution to this problem is $p=5$.