elementary number theory - If $a^2 + 1$ is prime then the unitary digit of $a$ must be either of 4,6 or 0 for $forall a geq 3 in mathbb{N}$.

Let $a \geq 3$ and suppose $a^2 + 1$ is a prime number. How do I prove the unitary digit of $a$ must be one of $6, 4$ or $0$. I can see it's true for $a^2+1=17, 37, 101, 197, 257...$etc. where the $10^0$ digit of $a$ is $6, 4$ or $0$ and the pattern repeats but how do I show this and formulate it into a proof using modular arithmetic?