How do I prove if $x$ is an even prime and $x \geq 10$ then $x$ is divisible by 3?

Question

I know that for a number to be divisible by 3 the sum of its digits must be divisible by 3.

It is also known that all primes greater than 2 and 3 are of the form $6k \pm 1$, but I need even primes and this is where I'm stuck.

Answer 1

The set of even primes that are at least $10$ equals the empty set. Every element of the empty set is divisible by $3$.