Prime numbers

The convention is that primes are restricted to the positive integers. A check of the primality of $-3$ on WolframAlpha confirms this convention, as does this link . Thus I believe that the answer is $1.$ (I'm sorry that I've reported your question, but I find that reporting is the quickest way to resolve any concerns.)

That being said, the reason that $3$ is the only such prime derives from the fact that if the sum of the digits of an integer is divisible by $3$ then the integer itself must also be divisible by $3.$ Proofs of this fact are given here .