Of course it depends on the definition but none of the ones still in use consider it a prime. It's kind of hard to nail down precisely why, the best I've been

Of course it depends on the definition but none of the ones still in use consider it a prime. It's kind of hard to nail down precisely why, the best I've been able to come up with is that Z/(p) is an integral domain for all primes p (and this is roughly equivalent to the definition of a prime) but not for p=1. Furthermore if you then plough on and redefine the Z/(1) i.e. zero ring to be an integral domain it becomes a pain to construct its field of fractions. Arguably 0 is a better prime, as it is a prime element.