It is mainly a matter of convenience not to call 1 a prime. Otherwise many theorems involving prime numbers would have to say "excluding 1". For example every integer can be expressed uniquely as a product of powers of primes. If you included 1, you would have to say "except 1" to have uniqueness.
Oh okay, that makes sense. Does anyone have any reading suggestions on primes specifically. I just started reading "Elementary Theory of Numbers" by LeVeque. Any critiques on this, or pointers to another text perhaps?