Strictly speaking, the moment you ask "Is -2 prime?" you are asking a fundamentally different question from "is 2 prime?" because -2 is not in N = {0?, 1, 2, 3, ...}, the set over which the notion "prime" is defined.
There is a more general notion of primes which can be applied to any ring (a set with "addition-like" and "multiplication-like" operations). That is the notion of "prime ideals": https://en.wikipedia.org/wiki/Prime_ideal
On this account, there are "primes" for Z, and -2 is the "same prime" as 2.
Another definition[1] of prime in an arbitrary ring is
p is prime if and only if p|ab implies p|a or p|b
which is equivalent to the prime ideal concept. Interestingly, these definitions mean that 0 is actually a prime in Z!
As explanation: the only number 0 divides is 0, and Z is an integral domain[2], i.e. ab = 0 implies a = 0 or b = 0, thus 0 divides at least one of a and b if 0 divides ab.
http://www.wolframalpha.com/input/?i=-2+prime