In fact, it doesn't matter whether one is a prime or not, and the distinction is entirely arbitrary. This doesn't stop people from arguing about it heatedly.
The "debate" over one's Prime-ness can be instructive:
Con: "Primes must be divisible by one and itself. Since that implies that one and the number are distinct, one cannot be Prime."
Pro: "One is not divisible by another Integer. Surely it is Prime."
Con: "It must be divisible by two integers! One is..."
And so on
What do we see here? Two arguments which skip past definitions, and jump squarely into the conclusions. Since the debaters haven't agreed on a definition, they could argue all day without producing anything but anger and frustration.
Remember what Voltaire said, "If you would debate me, first define your terms". I can't imagine how many arguments would be instantly resolved by this approach.