A factor of a number M is a number that evenly divides M with no remainder. Zero has infinitely many factors, definitely not prime.

...regarding -1, I can't think of anything relevant that I know about the relationship between negative numbers and prime numbers.

Later edit: Then I completely changed my mind... and decided 0 and -1 should be prime relative to how I would define it's essence. I note that you intuited what I really meant by prime better than I did!