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A prime number is a number that has exactly two factors. 2 is the only even prime number - it has the factors 1 and 2. Contrary to popular belief, 1 is not a prime number as it has only one factor, 1. I so often hear people -even Mathematicians! - define a prime number as a number that is divisible only by itself and 1. That's not correct, since under that definition, 1 would be prime, which it's not.What makes a number prime, anyway?
This is true. But how do you know there are an infinite number of numbers? Doesn't that also need to be proved?(In response, however, I would think that given the definition of what a prime number is, it would be broad enough to yield an infinite number of results given an infinate number of candidates. The value set would just approach infinity at a slower rate than that of the field of candidates.)