if you use a poor definition such as, "Prime is a number that is only divisible by itself and 1."

I have a fondness for this particular definition, and like to think of 1 as a "very special" prime number. To the extent that I usually give a little speech whenever an opportunity arises that (ahem) the only reason I know of that '1' is excluded from the primes (more often than not) is because almost every theorem about prime numbers would have to be modified with an "except 1" clause. But a natural definition (anything along the lines of "already completely factored") would include it. If you disagree, which definition --- or the satisfaction of which theorem -- do you think is more compelling?

(Just in case you perceived you were getting too much heat about "colour"...)