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Not to be a "pile on", but Numberphile did a great video on why 1 is not prime. http://www.youtube.com/watch?v=IQofiPqhJ_s

I understand "we got tired of saying 'excluding 1'", but I still don't grasp how the product of zero primes is 1 and not 0.

1 is the multiplicative identity. If you were to write a for loop calculating the product of a list of ints, what would be the initial value for the accumulator?

Multiplying 0 times is the "same" as raising something to the 0 power.

Oh, of course. x exp. 0 == 1. I got that he was using powers but my brain didn't equate 2 exp. 0 with how he explained it for some reason.

1 is not considered prime.

One is not prime.

http://primes.utm.edu/notes/faq/one.html

I think it depends on what school of thought you are coming from, but generally 1 is not considered a prime.

I haven't read the paper, but in other 'fun with primes' exercises, 1 is often excluded.