Things change.
1 was considered a Prime, now it isn't. That wasn't for fun, but for valid mathematical reasons.
So the definition of Primes changed to match. 1 is no longer considered Prime.
You've admitted "whole" should be added to the "simplest" defintion you provided.
To claim that just one
more word ("distinct") should
not be added is simply tilting at windmills.
http://wiki.answers.com/Q/Why_is_1_not_a_prime_number
Quote:
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If 1 is not a prime number, then any composite number (such as 12) can be written as a product of primes in only one way (here, 2*2*3), not counting different orders. However, if 1 were a prime number, there would be infinitely many ways! We could write 12 for example, as 2*2*3, or 1*2*2*3, or 1*1*1*1*1*2*2*3. Having only one way to write a number as a product of primes is very useful when doing math.
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http://mathworld.wolfram.com/PrimeNumber.html
Quote:
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...it requires special treatment in so many definitions and applications involving primes greater than or equal to 2 that it is usually placed into a class of its own.
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http://primes.utm.edu/notes/faq/one.html
etc.