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because there is only one factor for 1 and a prime number requires 2
caz many theorem will fail
The fundamental theorem of arithmetic states that you can represent any number uniquely as a product of primes
If 1 were prime, then a number like 12 can be written as
12 = 2*2*3
12 = 1*2*2*3
12 = 1*1*2*2*3
so 12 is being represented as a product of primes but it's not unique.
So make the representation unique, we exclude 1 from being prime
Note: the order of the factors doesn't matter
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Beacause its too COOL
because nothing can go into it besides itself
Every prime number has exactly two factors! For example, 2 is prime because it only has factors 1 and 2. 3 only has factors 1 and 3. 5 only has factors 1 and 5.
Now, most non-primes, it's easy to realize, "Oh, okay, it has more than 2 factors."
1 is the unique case where it has fewer than 2 factors. Just 1 =/