eli5-Why is the number 1 not considered a prime number even though there isn’t any number that divides it?
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A basic philosophy in math is that facts should be such that you don’t have to always refer to exceptions. For example, “any number can be factored uniquely into primes” is a perfectly beautiful fact if you do not include 1 as a prime. However, if you include 1 as a prime you now need to say “any number can be factored uniquely except for multiplication by some number of 1’s.”
This also leads us to question defining primes as numbers that cannot be further divided. In doing so we realize that 1 is quite different from all the other primes, so maybe this is not the best definition of prime! Then we try to figure out a better definition of prime that excludes 1.
The fact that primes cannot be further subdivided then becomes a result of the actual definition of prime, and this property just happens to be shared by the number 1.
This is often how mathematics is done. We define something and learn some cool stuff, then realize our definition isn’t the best choice because the resulting facts are not clean.
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