Who wrote these rules?
Why? One, is not prime. A prime is defined to be any natural number whose only integral divisors are one and itself, and is not one. So obviously, one is not prime. But why? A lot of math brain is to appeal to authority, and stop caring about that sub-problem. Sometimes you have to stop and ask why. Who came up with these rules, and are they any good? My guess is that one is not prime because its more useful this way. One is actually a pretty boring number, and we don’t actually care about its primality. So we can make some small sacrifice so other things work out smoother.
Consider the fundamental theorem of arithmetic. Every natural number has a UNIQUE prime factorization. However, One divides every number any number of times, so we lose this uniqueness property. So? Why do we care about having our factorizations unique? Who asked? The point I am trying to make is, mathematics has a lot of beauty, pattern matching in nature etcetc. But its viewed through rose colored spectacles which make things appear more beautiful and aesthetically pleasing than they actually are. Whenever anyone thinks that prime numbers are so cool, the next thought is some admiration for nature. My point is that yea prime numbers are cool, but explicitly because we made them cool, they weren’t found like that. Actually I think nature is pretty boring. Ever seen a pile of rocks?