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human
Prime numbers are positve integers that are divisible without remainder by exactly two different positive integers.

Since every positive integer is divisible by 1 and itself, every prime number has a minimal number of divisors: 2.

Since 1 only has one divisor it's not prime.

This is not completely formally correct but should cover the idea of it.

Edit:
The exclusion of 1 isn't arbitrary. Primes are supposed to be the building blocks of multiplication. Every positive integer can be written as *unique* product, where all factors are prime.

1 doesn't do any building. It's the multiplication equivalent of adding zero.
Calling it a prime wouldn't make sense.
gpt
Ok, this explanation is kinda making more sense to me. Although my gut is still telling me that 1 is being cheated out of its primacy, and I think we can all agree that math is mostly about going with your gut feelings.