Anyways, about numbers and logic: why does a set of symbols, the Arabic numerals, have a logic that we can't write an explicit formula for--prime numbers--and why is primality defined by division or a set of divisors?

So we can write: If n is prime, then the divisors of n are 1 and n, and no other numbers.

Since it's symmetric we also have: If n and 1 are the only divisors of n then n is prime.

This is more or less useless if we have a number, n, and want to know if it's prime. We need more logic!