The definition is made for convenience sake based on what it implies. One being prime implies that other primes are evenly divisible by another prime but for some reason that doesn't stop them from being prime. So 1's primeness would have to be special relative to the primality of the other numbers.
Starting the primes at 2 makes all the definitions and implications simple, except for the one caveat that primes start at 2.
Either way you'll have to make a concession, we choose the one that only has to make it once.
The other way around you end up with things like: The square of a natural number is not prime (except 1). The product of two primes is not prime (unless one of them is 1). and so on...
The definition is made for convenience sake based on what it implies. One being prime implies that other primes are evenly divisible by another prime but for some reason that doesn't stop them from being prime. So 1's primeness would have to be special relative to the primality of the other numbers.
Starting the primes at 2 makes all the definitions and implications simple, except for the one caveat that primes start at 2.
Either way you'll have to make a concession, we choose the one that only has to make it once.
The other way around you end up with things like: The square of a natural number is not prime (except 1). The product of two primes is not prime (unless one of them is 1). and so on...