What defines prime numbers?

Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. This definition leads to the conclusion that prime numbers are always positive, as negative numbers and zero do not meet the requirement of being greater than 1.

While it is true that the only even prime number is 2, which is also the smallest prime number, all other primes are odd. Therefore, prime numbers cannot be classified as always even, ruling out that option. The notion that they can be even or odd is partially correct, but it does not define prime numbers, since the majority of primes are not even.

Ultimately, the defining quality of prime numbers is their positivity, which is captured by stating that they are always positive. This characteristic sets the foundation for understanding primes within the broader context of number theory.