How are prime numbers defined?

Prime numbers are defined specifically as numbers greater than one that have exactly two distinct positive factors: one and the number itself. This means that a prime number cannot be evenly divided by any other integer except for these two. For example, the number 5 is prime because it can only be divided by 1 and 5 without resulting in a fraction, while the number 4 is not prime since it can be divided evenly by 1, 2, and 4, giving it more than two factors.

The other options do not accurately describe prime numbers. The first option incorrectly implies that prime numbers can be divisible by any integer, which contradicts their definition. The third choice states that all even numbers are prime; however, the only even prime number is 2, as all other even numbers can be divided by 2 and thus have more than two factors. The last option suggests that prime numbers can have multiple factors beyond just one and themselves, which again misaligns with the definition of a prime number.