Prime Number Identification: Testing Number Properties

To solve this problem, we identify which of the given numbers is a prime number.

Let's evaluate each provided number:

• $13$: This number is only divisible by 1 and 13 itself. Therefore, 13 is a prime number.

• $12$: This number is divisible by 1, 2, 3, 4, 6, and 12. Since it has divisors other than 1 and itself, it is not prime.

• $15$: This number is divisible by 1, 3, 5, and 15. Since it has divisors other than 1 and itself, it is not prime.

• $4$: This number is divisible by 1, 2, and 4. Since it has divisors other than 1 and itself, it is not prime.

Therefore, the only prime number among the choices is $13$.