Prime Number Identification: Which Number Fits the Definition?

To determine which of the given numbers is a prime number, we need to check each number for divisibility:

• For $9$: It is divisible by $3$ (since $9 \div 3 = 3$), so it is not a prime number.

• For $10$: It is divisible by $2$ (since $10 \div 2 = 5$), so it is not a prime number.

• For $7$: It is only divisible by $1$ and $7$ (itself). It cannot be divided by any other numbers except 1 and itself without leaving a remainder, so $7$ is a prime number.

• For $12$: It is divisible by $2$ (since $12 \div 2 = 6$), so it is not a prime number.

Thus, the only number in the list that satisfies the condition of being prime, having exactly two distinct positive divisors, is $7$.

Therefore, the solution to the problem is $7$.