1. The problem is to understand what prime numbers are. 2. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 3. For example, 2, 3, 5, 7, 11 are prime numbers because they cannot be divided evenly by any other numbers except 1 and themselves. 4. Numbers like 4, 6, 8, 9 are not prime because they have divisors other than 1 and themselves (e.g., 4 is divisible by 2). 5. The smallest prime number is 2, which is also the only even prime number. 6. To check if a number $n$ is prime, you test divisibility by all integers from 2 up to $\sqrt{n}$. 7. If none divide $n$ evenly, then $n$ is prime. 8. This is important in many areas of mathematics and computer science, especially in cryptography.