Yes, you are correct.

Explanation:

• Two distinct prime numbers are always coprime: If you have two distinct prime numbers, say $p_1$ and $p_2$, then their only common divisor is 1. This is because the only divisors of a prime number are 1 and the number itself. Since $p_1$ and $p_2$ are distinct, they cannot divide each other, so their greatest common divisor (GCD) is 1. Thus, they are coprime.

• The converse is not true: The converse would state that if two numbers are coprime, then they must be prime. However, this is not true. For example, consider the numbers 8 and 15. These numbers are coprime because their GCD is 1, but neither 8 nor 15 is a prime number (8 is divisible by 2 and 15 is divisible by 3 and 5). Therefore, the converse statement is false.

Would you like more details on this topic or have any questions?

Here are some related questions:

1. What is the definition of a coprime number?
2. How can you determine if two numbers are coprime?
3. Can the product of two prime numbers be coprime with another number?
4. Are there any special properties of numbers that are coprime with each other?
5. Can two composite numbers be coprime?

Tip: When checking if two numbers are coprime, the quickest method is to find their greatest common divisor (GCD). If the GCD is 1, they are coprime.