Which of the following pairs are twin primes? a. (19, 21) c. (39, 41) b. (29, 31) d. (49, 51)

To determine which pairs are twin primes, we first need to check whether both numbers in the pair are prime, and then check if their difference is 2. Twin primes are pairs of prime numbers whose difference is exactly 2.

Let's check each pair:

1. **(19, 21)**:
   - 19 is a prime number.
   - 21 is not a prime number (it's divisible by 3 and 7).
   - Therefore, this pair is **not twin primes**.

2. **(29, 31)**:
   - 29 is a prime number.
   - 31 is also a prime number.
   - The difference between 31 and 29 is 2.
   - Therefore, this pair **is twin primes**.

3. **(39, 41)**:
   - 39 is not a prime number (it's divisible by 3 and 13).
   - 41 is a prime number.
   - Since 39 is not a prime, this pair is **not twin primes**.

4. **(49, 51)**:
   - 49 is not a prime number (it's \(7^2\)).
   - 51 is also not a prime number (it's divisible by 3 and 17).
   - Therefore, this pair is **not twin primes**.

### Conclusion:
The only twin prime pair is **(29, 31)**.

Would you like further details or have any questions? 

Here are 5 related questions:
1. What are the smallest twin primes?
2. Can twin primes be consecutive numbers?
3. Are there infinitely many twin primes?
4. How do we determine if a number is prime?
5. What are the largest known twin primes?

**Tip**: A number is prime if it has no divisors other than 1 and itself.

Explore how to identify twin primes by checking prime number pairs. This problem covers key number theory concepts, focusing on prime numbers and twin primes, and is suitable for Grades 6-8.

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