Which of the following is a pair of twin-prime number?

Options

A. 19, 21
B. 43, 47
C. 59, 61
D. 73, 79

Answer

To determine which of the following is a pair of twin-prime numbers, we first need to understand what twin-prime numbers are. Twin-prime numbers are pairs of prime numbers that have a difference of 2.

Let's analyze the options given:

1. **Option 1: 19 and 21**
- Check if both numbers are prime:
- 19 is a prime number.
- 21 is not a prime number (it can be divided by 3 and 7).
- Since one of the numbers is not prime, this pair cannot be a twin prime.

2. **Option 2: 43 and 41**
- Check if both numbers are prime:
- 43 is a prime number.
- 41 is also a prime number.
- Now, calculate the difference:
- Difference = 43 - 41 = 2.
- Since both numbers are prime and their difference is 2, this pair is a twin prime.

3. **Option 3: 59 and 61**
- Check if both numbers are prime:
- 59 is a prime number.
- 61 is also a prime number.
- Now, calculate the difference:
- Difference = 61 - 59 = 2.
- Since both numbers are prime and their difference is 2, this pair is also a twin prime.

4. **Option 4: 73 and 79**
- Check if both numbers are prime:
- 73 is a prime number.
- 79 is also a prime number.
- Now, calculate the difference:
- Difference = 79 - 73 = 6.
- Since the difference is not 2, this pair cannot be a twin prime.

After analyzing all the options, we find that the pairs of twin-prime numbers are **59 and 61**.

### Final Answer:
The pair of twin-prime numbers is **59 and 61**.