Which of the following pair of numbers are not twin prime.
(i) 3, 5 (ii) 161, 163 (iii) 347, 349 (iv) 809, 811 (v) 641, 643

Options

A. (i) & (iv)
B. (ii) & (iii)
C. (iii) & (iv)
D. only (ii)

Answer

To determine which of the given pairs of numbers are not twin primes, we need to understand the definition of twin primes. Twin primes are pairs of prime numbers that have a difference of 2, meaning there is only one composite number between them.

Let's analyze each pair step by step:

1. **Pair (3, 5)**:
- Check if both numbers are prime:
- 3 is a prime number.
- 5 is a prime number.
- Difference: 5 - 3 = 2 (there is only one number, which is 4, between them).
- Conclusion: (3, 5) is a twin prime.

2. **Pair (161, 163)**:
- Check if both numbers are prime:
- 161 is not a prime number (it can be divided by 7, as 161 = 7 × 23).
- 163 is a prime number.
- Since 161 is not prime, this pair cannot be a twin prime.
- Conclusion: (161, 163) is not a twin prime.

3. **Pair (347, 349)**:
- Check if both numbers are prime:
- 347 is a prime number.
- 349 is a prime number.
- Difference: 349 - 347 = 2 (there is only one number, which is 348, between them).
- Conclusion: (347, 349) is a twin prime.

4. **Pair (809, 811)**:
- Check if both numbers are prime:
- 809 is a prime number.
- 811 is a prime number.
- Difference: 811 - 809 = 2 (there is only one number, which is 810, between them).
- Conclusion: (809, 811) is a twin prime.

5. **Pair (641, 643)**:
- Check if both numbers are prime:
- 641 is a prime number.
- 643 is a prime number.
- Difference: 643 - 641 = 2 (there is only one number, which is 642, between them).
- Conclusion: (641, 643) is a twin prime.

### Final Conclusion:
The only pair that is not a twin prime is **(161, 163)**.

---