Which among the following pairs of numbers are twin primes?
(a). (9, 11) (b). (13,17), (c). (29,31), (d). (59,61).

Options

A. 9, 11
B. 13, 17
C. 29, 31
D. 59, 61

Answer

To determine which pairs of numbers among the given options are twin primes, we need to first understand what twin primes are. Twin primes are pairs of prime numbers that have a difference of exactly 2.

Let's analyze each option step by step:

### Step 1: Check each pair of numbers for primality and difference
1. **Option (a): (9, 11)**
- Check if 9 is a prime number:
- 9 has factors: 1, 3, 9 (not a prime number).
- Since 9 is not a prime number, (9, 11) cannot be a pair of twin primes.

2. **Option (b): (13, 17)**
- Check if both numbers are prime:
- 13 has factors: 1, 13 (is a prime number).
- 17 has factors: 1, 17 (is a prime number).
- Calculate the difference: 17 - 13 = 4 (not equal to 2).
- Since the difference is not 2, (13, 17) cannot be a pair of twin primes.

3. **Option (c): (29, 31)**
- Check if both numbers are prime:
- 29 has factors: 1, 29 (is a prime number).
- 31 has factors: 1, 31 (is a prime number).
- Calculate the difference: 31 - 29 = 2 (equal to 2).
- Since both numbers are prime and their difference is 2, (29, 31) is a pair of twin primes.

4. **Option (d): (59, 61)**
- Check if both numbers are prime:
- 59 has factors: 1, 59 (is a prime number).
- 61 has factors: 1, 61 (is a prime number).
- Calculate the difference: 61 - 59 = 2 (equal to 2).
- Since both numbers are prime and their difference is 2, (59, 61) is also a pair of twin primes.

### Conclusion
The pairs of numbers that are twin primes from the given options are:
- (29, 31)
- (59, 61)

### Final Answer
The twin prime pairs are (29, 31) and (59, 61).

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