What are co-primes ? Write all the pairs of twin primes between 50 and 100.

Answer

### Step-by-Step Solution:

1. **Understanding Co-prime Numbers:**
- Co-prime numbers are defined as two numbers that have no common factors other than 1. This means their greatest common divisor (GCD) is 1.
- Example: The numbers 2 and 3 are co-prime because their only common factor is 1.

2. **Understanding Twin Prime Numbers:**
- Twin prime numbers are pairs of prime numbers that have a difference of 2. This means if one prime number is \( p \), the other will be \( p + 2 \).
- Example: The pair (3, 5) is a twin prime pair because both numbers are prime and their difference is 2.

3. **Finding Twin Primes Between 50 and 100:**
- We need to identify all the prime numbers between 50 and 100 first.
- The prime numbers in this range are: 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
- Now, we will check for pairs of these prime numbers that have a difference of 2:
- (59, 61) → Both are prime and differ by 2.
- (71, 73) → Both are prime and differ by 2.
- Therefore, the twin prime pairs between 50 and 100 are (59, 61) and (71, 73).

### Final Answer:
- Co-prime numbers are those that have a common factor of 1.
- The pairs of twin primes between 50 and 100 are (59, 61) and (71, 73).

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