How many pairs of twin primes are there between the integers 1 to 100?

Options

A. 5
B. 6
C. 7
D. 8

Answer

To find how many pairs of twin primes exist between the integers 1 to 100, we can follow these steps:

### Step 1: Understand Twin Primes
Twin primes are pairs of prime numbers that have a difference of 2. For example, (3, 5) and (11, 13) are pairs of twin primes.

### Step 2: Identify Prime Numbers Between 1 and 100
First, we need to list all the prime numbers between 1 and 100. The prime numbers are:
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

### Step 3: Find Pairs of Twin Primes
Now, we will check the list of prime numbers to find pairs that have a difference of 2:
- (3, 5)
- (5, 7)
- (11, 13)
- (17, 19)
- (29, 31)
- (41, 43)
- (59, 61)
- (71, 73)

### Step 4: Count the Pairs
From the pairs identified, we can count them:
1. (3, 5)
2. (5, 7)
3. (11, 13)
4. (17, 19)
5. (29, 31)
6. (41, 43)
7. (59, 61)
8. (71, 73)

### Conclusion
There are a total of **8 pairs of twin primes** between the integers 1 and 100.

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