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

Question

Accepted Answer

Twin primes are pairs of prime numbers that have a difference of two. To determine how many pairs of twin primes exist between the integers 1 to 100, we need to identify all the prime numbers in this range and then find the pairs that satisfy the twin prime condition.

Let's list the prime numbers between 1 and 100:
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

Now, let's identify the twin prime pairs:
1. (3, 5)
2. (5, 7)
3. (11, 13)
4. (17, 19)
5. (29, 31)
6. (41, 43)
7. (59, 61)
8. (71, 73)

There are 8 pairs of twin primes between 1 and 100. Therefore, Option 4 is correct.

Explanation for why each of the other options is incorrect:
- Option 1 (5 pairs): This option is incorrect because there are more than 5 pairs of twin primes in the given range.
- Option 2 (6 pairs): This option is incorrect because there are more than 6 pairs of twin primes in the given range.
- Option 3 (7 pairs): This option is incorrect because there are more than 7 pairs of twin primes in the given range.

In conclusion, the correct answer is Option 4, as there are exactly 8 pairs of twin primes between the integers 1 and 100.