How many twins’ prime numbers pairs are there between 51 to 100?

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answer is D.

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Detailed Solution

Concept- The definition of twin prime numbers, which is stated as "a prime number that is either two less or two more than another prime number," must first be understood. The twin prime pair, for instance, is (41,43). This idea allows us to locate twin prime numbers in the range of 51 to 100.
Here, we shall learn what twin prime numbers mean.
Twin prime pairs- Pair of prime numbers which has a prime gap of two is twin prime pair. The pair

is typically not regarded as a pair of twin primes because there is just one gap between them. Twin primes are therefore the closest to one another of any other pair of primes.
For example - Pairs like

is the only pair in which 3 is a member of both pairs.
Let's first review the prime numbers between 51 and 100. As we know a prime number is a number which has only two factors namely 1 and itself. Prime numbers between 51 and 100 are as follows:

From the list above, we must group the pairs of numbers whose distance is two, i.e., the distance between two numbers should be two.
Therefore, if we group

, the distance is more than 2, or

. Therefore, these cannot be combined.
Similar to the previous example, if we group

, the gap is exactly 2, or

. So, this is our first set of twins.
Similar to how grouping two integers and calculating the difference will reveal the existence of two twin pairs with an exact two-digit gap.
Thus, two twin pairs are