Answer

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Hint: First, we have to understand what is the meaning of twin prime numbers which is given as “prime number that is either 2 less or 2 more than another prime number”. For example: the twin prime pair is \[\left( 41,43 \right)\] . By using this concept, we can find twin prime numbers between 51 to 100.

Complete step by step answer:

Here, we will understand the meaning of twin prime numbers.

Twin Prime numbers: It is prime that has a prime gap of two. Usually, the pair \[\left( 2,3 \right)\] is not considered to be a pair of twin primes because this pair differs by one gap only. Thus, twin primes are as closely spaced as possible any other two primes.

For example: pairs like \[\left( 3,5 \right),\left( 5,7 \right)\] is the only pair where 3 belongs to both pairs.

Now, first here we should know the prime numbers between 51 to 100. So, it is found as numbers having only two factors i.e. 1 and number itself. Therefore, prime numbers between 51 to 100 as below:

\[\left\{ 53,59,61,67,71,73,79,83,89,97 \right\}\] ………………..(1)

From the above list we have to group those two numbers whose gap is 2 i.e. the gap between 2 numbers should be 2.

So, if we group \[\left( 53,59 \right)\] then the gap is greater than 2 i.e. \[59-53=7\]. Thus, this cannot be grouped together.

Similarly, if we group \[\left( 59,61 \right)\] then the gap is exactly 2 i.e. \[61-59=2\] . Thus, this is our first twin pair.

In the same way, when we do the grouping of 2 numbers and find the difference, we will come to know that there are two twin pairs having the gap of exact 2.

So, those are 2 twin pairs i.e. \[\left( 59,61 \right),\left( 71,73 \right)\] .

Note: Remember that there is minor difference between prime numbers and twin prime numbers. So, do not group all the prime numbers between 51 to 100 and consider it as twin prime numbers which will result as \[\left( 53,59 \right),\left( 61,67 \right),\left( 71,73 \right),\left( 79,83 \right),\left( 89,97 \right)\] . By doing this there will be 5 twin pairs which is wrong. So, do not make this mistake and be clear with understanding of twin prime numbers.

Complete step by step answer:

Here, we will understand the meaning of twin prime numbers.

Twin Prime numbers: It is prime that has a prime gap of two. Usually, the pair \[\left( 2,3 \right)\] is not considered to be a pair of twin primes because this pair differs by one gap only. Thus, twin primes are as closely spaced as possible any other two primes.

For example: pairs like \[\left( 3,5 \right),\left( 5,7 \right)\] is the only pair where 3 belongs to both pairs.

Now, first here we should know the prime numbers between 51 to 100. So, it is found as numbers having only two factors i.e. 1 and number itself. Therefore, prime numbers between 51 to 100 as below:

\[\left\{ 53,59,61,67,71,73,79,83,89,97 \right\}\] ………………..(1)

From the above list we have to group those two numbers whose gap is 2 i.e. the gap between 2 numbers should be 2.

So, if we group \[\left( 53,59 \right)\] then the gap is greater than 2 i.e. \[59-53=7\]. Thus, this cannot be grouped together.

Similarly, if we group \[\left( 59,61 \right)\] then the gap is exactly 2 i.e. \[61-59=2\] . Thus, this is our first twin pair.

In the same way, when we do the grouping of 2 numbers and find the difference, we will come to know that there are two twin pairs having the gap of exact 2.

So, those are 2 twin pairs i.e. \[\left( 59,61 \right),\left( 71,73 \right)\] .

Note: Remember that there is minor difference between prime numbers and twin prime numbers. So, do not group all the prime numbers between 51 to 100 and consider it as twin prime numbers which will result as \[\left( 53,59 \right),\left( 61,67 \right),\left( 71,73 \right),\left( 79,83 \right),\left( 89,97 \right)\] . By doing this there will be 5 twin pairs which is wrong. So, do not make this mistake and be clear with understanding of twin prime numbers.

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