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# Write all the twin prime numbers between 51 to 100.

Last updated date: 20th Sep 2024
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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.

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