Following are the prime numbers between 100 and 200. Find the pair of twin prime numbers from the following prime numbers.
101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

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109, 139

131, 173

101, 157

197, 199

answer is D.

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Detailed Solution

Concept- Students should recall the definition of the phrase "twin prime" before answering this sort of question. Twin primes are prime numbers that have a two-digit difference between them. A prime number is one with only two elements, one and the number itself. Let us tackle the above problem using the notions of prime numbers and twin prime numbers.
In the question, prime numbers from 100 to 200 are given.
They are as follows: 101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191, 193, 197, 199 .
Let us check the difference between these prime numbers.
Consider the numbers 101 and 103 . Their difference is 2 . So, the pair of twin prime numbers (101, 103) is a pair.
Consider the numbers 103 and 107 . Their difference is 4 . So, (107, 103) is not a possible pair of twin prime numbers.
Consider the numbers 107 and 109 . Their difference is 2 . So,

is not a possible pair of twin prime numbers.
Consider the numbers 109 and 113 . Their difference is 4 . So,

is not a possible pair of twin prime numbers.
Consider the numbers 113 and 127 . Their difference is 14 . So,

is not a possible pair of twin prime numbers.
Consider the numbers 127 and 131 . Their difference is 4 . So, (127, 131) is not a possible pair of twin prime numbers.
Consider the numbers 137 and 131 Their difference is 6 . So, (137, 131) is not a possible pair of twin prime numbers.
Consider the numbers 137 and 139 . Their difference is 2 . So,

is a pair of twin prime numbers.
Consider the numbers 139 and 149 . Their difference is 10 . So,

is not a possible pair of twin prime numbers.
Consider the numbers 149 and 151 . Their difference is 2 . So,

is a pair of twin prime numbers.
Consider the numbers 157 and 151 . Their difference is 6 . So, (157, 151) is not a possible pair of twin prime numbers.
Consider the numbers 157 and 163 . Their difference is 6 . So, (157, 163) is not a possible pair of twin prime numbers.
Consider the numbers 167 and 163 . Their difference is 4 . So, (167, 163) is not a possible pair of twin prime numbers.
Consider the numbers 167 and 173 . Their difference is 6 . So,

is not a possible pair of twin prime numbers.
Consider the numbers 179 and 181 . Their difference is 2 . So,

is a pair of twin prime numbers.
Consider the numbers 191 and 181 . Their difference is 10 . So, (191, 181) is not a possible pair of twin prime numbers.
Consider the numbers 191 and 193 . Their difference is 2 . 191, 193 are hence a pair of twin prime numbers.
Consider the numbers 197 and 193. Their difference is 4 . So, (197, 193) is not a possible pair of twin prime numbers.
Consider the numbers 197 and 199 . Their difference is 2 . Thus, the pair of twin prime numbers (197, 199) is a pair.
So, the pairs of twin-prime numbers are

,
So, the correct answer is "

Hence, the correct answer is option 4.

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