Answer

Verified

392.4k+ views

**Hint**: In this type of question, students should remember the definition of the term ‘twin prime’. Twin prime are those prime numbers which have a gap of 2 in between them. A prime number is a number which has only 2 factors i.e. 1 and the numbers itself. Let us apply the concepts of prime numbers and twin prime numbers to solve the given question.

**:**

__Complete step-by-step answer__In the question, a list of prime numbers from 100 to 200 is 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. The difference between 103 and 101 is 2. So, $ \left( {101,103} \right) $ is a pair of twin prime numbers.

Consider the numbers 103 and 107. The difference between 103 and 107 is 4. So, $ \left( {107,103} \right) $ is not a pair of twin prime numbers.

Consider the numbers 107 and 109. The difference between 109 and 107 is 2. So, $ \left( {107,109} \right) $ is a pair of twin prime numbers.

Consider the numbers 109 and 113. The difference between 109 and 113 is 4. So, $ \left( {109,113} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 113 and 127. The difference between 113 and 127 is 14. So, $ \left( {113,127} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 127 and 131. The difference between 127 and 131 is 4. So, $ \left( {127,131} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 137 and 131. The difference between 137 and 131 is 6. So, $ \left( {137,131} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 137 and 139. The difference between 137 and 139 is 2. So, $ \left( {137,139} \right) $ is a pair of twin prime numbers.

Consider the numbers 139 and 149. The difference between 139 and 149 is 10. So, $ \left( {139,149} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 149 and 151. The difference between 149 and 151 is 2. So, $ \left( {149,151} \right) $ is a pair of twin prime numbers.

Consider the numbers 157 and 151. The difference between 157 and 151 is 6. So, $ \left( {157,151} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 157 and 163. The difference between 157 and 163 is 6. So, $ \left( {157,163} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 167 and 163. The difference between 167 and 163 is 4. So, $ \left( {167,163} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 167 and 173. The difference between 167 and 173 is 6. So, $ \left( {167,173} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 179 and 173. The difference between 179 and 173 is 6. So, $ \left( {179,173} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 179 and 181. The difference between 179 and 181 is 2. So, $ \left( {179,181} \right) $ is a pair of twin prime numbers.

Consider the numbers 191 and 181. The difference between 191 and 181 is 10. So, $ \left( {191,181} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 191 and 193. The difference between 191 and 193 is 2. So, $ \left( {191,193} \right) $ is a pair of twin prime numbers.

Consider the numbers 197 and 193. The difference between 197 and 193 is 4. So, $ \left( {197,193} \right) $ isn’t a pair of twin prime numbers.

Consider the numbers 197 and 199. The difference between 197 and 199 is 2. So, $ \left( {197,199} \right) $ is a pair of twin prime numbers.

Therefore, the pairs of twin-prime numbers are $ \left( {101,103} \right) $ , $ \left( {107,109} \right) $ , $ \left( {137,139} \right)$ , $ \left( {149,151} \right) $ , $ \left( {179,181} \right) $ , $ \left( {191,193} \right) $ , $ \left( {197,199} \right) $ .

**So, the correct answer is “ $ \left( {101,103} \right) $ , $ \left( {107,109} \right) $ , $ \left( {137,139} \right)$ , $ \left( {149,151} \right) $ , $ \left( {179,181} \right) $ , $ \left( {191,193} \right) $ , $ \left( {197,199} \right) $ .”.**

**Note**: Students often make the mistake of considering a single number as a pair of twin prime numbers. A pair of twin prime numbers consists of two numbers. Students must take utmost care while calculating the difference between the prime numbers and categorise the pair of prime numbers as twin prime numbers only when the difference between the numbers is 2

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Name 10 Living and Non living things class 9 biology CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail