Question

An example for twin primes is
(a) 5, 11
(b) 3, 5
(c) 11, 17
(d) 3, 7

Answer 1

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 pairs.

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.
From the above option list, we have to see whose gap is 2 i.e. the gap between 2 numbers should be 2.
So, if we take option (a): 5, 11 then the gap is greater than 2 i.e. \[11-5=6\]. Thus, this cannot be a twin pair.
Similarly, if we take option (b): 3, 5 then the gap is exact 2 i.e. \[5-3=2\] . Thus, this is our twin pair.
We take option (c): 11, 17 then the gap is greater than 2 i.e. \[17-11=6\] . Thus, this cannot be a twin pair.
We take option (d): 3, 7 then the gap is greater than 2 i.e. \[7-3=4\] . Thus, this cannot be a twin pair.
So, only option (b) is the correct answer.

Note: Remember that there is minor difference between prime numbers and twin prime numbers. In the option all the pairs are of prime numbers only, but we have to find a twin prime pair. So, be clear with the concept of both prime and twin prime and then select the correct answer.