Question

The two consecutive prime numbers with difference 2 are called
(a) Co – primes
(b) Twin primes
(c) Composite
(d) None

Answer 1

Hint: First of all, try to recollect the definition of each type of numbers like co-primes, twin prime, composite, etc. and then check which numbers have a similar definition as given in the question.

Complete step-by-step answer:
In this question, we have to tell what the two consecutive prime numbers with a difference of 2 are called among co-primes, twin primes, and composite numbers. Before proceeding with the question, let us talk about a few terms.
1) Prime number: Prime numbers are the positive integers greater than 1 having only two factors, 1 and the integer itself - 2, 3, 5, 7 are few first prime numbers we have. Here we can see that all these numbers have no other factors apart from 1 and the number itself.
2) Composite number: Composite numbers are the positive integers greater than 1 which have factors other than 1 and the number itself. We can say that positive integers greater than 1 which are not prime are composite numbers - 4, 6, 8, 9 are the first composite numbers we have. Here we can see that for example, 6 has factors 1, 2, 3, 6 that are more than two factors.
3) Co-prime numbers: Co-prime numbers are a set of numbers or integers that have only 1 as their common factor or we can say that their highest common factor (HCF) will be 1. They can be any out of composite or prime numbers. For example, 23 and 24 are co-prime because they have only one common factor and that is 1.
4) Twin prime numbers: Two prime numbers whose difference is two are called twin primes. Unlike co-prime numbers, twin prime numbers must constitute prime numbers only. For example, 5 and 7 are twin prime because they both are prime numbers and they have a difference of 2 between them.
Now let us see our question. As we have seen and understood the definition of different types of numbers, we can say that the two consecutive prime numbers with a difference of 2 are called twin prime numbers
Hence, option (b) is the correct answer

Note: Students must note that before learning what twin prime numbers are, they must have knowledge of prime and composite numbers. Also, some students have this misunderstanding that all odd numbers are prime numbers which is wrong because as we can see that odd numbers like 9, 15, 57, etc. are odd but have factors apart from 1 and the number itself so these are composite numbers.