Question

Two and three are consecutive prime numbers. Why are not there any other pairs of consecutive prime numbers?

Answer 1

Hint: For this type of problem we have to concept about prime numbers and composite numbers. First we know about prime numbers and composite numbers. After that we find the other consecutive number and check if any one of them is divisible by $2$ or not. After that we conclude the required answer.

Complete step by step answer:
For this type of question, we first know about prime numbers.
A prime number is a natural number greater than $1$ that is a product of two smaller natural numbers or we can say prime number is a number that has only two factors which are 1 and the number itself. A natural number greater than $1$ that is not prime is called a composite number. Therefore the composite numbers are those numbers which is a natural number greater than $1$ that is a product of more than two smaller natural numbers.
i.e., the prime numbers are $2,3,5,7,11,.....$ and composite numbers are $4,6,8,9,10,........$ .
Any two consecutive numbers i.e., $12,13;45,46;67,68;.........$ are all not prime. Any one of them will always be even and hence divisible by $2$ .
Now , although $2$ is an even number, there is no prime factor other than $1$ and itself. i.e., $2$ is an even prime number.
Also $3$ is an odd number, as there is no prime factor other than $1$ and itself. i.e., $3$ is an odd prime number.
Therefore from the above we say that $2$ and $3$ are the only consecutive prime numbers.
All consecutive numbers are not prime.

Note:
To solve this type of problem we have to know about even numbers and odd numbers. Even numbers are those numbers which are divisible by $2$ . I.e., $2,4,6,8,10,.......$ are all even numbers. Odd numbers are those numbers which are not divisible by $2$ . i.e., $3,5,7,9,11,.........$ are all odd numbers. You must use the concepts of prime numbers, composite numbers, even numbers and odd numbers.