Question

Find the ${{15}^{th}}$ prime number if they are listed in order.

Answer 1

Hint: We first discuss the categorisation and characteristics of prime and a composite number. We try to understand the concept with the examples. We also find the list of the prime numbers starting from 2 to find the ${{15}^{th}}$ prime number.

Complete step by step answer:
Every natural number can be categorised into two parts of prime and composite numbers.
We first discuss the characteristics of the prime and composite numbers.The numbers which have only two factors as 1 and that number itself are called prime numbers. The prime numbers are only divisible by 1 and that number.For example, the numbers 5, 7, 11 are the prime numbers.

All other natural numbers other than prime numbers are called composite numbers.This means that composite numbers have more than two factors of 1 and that number.For example, the numbers 4, 33, 111 are the composite numbers.The factorisation of prime numbers is the multiplication of 1 and that number.11 can be written as $11=1\times 11$ whereas 33 can be written as $33=3\times 11=1\times 33$.The list of prime numbers starts from 2. The following prime numbers are $3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,....$.

Hence, the ${{15}^{th}}$ prime number if they are listed in order is 47.

Note: All even numbers are composite numbers except 2. There aren’t enough smaller numbers than 2 to form the factors of 2. Therefore, it’s considered as prime numbers. 1 belongs to neither the prime nor the composite numbers.