Question

What is the ${{10}^{th}}$ prime number, if they are listed in order?

Answer 1

Hint: We first discuss the categorisation and characteristics of prime numbers. We try to understand the concept with the examples. We also find the factorisation of those numbers to find the difference between prime and composite numbers. Then we find the list of the prime numbers and find the ${{10}^{th}}$ prime number.

Complete step-by-step solution:
Every natural number can be categorised into two parts of prime and composite numbers.
We first discuss the characteristics of the prime 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.
The factorisation of prime numbers is the multiplication of 1 and that number.
11 can be written as $11=1\times 11$
The number of factorisations for prime numbers is always one but for composite numbers it is at least 2.
The list of prime numbers is $2,3,5,7,9,11,13,17,19,23,29,31,37,41,43,47,......$.
The ${{10}^{th}}$ prime number is 23.

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.