Question

What is a prime number?

Answer 1

Hint: Basic theoretical knowledge of mathematics will be used. Also, the concept of number system will be used.
In earlier times, the number system was introduced. Certain classification of the numbers was done for example, Natural numbers, Whole numbers, Integers, Rational Numbers, Real Numbers, Complex numbers etc.

Complete step-by-step answer:
Now, in the question we are asked to define prime numbers, for this we will work on the set of Natural numbers. Set of Natural numbers contains all positive real numbers i.e. \[1,2,3,4,5,6,7, \ldots \]. These numbers are further classified as even numbers, odd numbers, prime numbers and composite numbers.
Prime numbers are the numbers which are divisible by itself and \[1\]. There is no common number except one which can be a factor of such numbers. For example, \[2,3,5,7,11,13\] and so on. We observe that number two can only be obtained by the following expression\[2 \times 1\], here we cannot find any other factor except \[1\] and \[2\] of number \[2\]. Similarly, the other numbers mentioned above can be written as the product of \[1\] and itself.
Now, we will discuss the numbers which are not prime numbers. Consider the set of Natural numbers again, the non-prime numbers are given as, \[4,6,8,9\] and so on. Let’s choose the number \[6\], this number can be expressed as the product of numbers \[3\] and \[2\] i.e. \[3 \times 2\].

Note: Another property of prime numbers is that the product of two prime numbers always gives a non-prime number except the condition\[2 \times 1\]. For example, in the above section, number 6 was expressed as the product of numbers \[3\] and \[2\] i.e. \[3 \times 2\], where \[3\] and \[2\] are prime numbers.