What are Prime Numbers

A prime number is any natural number that is divisible by itself and one only. Integers are sets of positive and negative whole numbers. These numbers can be divided into separate groups according to the different properties they possess like positive numbers, negative numbers, prime numbers, composite numbers and so on.

A prime number is defined as a natural number which is greater than 1 and has no other positive divisors other than 1 and the number itself.

Properties of Prime Numbers

A prime number is a natural number that has two distinct natural numbers as divisors, itself and one only. A prime number is an integer possessing certain properties.

Properties of prime numbers:

Property 1:

All prime numbers must be natural numbers.
Natural numbers are just ordinary numbers used for counting, like 1, 2, 3….. Hence they will also be only positive numbers.
 
Property 2:

All prime number must be greater than 1. So 1 cannot be a prime number, as it cannot be greater than itself.

Property 3:

The prime numbers are not allowed to take any negative divisors.

Example:
2 can also be written as $2 = -1*-2$

So we can say -1 and -2 are divisors of 2, but in prime numbers, its not allowed to take negative divisors. So only positive divisors must be taken.
 
Property 4:

All prime numbers can only have two positive divisors, which are 1 and the number itself.

For example: 2 is a prime number as the only factors of 2 are 1 and 2 itself.

Any number, n, is called a prime number, if
  • It is greater than 1
  • None of the numbers are greater than 1 and less than n can divide n without leaving any reminder.

Is One a Prime Number

A prime number is a number that is divisible by itself and one only. Lets consider the natural numbers between 1 to 7. Lets check each number whether it is prime or not, starting from 2,

2 is a prime number as its only divisors are 1 and 2.

3 is a prime number as its only divisors are 1 and 3.

4 is not a prime number as it has more divisors other than 1 and 4, which is 2.

5 is a prime number as its only divisors are 1 and 5.

6 is not a prime number as it has more divisors than 1 and 6, which are 2 and 3.

7 is a prime number as its only divisors are 1 and 7.

When we consider the number 1 =  1 * 1, it can also have two divisors, 1 and the number itself, which is again 1. So the number $1$ can have only one divisor, which doesn’t satisfy the definition of a prime number. So $1$ is not a prime number.