## Prime Number

We know that the prime numbers are the ones with only two factors, but how can we find them out? Let us learn a bit more about it.

## Prime Number Definition

When a number has only two factors, that is 1 and the number itself, then it is called as a prime number. The numbers with more than two factors are called composite numbers. 1 is not considered as either.

## Prime Number Formula

There are two methods to find out whether a number is prime number or not.

**1 ^{st} Method:**

Each prime number can be written as 6n + 1 or 6n – 1 (with the exception of the products of indivisible numbers, for example 2, 3, 5, 7, 11), where n is a characteristic number an n > 3.

**2 ^{nd} Method:**

For prime numbers > 40, the below formula is applied.

n^{2} + n + 41, where n = 0, 1, 2, … .., 39

In order to identify, whether a number is prime number or not, we need to find the factors of that number.

### Examples

**Ex 1. Find is 33 a prime number or not.**

**Solution:**

The factors of 33 are 1 and 33.

So, 33 is divisible by only 1 and 33.

Hence, 33 is a prime number.

**Ex 2. Find out if 63 a prime number.**

**Solution: **

The factors for 63 are 1, 7, 9, 63.

So, we can say that it has more than two factors.

Hence, it is not a prime number.

**Ex. 3. Check if 541 is a prime number.**

**Solution: **

Divide 541 by 6

The remainder is 1.

Hence 541 can be represented as

6 (n)+1

i.e. 6(90) + 1

Hence, we can deduce that 541 is a prime number.