# Prime Numbers

Chapter Contents

## Prime Number

Any Natural number greater than 1, which is divisible by 1 and only by itself is called Prime Number.

Example

2, 3, 5, 7, 11 etc.

Note

2 is the smallest Prime Number.

Prime numbers cannot be represented by a rectangle or square.

Representation of prime numbers

## Composite Number

Any Natural number, which is greater than 1 and is not a Prime Number is called a Composite Number.

Example

4, 6, 8, 9, 10 etc.

Note

1 is neither a Prime Number nor Composite Number.

Composite numbers can be represented by a rectangle or square.

Representation of composite numbers

## Coprimes

Two numbers are called to be coprime or co-prime if they have only 1 as a common factor.

In other way, we can say if greatest common divisor of two numbers is 1, then the two numbers are coprimes.

Example

(2,3), (14,15), (8,13) etc.

## Twin Primes

Two numbers are called Twin Primes if they differ by 2 only or we can say that there is only one composite number between them. One prime number can be 2 more or 2 less than another prime number.

Example

(3,5), (29,31), (71,73) etc.

## Prime Triplets

A set of three consecutive Prime Numbers if the smallest and the largest differ by 6 and must be in the form of (p, p + 2, p + 6) is called a Prime Triplet.

Example

(5,7,11)
Why?
Because, 5, 7 and 11 is in the form of p, p + 2, p + 6
where p = 5
p + 2 = 5 + 2 = 7
and p + 6 = 5 + 6 = 11