# Prime Numbers

## 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 number 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 number 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 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