# Arithmetic » Prime numbers

## What are prime numbers?

A number is a prime number when it is only divisible by 1 and itself.

Example: 7 is a prime number, because only when you divide by 1 or 7 the answer will be a whole number.

The number 1 is not a prime number.

There are an infinite number of prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, ..., ..., ...,

The first 10 000 prime numbers can be found at Prime Pages.

## When do we use prime numbers?

In the world of computers (very closely related with mathematics) prime numbers are used to encrypt data. The encryption key is always a prime number. The higher the prime number, the more difficult it is to decipher the encryption.

In mathematics prime numbers are especially important when factorising formulas.

Below it is shown how a number is written as its prime factors.

Try not to use a calculator. In this example the next lowest prime factor possible is found in every step.

1176 2 × 588 2 × 2 × 294 2 × 2 × 2 × 147 2 × 2 × 2 × 3 × 49 2 × 2 × 2 × 3 × 7 × 7 = 2 ^{3} × 3 × 7^{2} |

On paper you can try to save room and time by using larger factors first.

This is what you might get:

1176 8 × 147 2 × 4 × 3 × 49 2 × 2 × 2 × 3 × 7 × 7 = 2 ^{3} × 3 × 7^{2} |

It is not always necessary to write down the last step.