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From online transactions to paying by card, whenever private information is transmitted, security is vital.

To safeguard our information, banks, shops and online service providers exploit a mysterious set of numbers that have captivated mathematicians for centuries – the prime numbers.

**Prime Numbers**

A prime number is any whole number that is divisible only by itself and 1. Though 1 is not considered a prime.

So 13 is a prime number – it can only be divided by 13 and 1.

Whereas 24 is not a prime.

**Prime number:Any whole number divisible by itself and one**

**7 x 13 = 912 x 5 x 7 = 702 x 2 x 2 x 3 x 5 = 120**

Prime numbers are useful because, by multiplying them together, you can create every other number that isn't a prime.

Conversely, you can break any non-prime number down into what are called its 'prime number factors'.

**Prime number factors:Two or more prime numbersWhich multiply to give the original number**

**Prime Number Factors**

Because of the special properties of prime numbers a prime number's factors are unique, and can be calculated in only one way.

This makes prime numbers ideal for encoding information. Although it's easy to multiply two prime numbers together.

Undoing the process to find the factors of a prime number is far more difficult.

It is very easy to work out that 3 x 5 x 7 x 11 = 1155.

But reversing the process to find the primes factors of 1155 is more difficult.

To do this you must take two numbers which multiply to make 1155.

Then find two numbers which multiply to make those numbers.

Repeat the process until you are left with only prime numbers.

Unlike this simple example the numbers used by banks and online shops to encrypt your private information are huge.

And by multiplying these large prime numbers together they create yet more complex numbers.

Finding the prime number factors to break these codes is near impossible, even with computer power.

Encryption codes can generate numbers anywhere between 1 and 39 digits.

For another computer to crack a code this long even if it could check a trillion possibilities a second would take longer than the universe has been in existence.