# Optimus Prime, Prime Minister… but what about Prime Numbers?

Spark Academy’s Maths department are so excited to introduce you to a new mathematical discovery. It’s all about the prime numbers here!

We are only in the second month of 2018 and the Mathematical community has already been shaken by the discovery of the largest prime number known to date!

### Wait wait wait. What is a Prime Number?

Students at Spark begin to look at prime numbers in Year 6, and are taught that a number is a prime number only if they have only two factors; 1 and itself.

Some basic examples include the first three prime numbers;

2

3

5

These numbers can only be divided by themselves and 1. 2 is something of an odd one out in this list… Can you guess why? Leave your ideas in the comments.

We can check to see if a number is prime by factorising a number. Factorising is where we break a number down into its smallest possible numbers of factors ie. numbers that divide into a bigger number.

For example: the factors of 30 are 1, 30, 2, 15, 3, 10, 6, and 5. These are all of the numbers that you can divide 30 by.

#### Can you find the factors of 50? What about 124? Comment your thoughts below!

For a number like 719, the factors are 719… and 1.

If there are exactly 2 factors, then it will be prime! Pretty simple, right?

### What’s the easiest way to find out if a number is prime?

Now this is where the property of prime numbers comes into play; is there an efficient way to determine if a large number is prime or not?

Unfortunately, this very question has stumped the best mathematicians over many centuries, and there just doesn’t seem to be any simple way to factor a number efficiently. Computers use brute force and processing power to work it out. This involves checking every possible combination of factors to see if it is divisible by any number. ### What is the number then?

To put into perspective the size of the new largest prime number is 23,249,325 digits long. The factorisation process took six complete days of non-stop computing to verify it.

To get some idea of the size of this number, and to see this number in all its glory, it would take just over 9,000 A4 pages if printed out fully. It’s a little too big for us to print here!

This new number is 910,807 digits longer than the previous record holder, which was discovered only 12 months ago!

### But you ask: What is the point of all this?!

It was during the 1970’s, along with the advances of computer processing technology at the time, that it became apparent that prime numbers become very important to the encryption of data. These numbers are used to hide important secrets. Governments and intelligence agencies use data encryption all the time. Encryption algorithms rely on the fact that it is very easy to multiply two (very large) prime numbers together, whilst it is extremely difficult to find a possible factor by dividing. This makes it very difficult to just simply guess what number was used in the encryption in the first place.

It is because of prime numbers which can allow intelligence agencies around the world this such as MI5, the CIA and the KGB to transfer national secrets without it falling into the wrong hands and spilling the proverbial beans. Did you ever think numbers could be linked to spies?

In an upcoming blog, we will be looking further how you can find your very own record breaking number, so stay tuned!