
13 is a prime number because it will only divide exactly by 1 or 13. If you have 13 eggs, the only box they will neatly fit into has one row of 13 eggs. If you try boxes that are shorter and wider, you'll never neatly fit all 13 eggs in. 
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 ... ...and they go on for ever. So far nobody has found a pattern to predict them and they can't decide if 1 is prime or not! 
Mathematicians LOVE prime numbers because just about all of maths is made out of prime numbers. In the same way, scientists LOVE atoms because just about everything we know is made out of atoms.
You can find out how the ancient Greeks found prime numbers up to 100 and beyond using the Sieve of Eratosthenes.
So now we know what prime numbers are, what can we do with them?
Before we see the trick, here's a neat toy for you to try. It's a special calculator which can tell you if a number is prime or not. All you need to do is type a number in the box, and then hit the ACTIVATE button. (Warning: if you put in numbers with lots and lots of digits your computer might get a bit cross!)
was invented by Abraham Joffe 
What's the BIGGEST prime number you can find?
GREAT INTERNET MERSENNE PRIME SEACH 
E.g. 11^{2} = 121 then 121  1 = 120 and yes 120 does divide by 24.
WHY?
If you understand algebra, (and you've read The Phantom X ) then you'll know that all prime numbers can be written as (6n+1) or (6n1).
(6n+1)^{2} = 36n^{2}+12n+1. So (6n+1)^{2} 1 = 36n^{2}+12n. This factorises to 12n(3n+1). Either n or (3n+1) must be even, therefore the whole expression must be divisible by 24.
(6n1)^{2} = 36n^{2}12n+1. So (6n1)^{2} 1 = 36n^{2}12n. This factorises to 12n(3n1). Either n or (3n1) must be even, therefore the whole expression must be divisible by 24.
Find out more about prime numbers in these Murderous Maths books:  





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