In maths, we have been learning about prime numbers and square numbers. Obviously, there is no way the same number can be both a prime number and a square number. The picture below shows that this is the case for numbers up to 100, but can you explain why it is the case for any number?
However, my Dad has told me that there is an amazing link between square numbers and prime numbers. If a prime number is 4 times something + 1, then it is always the sum of two square numbers added together. This is true for all prime numbers!
This was first proven by the famous mathematician Euler (remember the Konigsberg Bridge problem?).
Here are some examples that we made using a spreadsheet:
Can you find some more examples?
It is also true that if a prime number is 4 times something + 3, then it never equals the sum of two square numbers added together. This is quite easy to prove. Can you prove it?