Pierre Fermat, Holly, prime numbers and square numbers

Back in January Holly introduced us to an interesting fact about prime numbers and square numbers. This is something that was discovered by a famous mathematician from Toulouse called Pierre Fermat. The green prime numbers circled here can all be made by adding two square numbers together:

Today in 4G we checked this:

And here are all the ones we did:

One little correction...

More on Holly's post

Holly posted a fantastic post at the weekend about square numbers and prime numbers. If you haven't had a look at it yet, it's really interesting: have a look! Also read the comments.

It's certainly made me, Mr Gregg, think. In 4G today we looked at the numbers Holly's dad had talked about, and used it for our counting circle:

These are all the "four times table plus one" numbers, they are the " 4 times something + 1" that Holly's dad talked to her about.

We looked for prime numbers among these. We used a 100 square, but it would have been better on a hundred-rectangle like this:

All the prime numbers are circled. The ones that we're looking at are the green ones. (It never works with the red primes.)

Then we found that all of them could be made by adding two square numbers.

1    4    9    16    25    36    49     64    81

Can you do it? If you can make any of those green primes by adding two square numbers, write it in the comments below.