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The Number Devil and prime facts

March 25, 2015

In a recent episode of Wrong, but Useful, I mentioned that I bought a book called the Number Devil (amazon link) but hadn’t started to read it yet. Well, I have started to read it now and, only three chapters in, I’ve learnt a couple of things I thought I’d share with you. They relate to prime numbers.

You may have heard of Goldbach’s conjecture. It states that every even integer greater than 2 can be written as the sum of two primes. It’s a long standing standing problem (from 1742) and you can win a million dollar prize if you can prove or disprove it. However, did you know that if you pick any number over 5, you can find three primes that will add to make it.

Examples:

10 = 2 + 3 + 5

41 = 5 + 17 + 19

Another thing I’ve learnt is that if you pick any integer greater than 1 and double it, there will be a prime number between your starting number and its double. Always. Now, I like this result, it’s simple to understand easy to verify in simple cases but starts to pick at the fact that there are things we know about things we don’t know much about. We do know quite a lot about prime numbers but there’s a lot more to learn.

Both of these things are the kind of maths I can introduce to students from year 7 upwards and they can see what I’m talking about while also showing them that maths isn’t ‘done’ – there’s always more to find out!

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