Most of you will have come across the notion of the number 7 being lucky and it persists in being the world's favourite number. The few surveys on favourite numbers seem to all have 7 at the top, usually followed by 3, 11 and 13. It's used in all manners through modern culture, from Game of Thrones' 7 kingdoms to Lucky7 clothing. It is not just a newfangled internet generation concept either; like so many other things we like to think that we invented (sex, drugs, rock'n'roll, brogues etc.), it turns out this one isn't ours either, as the history books, like our parent's mortifying photo albums, show us. Seven hills of Constantinople and seven kings of Rome. Seven seas and seven wonders of the world, not to mention the 7 days of creation.
So why 7? Well it has a few genuinely interesting mathematical properties which are a lot more accessible than you think.
Seven is prime:
A prime is a number which can only be divided by 1 and itself. Mundane? No.
Primes are useful for many reasons; in internet banking encryptions for example. Without primes, paying for things over the internet would be like posting your credit card details to the company in a see-through envelope. The main reason they are interesting in maths (and why they work in encryption) is that we don't know how to find them. That is, we don't have a formula for them or how they're distributed. We can use clever algorithms to find primes but they are all based on taking numbers and checking if they're prime. That sort of approach is looked down upon by pure mathematicians, much like a pre-Raphaelite fan reacts at the mention of modern art. Discovering a formula for primes is an open question in mathematics and is the key missing piece which would prove things like the Riemann hypothesis.
Seven is a Happy Number:
They exist; here's how to find them:
1. Take any positive integer.
2. Square each of its digits and add them together.
3. Keep doing this until you either get 1, or the original number.
4. If you reach 1 then the original number was a happy number, otherwise it is an unhappy number.
For 7 we have: 72 = 49, 42 + 92 = 97, 92 + 72 = 130, 12 + 32 + 02 = 10, 12 + 02 = 1.
There isn't really much that's useful about a happy number, it just gives mathematicians that warm feeling inside, which most of us get from champagne.
Seven is a Lucky Number:
It turns out maths agrees that seven is lucky. A lucky number is found like this:
1. Take the sequence of numbers going up from 1 and remove every second number. Leaving the odd numbers: 1, 3, 5, 7, 9, 11, 13....
2. 3 is the first remaining term so now we delete every 3rd number, leaving:: 1, 3, 7, 9, 13....
3. The next is 7 so delete every seventh and so on.
We can see by this point though that 7 is safe from this onslaught of selective deletion and is therefore a “lucky number”. These aren't very useful either, but we can take it as proof that all our assertions about 7 being lucky are correct.
Of the most popular favourite numbers (7, 3, 11, 13), only 7 satisfies all three of the above properties. So there you have it: indisputable evidence that 7 is in fact the best number and if anyone says different, simply woo them with your maths.