Evil and Odious

It was the discovery of this that inspired me to make this blog.

In addition to the (relatively) obvious number facts, such as ‘prime’, ‘cubed’ or ‘odd’, there are lots of little factettes that I knew but hadn’t really considered to be ‘number properties’, but which make numbers a bit more colourful.

17, for example, has the following unique properties:

• There are 17 distinct sets of regular polygons that can be packed around a point (e.g., 4 squares, 2 hexagons and 2 triangles, etc)
• There are exactly 17 ways to express 17 as the sum of 1 or more primes – 17 is the only integer which is equal to the number of prime partitions of itself
• 17 is the number of wallpaper groups
• 17 is the only prime of the form pq + qp, where p and q are prime
• 17 is the only multidigit number n such that n + SOD(n) and n – SOD(n) are square numbers, where SOD means sum of digits
• 17 is described at MIT as ‘the most random number’, according to hackers’ lore
• 17 is the number of syllables in a haiku
• 17 is the smallest odd prime such that no odd Fibonacci number is divisible by it

I love that, in addition to the patently mathsy (I trust that you, too, felt compelled to work out what p and q were), we get haikus and hackers.

(For those wondering what ‘wallpaper group’ means, I recommend suggest Ian Stewart’s explanation in his ‘Cabinet of Mathematical Curiosities’.)

We also learn that a rare property of 17 is that it is hungry (I’m not totally confident I understand this…yet), and its common properties are that it is

The best property I’ve found so far is numbers that are ‘cake’ – you’ll have to look at Tanya’s website to find out what it means.