What makes the number interesting?

Obviously there will be many answers to this. Here are a couple of special things about which have turned up in my first year module recently (and in one case this was unplanned!)

- is the only square number which is exactly one more than a prime number
- is the only positive integer such that is not prime, and yet is not divisible by . (Here we follow the convention that .)

Do you have any other favourite exceptional properties of ?

Aren’t the special properties of the first few integers simply because they are the first few integers rather than anything intrinsic to the integers themselves? I hope that makes sense. I’m thinking that the “rules” that are true for the higher integers are somewhat predicated on an accumulation of integers “below” them.

Good artilce