# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 289

- 289 is the smallest number for which the absolute values of the abundances of itself, its square and its cube are all prime numbers
- 289 is the largest 3-digit square with increasing digits (submitted by Alexey Radul)
- 289 is the smallest number with all different non-zero digits such that when it is divided by its digits the remainder is the same non-zero number: when 289 is divided by 2, 8, or 9, the remainder is 1