# 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 2197

- 2197 is the smallest cube (13
^{3}) that may be obtained by concatenating primes in two different ways: 2, 197 and 2, 19, 7
- 2197 is the smallest cube whose digits sum to a prime
- 2197 is the smallest odious cube that is not a power of 2

## Rare Properties of 2197

The number n is a *cube* if it is the cube of an integer.

## Common Properties of 2197

A positive integer greater than 1 that is not prime is called *composite*.

Composite numbers are opposite to prime numbers.

The number n is *deficient* if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant numbers.

A number is *odd* if it is not divisible by 2.

Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.

The number n is *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.

An integer n is *powerful* if for every prime p dividing n, p^{2} also divides n.

How much power? They all can be written as a^{2} b^{3}.