# 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 212

- 212 is the smallest even three-digit integer n such that n divided by the product of its digits is prime
- 212 is the only number whose 5-digit square has 4 identical digits: 212
^{2} = 44944
- 212 is the smallest palindromic number with sum of digits prime and number of prime digits prime

## Common Properties of 212

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 *even* if it is divisible by 2.

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

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

Guess what odious numbers are.

A *palindrome* is a number that reads the same forward or backward.

*Undulating* numbers are numbers of the form abababab... in base 10.

This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.