# 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 2421

- 2421 is the largest possible sum of three 3-digit primes that together use all non-zero digits 1 through 9
- 2421 = prime(2)
^{2} + prime(4)^{4} + prime(2)^{2} + prime(1)^{1} and 2421 is the smallest number with this property (proved by Alexey Radul and David Wilson)

## Common Properties of 2421

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.