# 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 20

- 20 is the maximum number of moves needed to solve the Rubik's cube
- In a game of chess both players have 20 first moves from which to choose
- 20 is the smallest number that cannot be either prefixed or followed by one digit to form a prime
- 20 is the largest number of set cards without a set
- 20 is the smallest number n such that 6n-1 and 6n+1 are composites

## Rare Properties of 20

The number is called *pronic* if it is the product of two consecutive numbers.

They are twice triangular numbers.

A *tetrahedral* number is the number of balls you can put in a triangular pyramid.

This is the space generalization of triangular and square numbers.

## Common Properties of 20

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

They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.

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

Composite numbers are opposite to prime 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.

The number n is *practical* if all numbers strictly less than n are sums of distinct divisors of n.