# 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 66

- 66 is the lowest non-strobogrammatic number that shares a strobogrammatic prime factor with its invertible partner, i.e., 66 and 99 are both divisible by 11
- In Star Wars, Order 66 is a prepared order to the clone troopers to kill the Jedi commanding them
- 66 is the smallest abundant palindrome
- 66 is the number of triangular polyominoes with 8 cells
- 66 is the smallest palindrome which is a product of three distinct primes (submitted by Massimo Kofler)
- 66 is the smallest triangular number which is a product of three primes

## Common Properties of 66

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.

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

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

A number is said to be *square-free* if its prime decomposition contains no repeated factors.

If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a *triangle* number.

Compare to square, pentagonal and tetrahedral numbers.