# 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 668

- 668 is the number of legal pawn moves in chess, as the moves are written in transcripts; that is, different captures are counted separately
- There are 668 palindromic primes with 7 digits

## Common Properties of 668

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

Guess what evil numbers are.

The next *Ulam* number is uniquely the sum of two earlier distinct Ulam numbers.

The *untouchable* numbers are those that are not the sum of the proper divisors of any number.