# 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 688

- 688 is the number of months in a 400-year cycle that have the thirteenth day of the month fall on Friday, more often than on any other day
- 688 is the smallest number n such that n = a*b where ab is cyclic permutation of n: 688 = 86 * 8

## Rare Properties of 688

The number n is called a *vampire* number if there exists a factorization of n using n's digits (counting multiplicity).

## Common Properties of 688

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.

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