# 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 123

- 123 is the smallest semiprime which is the concatenation of the numbers 1 through n for some n
- 123 is the smallest squarefree number whose external as well as internal digits form a squarefree number
- Start with any number, then write out the number of even digits followed by the number of odd digits followed by the total number of digits. After a finite number of repetitions the result will be 123

## Common Properties of 123

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.

The number n is *evil* if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

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.

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