# 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 2003

- 2003 is the first prime year in our millennium

## Rare Properties of 2003

The k-th *hungry* number is the smallest number n such that 2^n contains the first k digits of the decimal expansion of pi.

They are named *hungry* numbers because they try to eat as much "pi" as possible.

- ...,
- 74,
- 144,
- 144,
**2003**, - 37929,
- 82810,
- 161449,
- ...

## Common Properties of 2003

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.

One can take the sum of the squares of the digits of a number. Those numbers are *happy* for which iterating this operation eventually leads to 1.

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 *prime* is a positive integer greater than 1 that is divisible by no positive integers other than 1 and itself.

Prime numbers are opposite to composite numbers.

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