# 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 1999

- 1999 is the least prime number such that the sum of its digits is a perfect number
- 1999 is the smallest positive convenience store number, aka number n of the form − 7
^{n} + n^{11}
- 1999 is the smallest penultimate year of a millennium that is prime
- 1999 is the smallest prime of the form 666n + 1

## Common Properties of 1999

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 *odd* if it is not divisible by 2.

Numbers that are not odd are even. 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.

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.

A prime number is called a *twin* prime if there exists another prime number differing from it by 2.