# 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 829

- 829 is the larger of the smallest pair of twin primes such that both twins can be represented as a sum of a square and a cube (827 = 22
^{2}+7^{3} and 829 = 9^{3}+10^{2})
- 829 is the smallest number such that ten 'Reverse and Add' steps are needed to reach a palindrome

## Common Properties of 829

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.