# 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 439

- 439 is the smallest prime for which inserting the same digit between every pair of digits never yields another prime (40309, 41319, 42327, 43339, 44349, 45359, 46369, 47379, 48389, and 49399 are all composite)
- 439 the smallest prime p such that the sum of three consecutive prime numbers, beginning with p, is a cube

## Common Properties of 439

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.