# 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 314

- 314 form the first three digits of pi
- 314 is the only number which together with its sixth power 958468597212736 has each digit from 1 to 9 occurring exactly twice
- 314 is the smallest even number n such that φ(n) > φ(n+1)
- 314 is the first century with four prime years

## Common Properties of 314

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.

A number is *even* if it is divisible by 2.

Numbers that are not even are odd. 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 number is said to be *square-free* if its prime decomposition contains no repeated factors.