# 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 74

- 74 is the alphanumeric value of HUNDRED
- There are 74 different non-Hamiltonian polyhedra with 11 vertices, which is the minimum number of vertices for such polyhedra to exist

## Rare Properties of 74

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.

## Common Properties of 74

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.