# 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 59

- 59 is the center prime number in a 3x3 prime magic square that has the smallest possible magic constant 177
- The regular icosahedron has 59 stellations
- 59 is the first century with seven prime years
- 59 is the smallest number which when divided by 2, 3, 4, 5, and 6 leaves remainders of 1, 2, 3, 4 and 5, respectively

## Common Properties of 59

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.