# 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 271

- 271 is the smallest prime so that both its predecessor and successor are divisible by cubes
- 271 is the smallest number sandwiched between two numbers that are products of 5 primes

## Rare Properties of 271

The n-th *Google* number is the first n-digit prime found in the decimal expansion of e.

They are named *Google* numbers because of the unusual hiring ad that *Google* put up.

- 2,
- 71,
**271**, - 4523,
- 74713,
- 904523,
- ...

## Common Properties of 271

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.