# 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 5005

- 5005 is the smallest product of a prime quadruple (prime quadruples are formed by prime numbers n, n+2, n+6 and n+8)
- 5005 is the smallest palindrome that is the product of four consecutive primes (5*7*11*13)

## Common Properties of 5005

The number n is called an *apocalyptic power* if 2^{n} contains the consecutive digits 666 (in decimal).

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 *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 *palindrome* is a number that reads the same forward or backward.

A number is said to be *square-free* if its prime decomposition contains no repeated factors.