# 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 582

- 582 is the smallest number that is the sum of two reversed consecutive primes in more than one way (582 = 191 + 391 = 386 + 196, where 191,193 and 691,683 are two pairs of consecutive primes)
- 582 is the smallest number such that its largest prime factor equals the sum of the 4th power of the other prime factors (prime factors of 582 are 2, 3 and 97, and 97 = 2
^{4} + 3^{4})

## Common Properties of 582

The number n is *abundant* if the sum of all its positive divisors except itself is more than n.

They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.

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.

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 *evil* if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

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