# 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 590

- 590 is the smallest number n such that n concatenated with n+2 gives the product of two consecutive numbers (590592 = 768*760)
- 590 is the only three-digit number n such that n ones plus n is prime
- 590-th prime is the smallest followed by a gap (distance to next larger prime) of 30

## Common Properties of 590

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.