# 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 239

- 239 is the smallest number such when it is summed with the product of its digits generates a nontrivial permutation of its digits (239 + 2*3*9 = 293)
- 239 The smallest prime p such that the decimal period of 1/p is 7
- An article in Math World on number 239
- 239 is the largest integer that cannot be written as a sum of 8 or fewer cubes (the only other number is 23)
- This prime number appears in one of the earliest known geometrically converging formulas for computing Pi: Pi/4 = 4 arctan(1/5) - arctan(1/239)
- 239 is the smallest number n such that sum of reciprocals of terms in the period of the continued fraction for square root of n is an integer

## Common Properties of 239

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.

One can take the sum of the squares of the digits of a number. Those numbers are *happy* for which iterating this operation eventually leads to 1.

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.