# 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 353

- 353 is the smallest multidigit palindromic prime whose digits are all prime
- 353 is the smallest number whose 4th power can be written as the sum of four positive 4th powers (353
^{4}=30^{4}+120^{4}+272^{4}+315^{4})
- 353 is the smallest convenience store prime: prime of the form |7
^{n} - 2^{11}|

## Common Properties of 353

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.

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 *odd* if it is not divisible by 2.

Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.

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

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.

*Undulating* numbers are numbers of the form abababab... in base 10.

This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.