# 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 17

- There are 17 distinct sets of regular polygons that can be packed around a point (e.g., 4 squares, 2 hexagons and 2 triangles, etc)
- There are exactly 17 ways to express 17 as the sum of 1 or more primes - 17 is the only integer which is equal to the number of prime partitions of itself
- 17 is the number of wallpaper groups
- 17 is the only prime of the form p
^{q}+ q^{p}, where p and q are prime - 17 is the only multidigit number n such that n + SOD(n) and n - SOD(n) are square numbers, where SOD means sum of digits
- 17 is described at MIT as 'the most random number', according to hackers' lore
- 17 is the smallest odd prime such that no odd Fibonacci number is divisible by it
- 17 is the minimum number of Sudoku clues that produces a unique answer
- 17 is the smallest number of vertices for a complete graph to have, so that when the graph's edges are colored in three colors, there always exists a monochromatic triangle
- Web pages about the number 17:
- Properties of 17
- Mathematical properties of 17 at yellowpigs.net

- 17 is the only integer which is equal to the number of prime partitions of itself
- 17 is the smallest number n such that there is a set of n consecutive integers none of which is relatively prime to all the others
- 17 is the smallest prime whose sum of digits is a cube
- 17 is the smallest prime with no non-squarefree neighbors