# 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 21

- 21 is the smallest number of distinct integer-sided squares needed to tile a square
- 21 is the number of spots on a standard cubical die (1+2+3+4+5+6)
- A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection. The smallest number of squares participating in a perfect dissection is 21
- 21 is the number of connected graphs with 5 vertices
- 21 is the first century with ten prime years
- 21 is the smallest integer n such that the concatenation of n in base 10 down up to base 2 is prime
- 21 is the smallest triangular number whose sum of aliquot divisors is prime
- 21 is the smallest semiprime Fibonacci number (submitted by Massimo Kofler)