## 7 May 2017

### Six

$6$ is a congruent number because it is the area of a right-angled triangle whose side lengths are rational numbers: $3$, $4$ and $5$.

The product of three consecutive integers is divisible by $6$. Prove it by mathematical induction!

A hexagon has $6$ sides.

$6$ is a triangular number, ie, it is a natural number which can be represented by an equilateral triangle.

$6$ can be written as the sum of two primes $6=3+3$. According to the Goldbach's Conjecture every even integer greater than $2$ can be expressed as the sum of two primes.

$6$ is the number of faces of the hexahedron, also called cube.