6

6 (six) is a positive integer following 5 and preceding 7. Its ordinal form is written "sixth" or "6th."

Properties
6 is an, the third , and the third factorial number. 6 is equal to the sum of its proper divisors: 1 + 2 + 3 = 6. This makes it a, and in fact the smallest number with that property, with the next being 28.

In googology
Some googologisms based on 6 are sextoogol, superhex and hexalogue. It is not commonly found in googology.

Six is the base of Robert Munafo's idea of classes. 6 is the boundary between class 0 and class 1 numbers, 10^6 is the boundary between class 1 and class 2 numbers, 10^10^6 is the boundary between class 2 and class 3 numbers, etc.

In Greek-based number naming systems, 6 is associated with prefix hexa-, and with prefix sexti- in Latin systems.

Googological functions returning 6

 * Rado's Sigma Function: \(\Sigma(3)=6\)
 * Laver table: \(q(4)=6\)
 * Subcubic graph number: \(\text{SCG}(0)=6\)
 * Xi function: \(\Xi(5) = 6\)