Googology Wiki
Googology Wiki

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


Visualization of 6

  • 6 is an even number, the third triangular number, the third factorial number, and 3 or 4 primorial.
  • 6 is equal to the sum of its proper divisors: 1 + 2 + 3 = 6. This makes it a perfect number[1], and in fact the smallest number with that property, with the next being 28.
  • 6 is equal to the sum of its unitary proper divisors, that is to say divisors d such that d and n/d are relatively prime. These are called unitary perfect numbers. It is the smallest number with this property.
  • It is the only semiprime number to not also be a deficient number.
  • It is the smallest number N such that all multiples of N are abundant. All perfect or abundant numbers have this property.
  • In the Czech language, 6 is called "půltucet", meaning "half-twelve".

In googology

  • Some googologisms based on 6 are sextoogol, superhex and the hexalogue. It is not commonly found in googology.
  • Six is the basis of Robert Munafo's idea of classes. 6 is the boundary between class 0 and class 1 numbers, 106 is the boundary between class 1 and class 2 numbers, 10106 is the boundary between class 2 and class 3 numbers, and so on.
  • The Misalian seximal system uses base six, which is also called senary or heximal.
  • In Greek-based number naming systems, 6 is associated with prefix hexa-, and with prefix sexti- in Latin systems.
  • 6 is the last digit of mega.
  • Flan number 4 version 2 (or フラン数第四形態改二 in Japanese) is equal to 6. This started a joke in the Japanese googology community that 6 was a large number.[2]
  • (or 全角の6 in Japanese) is a specific value of a function in a version N3.0 of N primitive. The shape of the letter looks quite similar to 6, but the value is shown to be greater than 6.

Googological functions returning 6


  1. MathWorld, Perfect Number
  2. 叢武, 6は巨大数, twitter.