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 6

  • 6 is the only even evil perfect number (submitted by Alexey Radul)
  • 6 is the order of the smallest non-abelian group (submitted by Sam Steingold)
  • 6 is the only number (except 1) such that the sum of all the primes up to 6 equals the sum of all the composite numbers up to 6 (inclusive)
  • 6 is the only even perfect number, for which repeatedly summing the digits you do not get 1
  • 6 is the only mean between a pair of twin primes which is triangular
  • The symmetric group S6 is the only finite symmetric group which has an outer automorphism
  • 6 is the minimum number of colors that is always sufficient to color any map on a Klein bottle or on a Möbius strip
  • 6 is the smallest perfect number
  • 6 is the only number that is both the sum and the product of the same three distinct positive integers
  • 6 is the only square-free perfect number (submitted by Alexey Radul)
  • A web page about 6: Some Thoughts on the Number Six, John Baez
  • 6 is the only even perfect pronic number
  • 6 is the largest integer to be both a factorial and a primorial
  • 6 is the only perfect number that is also a product of its proper divisors (submitted by Michael W. Ecker)
  • 6 is the largest square-free factorial
  • 6 is the only perfect factorial (submitted by Alexey Radul)
  • 6 is the number of convex regular polychora in 4D space (submitted by Carlo Séquin)

Rare Properties of 6

Automorphic (Curious)
Factorial
Narcissistic
Perfect
Primorial
Pronic (Heteromecic)

Common Properties of 6

Composite
Even
Evil
Palindrome
Practical
Square-free
Triangular
Ulam