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 4

  • 4 is the only compositorial square
  • 4 is the only positive number that is both the sum and the product of the same two integers
  • 4 is the order of the smallest non-cyclic group (submitted by Sam Steingold)
  • Every positive integer is the sum of at most 4 squares
  • 4 is the smallest number of colors sufficient to color any planar map
  • 4 is the only number in the English language for which the number of letters in its name is equal to the number itself
  • 4 is the only composite number that is equal to the sum of its prime factors
  • 4 is the only composite number n which doesn't divide (n-1)!

Rare Properties of 4

Cake
Compositorial
Narcissistic
Power of 2
Square
Tetrahedral (Pyramidal)

Common Properties of 4

Composite
Deficient
Even
Lazy caterer
Odious
Palindrome
Powerful
Practical
Smith (Joke)
Ulam