Knuth's up-arrow notation

method of notation of very large integers

Knuth's up-arrow notation is a way of expressing very big numbers.[1] It was made by Donald Knuth in 1976.[1] It is related to the hyperoperation sequence. The notation is used in Graham's number.

One arrow represents exponentiation, 2 arrows represent tetration, 3 for pentation, etc.:[2]

  1. Exponentiation
    a multiplied by itself, b times.
  2. Tetration
    a exponentiated by itself, b times.
  3. Third level
  4. etc.

This notation is used to describe the incredibly large Graham's Number.


  1. 1.0 1.1 "Arrow Notation - from Wolfram MathWorld". 2011-10-24. Retrieved 2011-10-30.
  2. "SS > factoids > big numbers". 1998-07-07. Retrieved 2011-10-30.