# Graham's number

Graham’s number is a… rather large number. Letting \(f(x) = 3\uparrow^n 3\) (in Knuth up arrow notation) and \(f^n(x) = \underbrace{f(f(f(\cdots f(f(x)) \cdots ))}_{n\text{ applications of }f}\), Graham’s number is defined to be \(f^{64}(4).\)

The result is sizable. For an explanation of how large this is and why, see Tim Urban’s explanation at Wait but Why.

Parents:

- Natural number
The numbers we use to count: 0, 1, 2, 3, …