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: