[summary:
Graham's number is a… rather large number. Tim Urban of *Wait but Why* gives a good introduction.

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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.