Graham's number

Graham's Number is the upper bound to the solution of the now-unsolved problem, concerning multi-dimensional cubes.

"Let $N^*$ be the smallest dimension n of a hypercube such that if the lines joining all pairs of corners are two-colored for any $n \geq N^*$, a complete graph $K_4$ of one color with coplanar vertices will be forced. Find $N^*$."

Graham's Number is recursively defined as $$g_{64}$$ in the series $$g_1 = 3\uparrow\uparrow\uparrow\uparrow 3$$ and $$g_n = 3\underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_{g_{n-1}}3$$, or $$3 \rightarrow 64 \rightarrow 1 \rightarrow 2$$ in Chained Arrow Notation.

In 1998, Tim Chow proved that Graham's Number is much larger than the Moser.