Graham's number

Graham's Number is the upper bound to the solution of the now-unsolved problem:

"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 $$g_{n} = 3\underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_{g_{n-1}}3$$.