Graham's number

A Graham's number is a very large number in googology that can test the computational abilities of languages. it is defined as G(64) where G is the graham's function,$G(0)=4,G(n+1)=hyper(3,G(n)+2,3),$ and the hyperoperator function is defined as $\operatorname {hyper} (x,z,y)={\begin{cases}&x+y&{\text{ if }}z=1\\&x&{\text{ if }}y=1\\&\operatorname {hyper} (x,z-1,\operatorname {hyper} (x,z,y-1))&{\text{ otherwise}}\end{cases}}$

The number can be approximated as $f_{\omega +1}(64)$ in the fast growing hierarchy, {3,64,1,2} in BEAF, and is approximately equal to $A^{6}4(6)$ using the Ackermann function with $A(x)=A(x,x)$.

It can also be represented accurately by Gardner's arrow notation: $3\ \underbrace {\uparrow \uparrow \uparrow \uparrow \uparrow \uparrow \cdots \uparrow \uparrow \uparrow \uparrow \uparrow } _{3\ \underbrace {\uparrow \uparrow \uparrow \uparrow \cdots \uparrow \uparrow \uparrow } _{3\ \underbrace {\uparrow \uparrow \cdots \uparrow } _{3\ \underbrace {\uparrow \uparrow \cdots \uparrow } _{\underbrace {\vdots } _{3\uparrow \uparrow \uparrow \uparrow 3}}\ 3}\ 3}\ 3}\ 3{\text{ (64 layers)}}$

Implementations

node.js

h=(x,z,y)=>z?y?h(x,z-1n,h(x,z,--y)):x:x+y;G(n)=n?h(3n,G(--n)+2n,3n):4n;console.log(G(64n))