It's fun to toy with big numbers, but all this iterated power stuff is primitive recursive. All primitive recursive functions are dwarfed by Ackermann's function for relatively small arguments, whereas the Ackermann function itself is in turn dwarfed by the Busy Beaver function.
It's fun to toy with big numbers, but all this iterated power stuff is primitive recursive. All primitive recursive functions are dwarfed by Ackermann's function for relatively small arguments, whereas the Ackermann function itself is in turn dwarfed by the Busy Beaver function.