User blog comment:Deedlit11/A lower upper bound for the Graham's number problem/@comment-5150073-20131213093640

In Wikipedia article on Graham's number even smaller upper bound has been proven and equal to $$2 \uparrow\uparrow (2 \uparrow\uparrow (2 \uparrow\uparrow (2 \uparrow\uparrow 9)))$$