User blog comment:LittlePeng9/Random Turing machines/@comment-5150073-20130406103030

Your last program is a great breakthrough in googology. Once Sbiis Saibian wrote in his blog:

"I've heard it said that before you would reach BB(100) the resourcefulness of the human imagination would be overwhelmed. Is this so? A gongulus already seems pretty complex. Just how close is it to something like BB(100)? The world may never know, but at least once mathematicians need a handy way to express BB(10) or BB(20), Bowers notations will already be on hand! That's got to count for something."

In fact, gongulus is smaller than even f_e_0(4), and you actually defined your function that on par with f_e_0(n) with 53 states and 6 colors. Therefore, you can add 2 states to write 4 ones and then apply your function to it. We get BB(55,6) > gongulus. However, I believe that Sbiis asked for BB(100,2). Can you prove that BB(100,2) > BB(55,6)?