So, if you didn't know, it's possible to compute the last \(n\) digits of the Graham's number quite easily, by observing the fact that
, and so on.
In fact, if you search on the internet you'll find several people that computed up to digits, digits, or digits.
Now, I admit I was pretty disappointed with this results. I couldn't find anyone that pushed up the calculations! (I may be wrong, in that case show me if anyone else actually calculated more than that)
So, I developed an algorithm that is sufficiently efficient to compute the first digits in only approximately seconds. With this algorithm, I was able to compute the last digits of Graham's number on my computer, in seconds (approximately hours).
I'm not entirely sure how, but I'm pretty sure it's possible to make the algorithm much more efficient than that, so that even calculating these digits should happen in a matter of few seconds. If you have any good ideas, tell me below (try it first, if possible).
Either way, here they are (new line every 70 digits):