User blog comment:Ikosarakt1/Apocalyptic function/@comment-25418284-20130322220331/@comment-5150073-20130322222754

Despite that the probability of number > 2^500000 being NAN is ridiculously small, it is not an exact proof of that. For tetration, it can be strictly proven that 2^^n cannot be NAN from n>=1213. I believe that for 2^n it can be proven using the cyclic considerations of last digits (they not converge, but form the some cycle).