Everyone else have given some good explanations about what tree3 is, including the excellent numberphile videos.  Id like to add another way to visualize its size.  If you used every atom in the universe, and considered them all calculators, and each calculator begin working on the proof of the tree3 number (the seed patterns of the game its from)  and each calculator found a unique pattern every planck second (the minimum of measurable time, the time it takes a photon to cross a planck length i believe)  if you had all of that working from bigbang and on into the future...the universe will recollapse according to entropic spontaneous reconfiguration before the proof can be finished.  So not only is it beyond any physical comparison, the physical reality as we understand it has no capacity to even define any of its characteristics.