"Busy Beaver Numbers"

Don't ask how I stumbled on this one!

The Biggest Numbers in the Universe


By Bryan Clair


" ....We have found a sort of holy grail for large numbers: even busy beaver twelve is bigger than everything else in this article put together. This is the mathematician's equivalent of deep space. It's the arrow to the right off the end of the number line. These numbers are so enormous that they're beyond comprehension, yet there is always an infinite horde waiting to make them look tiny. The busy beaver numbers are far exceeded by an even larger uncomputable sequence called the "super busy beaver" numbers, which are beaten by the "super super busy beavers," and so on.

But big numbers never get boring, because "and so on" isn't good enough -- the path you're on is always too slow. Piles of pebbles are dwarfed by powers of 10, which are dwarfed by towers of exponents, which are dwarfed by busy beavers. Each significant increase required a new idea, and always will. The big number hunt is still on!"