CH. Rayo’s Number!

A contestant for our Million-Dollar-Give-Away sent in Rayo’s Number, hitherto the largest number ever used for any real purpose: to wit, winning the



Check out the article by Scot Aaronson that inspired them to duke it out! And this thread on the math forum is quite interesting as well.


  1. strauss said,

    April 15, 2007 at 12:02 pm

    The Busy Beaver Function, mentioned in this segment, is really quite amazing; one particularly mind-blowing property is that it grows faster than any computable function!!!

    (More correctly, no computable function bounds the busy beaver function; i.e. anything you can actually compute, in any way whatsover, will sooner or later be topped by the Busy Beaver!!) We’re planning to come back to this paradoxical sounding statement in a later segment…

    But that was just a way-station on the way to Rayo’s number, which is vastly larger than anything you can easily name: essentially, he calls for the biggest number that takes a googol’s worth of symbols to notate, in any well-defined way, and then tops that!

    As we saw last week, Graham’s number only takes, maybe, a hundred symbols to write out, so it is hard to get a handle on what Rayo’s number might be!

  2. Al Downing said,

    February 16, 2011 at 11:21 am

    First, how far does Rayos number surpass a meameamealokkapoowa oompa?. Second, the fact the Rayos number is in the Busy Beaver Function, are there ANY other computable functions which are beyond the Busy Beaver Function?.

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