Rayo's number

Rayo's number is an incredibly enormous number that won a large number battle pitting Agustín Rayo against Adam Elga. Rayo's number is, in Rayo's own words, "the smallest number bigger than any finite number named by an expression in the language of first order set theory with a googol symbols or less."

It is quite possibly the largest number ever named, although there is debate on how it compares to Jonathan Bowers' also massive number meameamealokkapoowa oompa.

Rayo and Elga's number duel was based on an article by Scott Aaronson.