Graham's number - one googolplex raised to the googolplexed power =~ Graham's number, which has been used in a proof. There have been larger numbers used in proofs but none yet as famous as Graham's number, about which Martin Gardner wrote a popular mathematics article. http://iteror.org/big/Source/Graham-Gardner/GrahamsNumber.ht...
Rayo's number is so big it is almost impossible to convey how big it is. It is certainly much much much bigger than Graham's number. (Unlike Graham's number, it appears not to serve any useful purpose beyond winning "who can name the biggest number?" games.)
https://en.wikipedia.org/wiki/Rayo%27s_number