TITLE: What is the biggest number ever used in a mathematical proof?
QUESTION [9 upvotes]: Probably a proof (if any exist) that calls upon Knuth's up-arrow notation or Busy Beaver.

REPLY [7 votes]: In one of Friedman's posts on the FOM mailing list, he mentions a number called SCG(13) that is far larger than TREE(3): http://www.cs.nyu.edu/pipermail/fom/2006-April/010362.html
I couldn't find a lot of other information about it, though.