The biggest number

I have given you all an index card. You have one minute to write down the biggest number that you can (barring infinity) using any mathematical function that you know (addition, subtraction, exponentation, ackermann, Knuth's up arrow, etc). Go.

>>31
However, Busy Beavers HAVE been nested, by Stephen Kleene in 1943.

Are you sure?  This is the first time I've heard of them to be honest, but the wikipedia article says the functions themselves were introduced in 1962.