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.

http://en.wikipedia.org/wiki/Busy_beaver

This is the answer. I win. It grows so explosively that we aren't sure of anything after BB(4). BB(5), BB(6), and BB(12) listed below are calculated MINIMUMS for the actual answer. The true result is likely far larger.

BB(0) = 0
BB(1) = 1
BB(2) = 4
BB(3) = 6
BB(4) = 13

BB(5) = at least 4098
BB(6) = at least 4.640 × 10^1439
BB(12) = at least 4098 ⇈ 166 (which is 4098 raised to the power of 4098 raised to the power of 4098, etc, in a stack 166 4098's high)
(4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098^4098)