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This took me 15 s:

9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9

Read the article and take another 15s. That was one of the naive examples he gives near the start.
The number that can only be named with too many words.
Maybe "Googolplex!" ?
Nope. Gotta use an infinite nested series of Busy Beaver functions, or something like that.