I find Loader's number [1] more interesting, as it is actually computable, yet far far larger than other famous computable numbers, like Friedman's TREE(3) or SCG(3).
I'm looking forward to one day programming it in the lambda calculus, and seeing how much smaller than the existing ~500 bytes of C-code it can be.
[1] https://www.youtube.com/watch?v=q6Etl4oGL4U&list=PL-R4p-BRL8...