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3{3{...{4}...}3}3 64 times

That sounds big!

It is, but not as big as my Bower's array notation reporter can calculate (even though it's googologically slow)

G1 = 3{4}3 = 3^^^^3, which is 3^^^3^^^3, which is 3^^3^^...^^3^^3 3^^^3 times, in which 3^^^3 is 3^^3^^3, which is 3^^7e12., which in general is 3^3^3^... 7 trillion times.

G2 = 3{G1}3 = 3{G1-1}3{G1-1}3 which is 3{G1-2}3{G1-2}... 3{G1-1}3 times.

G3 = 3{G2}3

Repeat this until you reach G64. That's exactly what this computes.