Pentation
Repeated tetration or hyper-4 is pentation or hyper-5. It can make HUGE numbers very, very quickly.
For example:
![$2[5]2 = 2[4]2 = 2^2 = 4$](http://latex.artofproblemsolving.com/a/7/a/a7a6ece5197db7e1048916542110fcab2c1b47f8.png)
If we increase the last 
of ![$2[5]2$](http://latex.artofproblemsolving.com/0/d/7/0d79074c6c4b9ee04b73b402cc09c2e34c643464.png)
, then let's see what happens:
![$2[5]3 = 2[4](2[4]2) = 2[4]4 = 2^{2^{2^{2}}} = 2^{16} = 65536$](http://latex.artofproblemsolving.com/9/3/f/93f2fbdff9ba7bc148f6777290d88b137a85c9d9.png)
Pentation grows much faster than what you're used to, like exponentiation.
We know that repeated addition is multiplication, repeated multiplication is exponentiation (a↑b), repeated exponentiation is tetration (a↑↑b), and what is repeated tetration, pentation (a↑↑↑b)!
