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Googoltriplex[1] (also known as googolplexplexplex,[2] googolplusplexplus,[3] googolplexianite[4], googolplexianth[5] or gargantugoogolplex[6]) is a number equal to $$10^{10^{10^{10^{100}}}}$$, or 1 followed by googolduplex zeroes. In Hyper-E Notation it can be written as E100#4. In down-arrow notation it can also be written $$10 \downarrow\downarrow ((10\downarrow\downarrow101)+1)$$. It is 101010100+1 digits long.

Writing down the full decimal expansion would take 101010100-6 books of 400 pages each, with 2,500 digits on each page (except for the first, which would have 2,501).

## Etymology

The Greek prefix "tri-" (3) is understood to iterate the "-plex" suffix three times, forming an abbreviation for the unwieldy "googolplexplexplex." None of the other names seem to have any logical etymology.

## Other names

Using Aarex Tiaokhiao's -illion generalization of Nirvana's -illions, this number is approximately:[7]

one trogarriji-trotractrogarreji-trotractrogarrekali-trotractrogarrillion

DeepLineMadom calls the number troogoltriplex, and is equal to 10[3]10[3]10[3]10[3]100 in DeepLineMadom's Array Notation[8].

## Approximations in other notations

Notation Approximation
Arrow notation $$10 \uparrow 10 \uparrow 10 \uparrow 10 \uparrow 100$$ (exact)
Chained arrow notation $$10 \rightarrow (10 \rightarrow (10 \rightarrow (10 \rightarrow 100)))$$ (exact)
Hyper-E notation $$\textrm{E}100\#4$$ (exact)
Hyperfactorial array notation $$(((69!)!)!)!$$
BEAF $$\{10,\{10,\{10,\{10,100\}\}\}\}$$ (exact)
Fast-growing hierarchy $$f_2^{4}(326)$$
Hardy hierarchy $$H_{\omega^2\times 4}(326)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega^{\omega^{\omega^2}}}}}(10)$$ (exact)