20,522
pages

View full site to see MathJax equation

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 a googolduplex or googolplexian 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) $$\approx 10 \uparrow\uparrow 5.30103$$
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)
Steinhaus-Moser Notation $$57[3][3][3][3]$$

Sources

Googol and related numbers

Originals: googol · googolplex
Cockburn's examples: gargoogolplex · fzgoogolplex · (mega)fugagoogolplex
Googol-n-plex: googolduplex · googoltriplex · -quadriplex · -quinplex · -sextiplex · -septiplex · -octiplex · -noniplex · -deciplex · -centiplex
Googol-103n-plex: googolmilliplex · -megaplex · -gigaplex · -teraplex · -petaplex · -exaplex · -zettaplex · -yottaplex · -xennaplex · -vekaplex · -mekaplex
Bowers' extensions: giggol · gaggol · geegol · boogol · biggol · troogol · goobol · more...
Saibian's extensions: googol-minutia · googolchime · googoltoll · googolgong · grangol · greagol · gigangol · gugold · graatagold · gugolthra · throogol · godgahlah · tethrathoth · more...
Miscellany: googolbang (10100!) · googolminex (10^-10100) · googolteen · googolty · great googol(plex) · gooprol · little googol/googolbit · zootzootplex

Googol plex bang stack numbers
Googol — Greagol
Greagol — Gugold
Throogol — Godgahlah-ex-grand godgahlah