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Googoltriplex

Googoltriplex in zeroes

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.

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.

Approximations in other notations

Notation Approximation
Up-arrow notation \(10 \uparrow 10 \uparrow 10 \uparrow 10 \uparrow 100\) (exact)
Chained arrow notation \(10 \rightarrow 10^{10^{10^{100}}}\) (exact)
Hyper-E notation \(E100\#4\) (exact)
Hyperfactorial array notation \((((69!)!)!)!\)
BEAF \(\{10,\{10,\{10,\{10,100\}\}\}\}\) (exact)
Fast-growing hierarchy \(f_2(f_2(f_2(f_2(324))))\)
Hardy hierarchy \(H_{\omega^24}(324)\)
Slow-growing hierarchy \(g_{\omega^{\omega^{\omega^{\omega^{\omega^2}}}}}(10)\) (exact)

Sources

See also

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

0-stack series: googol · googolplex · googolbang · googolplexplex · googolplexbang · googolbangplex · googolbangbang · googolplexplexplex · googolplexplexbang · googolplexbangplex · googolplexbangbang · googolbangplexplex · googolbangplexbang · googolbangbangplex · googolbangbangbang
1-stack series: googolstack · googolstackplex · googolstackbang · googolstackplexplex · googolstackplexbang · googolstackbangplex · googolstackbangbang · googolplexstack · googolplexstackplex · googolplexstackbang · googolbangstack · googolbangstackplex · googolbangstackbang · googolplexplexstack · googolplexbangstack · googolbangplexstack · googolbangbangstack
2-stack series: googolstackstack · googolstackstackplex · googolstackstackbang · googolstackplexstack · googolstackbangstack · googolplexstackstack · googolbangstackstack
3-stack series: googolstackstackstack

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