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
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 \(E100\#4\) (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)

Sources

See also

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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