Googoltriplex

GoogoltriplexAntonio Padilla (2023) "Fantastic numbers and where to find them: A journey to the edge of physics" Penguin Books. ISBN 978-0141992822 p.41 (also known as googolplexplexplex, googolplusplexplus, googolplexianite, googolplexianthWhich is bigger, a Googolplexianth or Graham's number? | Graham's Number - Quora or gargantugoogolplexPlexing & The Googol Series - Large Numbers by Sbiis Saibian) 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:Intermediate -illions: Continued (Retrieved 19 April, 2022)
DeepLineMadom calls the number troogoltriplex, and is equal to 10[3]10[3]10[3]10[3]100 in DeepLineMadom's Array NotationDeepLineMadom's googology - Numbers I've coined (Retrieved 4 May 2022).
== 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 ==
== See also ==
ja:グーゴルプレックスプレックスプレックス
zh:古戈爾特利普勒克斯
Category:Numbers
Category:Class 5
Category:Googol series
Category:Numbers with peer-reviewed source