Tritet Jr.

Tritet Jr. is equal to \(4 \uparrow\uparrow 4\) in up-arrow notationAscending with Up Arrows, or \( \lbrace 4,4,2 \rbrace \) in BEAF. The number used to be called tritet, a much larger number named and renamed by Jonathan Bowers. Sbiis Saibian coined the new name. Using Alistair Cockburn's megafuga- prefix, Tritet Jr. can be named "megafugafour".3.2.2 - The Fz, The Fuga & The Megafuga It can also be named "boogafour" using the booga- prefix, or "troogatwo" using the trooga- prefix.
It is approximately \(10^{8.0723 \times 10^{153}}\), meaning that it's somewhat larger than a googolplex. The decimal expansion of Tritet Jr. is: 23,610,226,714,597,313,206............36,860,456,095,261,392,896. The leading digits are computed using logarithms and the terminating digits are computed using modular exponentiation.
Its exact value can be computed using basic laws of algebra: \(4\uparrow\uparrow4 = 4^{4^{4^{4}}} = 4^{4^{256}} = 4^{2^{512}} = 2^{2^{513}}\).
It is currently unknown, whether its successor, which is the 513th Fermat number, is composite or prime.http://www.prothsearch.com/fermat.html
Wiki user Hyp cos calls this number a tetbo, and it's equal to s(4,4,2), s(4,2,3), s(4,2,1,2), or s(4,2{2}2) in strong array notation. Numbers from linear array notation | Steps Toward Infinity!
Googology wiki user HaydenTheGoogologist2009 calls this number Hayden's Tritet, and it's equal to 4(4)4 in Hayden's Array Notation.Hayden's Big Numbers. Retrieved 2022-04-18.
== -illion name ==
Using Jonathan Bower's -illions series, some -illion name terms for Tritet Jr. are:
23 	Twenty-three
duo-mepentaconto-
nonagintisescenti-pentaconto-
octosexagintiseptingenti-ennetetraconto-
duoquadragintiducenti-octetetraconto-
novem-heptetetraconto-
octoquadringenti-hexetetraconto-
novemquinquagintiquadringenti-pentetetraconto-
quattuornonagintiseptingenti-tetretetraconto-
deciducenti-tretetraconto-
doetriginticenti-duetetraconto-
unsexagintitrecenti-metetraconto-
novemnonagintiseptingenti-tetraconto-
sexseptuagintisescenti-ennetriaconto-
nonagintisescenti-octetriaconto-
quinquinquagintiquadringenti-heptetriaconto-
treseptuagintinongenti-hexetriaconto-
doedecinongenti-pentetriaconto-
quattuordecinongenti-tetretriaconto-
trequadragintitrecenti-tretriaconto-
quinquinquagintinongenti-duetriaconto-
quattuornonagintisescenti-metriaconto-
sexseptuagintiducenti-triaconto-
novemtriginticenti-enneicoso-
unseptuagintiquadringenti-octeicoso-
trenonagintiquadringenti-hepteicoso-
sexquinquagintioctingenti-hexeicoso-
centreti-penteicoso-
novemquadraginti-tetreicoso-
doetrigintiseptingenti-trioicoso-
septuagintinongenti-dueicoso-
quattuorsescenti-meiocoso-
nongenti-icoso-
novemquadringenti-enneco-
septenvigintioctingenti-octeco-
septendecioctingenti-hepteco-
septenvigintitrecenti-hexeco-
quinoctoginticenti-penteco-
octoquinquagintioctingenti-treteco-
septenquinquagintiducenti-treco-
doequinquaginti-dueco-
quinsexaginticenti-meco-
quinoctogintiquadringenti-veco-
sexquadragintiseptingenti-xono-
octoseptuaginticenti-yocto-
tretrigintiquadringenti-zepto-
novemviginti-atto-
sexaginticenti-femto-
quattuordeciquadringenti-pico-
sexnonagintinongenti-nano-
trequinquagintiseptingenti-micro-
treoctogintiseptingenti-milli-
quinseptingentillion
610 	Six hundred ten
duo-mepentaconto-
nonagintisescenti-pentaconto-
octosexagintiseptingenti-ennetetraconto-
duoquadragintiducenti-octetetraconto-
novem-heptetetraconto-
octoquadringenti-hexetetraconto-
novemquinquagintiquadringenti-pentetetraconto-
quattuornonagintiseptingenti-tetretetraconto-
deciducenti-tretetraconto-
doetriginticenti-duetetraconto-
unsexagintitrecenti-metetraconto-
novemnonagintiseptingenti-tetraconto-
sexseptuagintisescenti-ennetriaconto-
nonagintisescenti-octetriaconto-
quinquinquagintiquadringenti-heptetriaconto-
treseptuagintinongenti-hexetriaconto-
doedecinongenti-pentetriaconto-
quattuordecinongenti-tetretriaconto-
trequadragintitrecenti-tretriaconto-
quinquinquagintinongenti-duetriaconto-
quattuornonagintisescenti-metriaconto-
sexseptuagintiducenti-triaconto-
novemtriginticenti-enneicoso-
unseptuagintiquadringenti-octeicoso-
trenonagintiquadringenti-hepteicoso-
sexquinquagintioctingenti-hexeicoso-
centreti-penteicoso-
novemquadraginti-tetreicoso-
doetrigintiseptingenti-trioicoso-
septuagintinongenti-dueicoso-
quattuorsescenti-meiocoso-
nongenti-icoso-
novemquadringenti-enneco-
septenvigintioctingenti-octeco-
septendecioctingenti-hepteco-
septenvigintitrecenti-hexeco-
quinoctoginticenti-penteco-
octoquinquagintioctingenti-treteco-
septenquinquagintiducenti-treco-
doequinquaginti-dueco-
quinsexaginticenti-meco-
quinoctogintiquadringenti-veco-
sexquadragintiseptingenti-xono-
octoseptuaginticenti-yocto-
tretrigintiquadringenti-zepto-
novemviginti-atto-
sexaginticenti-femto-
quattuordeciquadringenti-pico-
sexnonagintinongenti-nano-
trequinquagintiseptingenti-micro-
treoctogintiseptingenti-milli-
quattuorseptingentillion
226 	Two hundred twenty-six
duo-mepentaconto-
nonagintisescenti-pentaconto-
octosexagintiseptingenti-ennetetraconto-
duoquadragintiducenti-octetetraconto-
novem-heptetetraconto-
octoquadringenti-hexetetraconto-
novemquinquagintiquadringenti-pentetetraconto-
quattuornonagintiseptingenti-tetretetraconto-
deciducenti-tretetraconto-
doetriginticenti-duetetraconto-
unsexagintitrecenti-metetraconto-
novemnonagintiseptingenti-tetraconto-
sexseptuagintisescenti-ennetriaconto-
nonagintisescenti-octetriaconto-
quinquinquagintiquadringenti-heptetriaconto-
treseptuagintinongenti-hexetriaconto-
doedecinongenti-pentetriaconto-
quattuordecinongenti-tetretriaconto-
trequadragintitrecenti-tretriaconto-
quinquinquagintinongenti-duetriaconto-
quattuornonagintisescenti-metriaconto-
sexseptuagintiducenti-triaconto-
novemtriginticenti-enneicoso-
unseptuagintiquadringenti-octeicoso-
trenonagintiquadringenti-hepteicoso-
sexquinquagintioctingenti-hexeicoso-
centreti-penteicoso-
novemquadraginti-tetreicoso-
doetrigintiseptingenti-trioicoso-
septuagintinongenti-dueicoso-
quattuorsescenti-meiocoso-
nongenti-icoso-
novemquadringenti-enneco-
septenvigintioctingenti-octeco-
septendecioctingenti-hepteco-
septenvigintitrecenti-hexeco-
quinoctoginticenti-penteco-
octoquinquagintioctingenti-treteco-
septenquinquagintiducenti-treco-
doequinquaginti-dueco-
quinsexaginticenti-meco-
quinoctogintiquadringenti-veco-
sexquadragintiseptingenti-xono-
octoseptuaginticenti-yocto-
tretrigintiquadringenti-zepto-
novemviginti-atto-
sexaginticenti-femto-
quattuordeciquadringenti-pico-
sexnonagintinongenti-nano-
trequinquagintiseptingenti-micro-
treoctogintiseptingenti-milli-
treseptingentillion
714 	Seven hundred fourteen
duo-mepentaconto-
nonagintisescenti-pentaconto-
octosexagintiseptingenti-ennetetraconto-
duoquadragintiducenti-octetetraconto-
novem-heptetetraconto-
octoquadringenti-hexetetraconto-
novemquinquagintiquadringenti-pentetetraconto-
quattuornonagintiseptingenti-tetretetraconto-
deciducenti-tretetraconto-
doetriginticenti-duetetraconto-
unsexagintitrecenti-metetraconto-
novemnonagintiseptingenti-tetraconto-
sexseptuagintisescenti-ennetriaconto-
nonagintisescenti-octetriaconto-
quinquinquagintiquadringenti-heptetriaconto-
treseptuagintinongenti-hexetriaconto-
doedecinongenti-pentetriaconto-
quattuordecinongenti-tetretriaconto-
trequadragintitrecenti-tretriaconto-
quinquinquagintinongenti-duetriaconto-
quattuornonagintisescenti-metriaconto-
sexseptuagintiducenti-triaconto-
novemtriginticenti-enneicoso-
unseptuagintiquadringenti-octeicoso-
trenonagintiquadringenti-hepteicoso-
sexquinquagintioctingenti-hexeicoso-
centreti-penteicoso-
novemquadraginti-tetreicoso-
doetrigintiseptingenti-trioicoso-
septuagintinongenti-dueicoso-
quattuorsescenti-meiocoso-
nongenti-icoso-
novemquadringenti-enneco-
septenvigintioctingenti-octeco-
septendecioctingenti-hepteco-
septenvigintitrecenti-hexeco-
quinoctoginticenti-penteco-
octoquinquagintioctingenti-treteco-
septenquinquagintiducenti-treco-
doequinquaginti-dueco-
quinsexaginticenti-meco-
quinoctogintiquadringenti-veco-
sexquadragintiseptingenti-xono-
octoseptuaginticenti-yocto-
tretrigintiquadringenti-zepto-
novemviginti-atto-
sexaginticenti-femto-
quattuordeciquadringenti-pico-
sexnonagintinongenti-nano-
trequinquagintiseptingenti-micro-
treoctogintiseptingenti-milli-
duoseptingentillion
597 	Five hundred ninety-seven
duo-mepentaconto-
nonagintisescenti-pentaconto-
octosexagintiseptingenti-ennetetraconto-
duoquadragintiducenti-octetetraconto-
novem-heptetetraconto-
octoquadringenti-hexetetraconto-
novemquinquagintiquadringenti-pentetetraconto-
quattuornonagintiseptingenti-tetretetraconto-
deciducenti-tretetraconto-
doetriginticenti-duetetraconto-
unsexagintitrecenti-metetraconto-
novemnonagintiseptingenti-tetraconto-
sexseptuagintisescenti-ennetriaconto-
nonagintisescenti-octetriaconto-
quinquinquagintiquadringenti-heptetriaconto-
treseptuagintinongenti-hexetriaconto-
doedecinongenti-pentetriaconto-
quattuordecinongenti-tetretriaconto-
trequadragintitrecenti-tretriaconto-
quinquinquagintinongenti-duetriaconto-
quattuornonagintisescenti-metriaconto-
sexseptuagintiducenti-triaconto-
novemtriginticenti-enneicoso-
unseptuagintiquadringenti-octeicoso-
trenonagintiquadringenti-hepteicoso-
sexquinquagintioctingenti-hexeicoso-
centreti-penteicoso-
novemquadraginti-tetreicoso-
doetrigintiseptingenti-trioicoso-
septuagintinongenti-dueicoso-
quattuorsescenti-meiocoso-
nongenti-icoso-
novemquadringenti-enneco-
septenvigintioctingenti-octeco-
septendecioctingenti-hepteco-
septenvigintitrecenti-hexeco-
quinoctoginticenti-penteco-
octoquinquagintioctingenti-treteco-
septenquinquagintiducenti-treco-
doequinquaginti-dueco-
quinsexaginticenti-meco-
quinoctogintiquadringenti-veco-
sexquadragintiseptingenti-xono-
octoseptuaginticenti-yocto-
tretrigintiquadringenti-zepto-
novemviginti-atto-
sexaginticenti-femto-
quattuordeciquadringenti-pico-
sexnonagintinongenti-nano-
trequinquagintiseptingenti-micro-
treoctogintiseptingenti-milli-
unseptingentillion
... ...	
2,690,768,242,009,408,459,794,210,132,361,799,676,690,455,973,912,914,343,955,694,276,139,471
,493,856,103,049,732,970,604,900,409,827,817,327,185,858,257,052,165,485,746,178,433,029,160
,414,996,753,783,695 more groups of -illion names.
456 	Four hundred fifty-six trillion
095 	Ninety-five billion
261 	Two hundred sixty-one million
392 	Three hundred ninety-two thousand
896 	Eight hundred ninety-six
== Approximations ==
Notation 	Lower bound 	Upper bound
Down-arrow notation 	\(4\downarrow\downarrow257\) 	\(4\downarrow\downarrow257\)
Steinhaus-Moser Notation 	79[3][3] 	80[3][3]
Copy notation 	7[7[154]] 	8[8[154]]
H* function 	H(2H(50)) 	H(3H(50))
Taro's multivariable Ackermann function	A(3,A(3,509)) 	A(3,A(3,510))
Pound-Star Notation 	#*((1))*(2,8,7,10,3)*11 	#*((1))*(9,0,9,2,7,5)*8
Hyper-E notation 	E[4]1#4 	E[4]1#4
Bashicu matrix system 	(0)(1)[22] 	(0)(1)[23]
Hyperfactorial array notation 	(96!)! 	(97!)!
Fast-growing hierarchy 	\(f_2(f_2(504))\) 	\(f_2(f_2(505))\)
Hardy hierarchy 	\(H_{\omega^22}(504)\) 	\(H_{\omega^22}(505)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^{\omega^\omega}}}(4)\)	\(g_{\omega^{\omega^{\omega^\omega}}}(4)\)
== Sources ==
== See also ==
*megafuga-
Category:Numbers
Category:3 entry linear
Category:Class 3
Category:Numbers by Sbiis Saibian
Category:Powers of 2
Category:Upper class 3
Category:Booga-
Category:Megafuga-