19,683 is a number equal to (33)3 = 332 = 39 = 273. It can be written as \(3 \downarrow \downarrow 3\) in down-arrow notation, and therefore it shows up frequently when working with threes in down-arrow notation, analogous to 7,625,597,484,987 in up-arrow notation.

With the fuga- prefix, this number can be named "fugathree".

19,683 is a Dudeney number, that is it's digits add up to its cube root: 1+9+6+8+3 = 27, and 273 = 19,683. It is the largest base-10 Dudeney number (the others are 512, 4,913, 5,832, and 17,576).

A 1 followed by 19683 zeros is called a sexmilliaquingentsexagintillion.

Approximation

Notation Lower bound Upper bound
Scientific notation \(1.9683\times10^4\)
Arrow notation \(3\uparrow9\)
Steinhaus-Moser Notation 5[3] 6[3]
Copy notation 1[5] 2[5]
Taro's multivariable Ackermann function A(3,11) A(3,12)
Pound-Star Notation #*(99)*2 #*(100)*2
BEAF {3,9}
Hyper-E notation E[3]9
Bashicu matrix system (0)[140] (0)[141]
Hyperfactorial array notation 7! 8!
Fast-growing hierarchy \(f_2(10)\) \(f_2(11)\)
Hardy hierarchy \(H_{\omega^2}(10)\) \(H_{\omega^2}(11)\)
Slow-growing hierarchy \(g_{\omega^{\varepsilon_0+\omega2}}(3)\)

See also

Numbers named with the fuga- family of prefixes

Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · gargoogol · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fzeleven · fztwelve · fzthirteen · fzfourteen · fzfifteen · fzsixteen · fzseventeen · fzeighteen · fznineteen · fztwenty · fzthirty · fzforty · fzfifty · fzsixty · fzseventy · fzeighty · fzninety · fzhundred · fzgoogol · fzmillion · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugaeleven · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugaeleven · megafugatwelve · megafugathirteen · megafugafourteen · megafugafifteen · megafugasixteen · megafugaseventeen · megafugaeighteen · megafuganineteen · megafugatwenty · megafugathirty · megafugaforty · megafugafifty · megafugasixty · megafugaseventy · megafugaeighty · megafuganinety · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex
Booga-: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaseven · boogaeight · booganine · boogaten · boogahundred · boogagoogol · boogagoogolplex
Gag: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaghundred · gaggoogol · gaggoogolplex

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