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".[1][2][3]
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).
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[]
Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · garmillion · gargoogol · gareceton · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex · megafugagrangol
Extensions:
Booga-:: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten · boogahundred · boogagoogol · boogagoogolplex
Gag-:: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex
- ↑ Cockburn, Alistair. A fuga really big numbers (archived 2016.
- ↑ Saibian, Sbiis. The Fz, The Fuga & The Megafuga. Retrieved 2021-07-22.
- ↑ Cookiefonster. 2.5A. Googological prefixes and suffixes - Pointless Large Number Stuff. Retrieved 2021-07-22.