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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).

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 $$g_{\omega^{\varepsilon_0+\omega2}}(3)$$