- Not to be confused with ducentillion.
- For the duocentillion by Curt Noll, see Duocentillion (Noll).
The duocentillion is equal to \(10^{309}\).[1] The term was coined by Jonathan Bowers. It is the smallest -illion number not expressible in the double-precision floating-point format, as it maxes out at \(2^{1,024}\).
Aarex Tiaokhiao gave the name cetertillion, referring to the value of this number.[2]
In the long scale, \(10^{309}\) is called unquinquagintilliard
Decimal Expansion
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{309}\) | |
| Arrow notation | \(10\uparrow309\) | |
| Steinhaus-Moser Notation | 143[3] | 144[3] |
| Copy notation | 9[309] | 10[155] |
| Taro's multivariable Ackermann function | A(3,1023) | A(3,1024) |
| Pound-Star Notation | #*((608))*11 | #*((609))*11 |
| BEAF | {10,309} | |
| Hyper-E notation | E309 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)[67317] | (0)(0)(0)(0)(0)(0)[67318] |
| Hyperfactorial array notation | 170! | 171! |
| Fast-growing hierarchy | \(f_2(1\,016)\) | \(f_2(1\,017)\) |
| Hardy hierarchy | \(H_{\omega^2}(1\,016)\) | \(H_{\omega^2}(1\,017)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^23+9}}(10)\) | |
Sources
See also
Main article: -illion
100–109: centillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)110–119: decicentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
120–129: viginticentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
130–139: trigintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
140–149: quadragintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
150–159: quinquagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
160–169: sexagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
170–179: septuagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
180–189: octogintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
190–199: nonagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
