- Not to be confused with ducentillion.
A duocentillion is equal to \(10^{309}\) in the short scale and \(10^{612}\) in the long scale by Conway and Guy's naming system[1][2][3][4] and with Jonathan Bowers system (short scale)[5] as it is the 102nd -illion number. It is the smallest -illion number not expressible in the double-precision floating-point format, as it maxes out at \(2^{1,024}\).
In the long scale, \(10^{309}\) is called unquinquagintilliard.
Aarex Tiaokhiao gave the name cetertillion, referring to the short-scale value of this number.[6]
Do not confuse this number with Landon Curt Noll's duocentillion which means \(10^{603}\) in the short scale or ducentillion in Conway's system.[7][8]
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] |
Chained arrow notation | \(10\rightarrow309\) | |
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 & Bird's array notation | {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[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-08.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-08.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-02-08.
- ↑ Illion Numbers
- ↑ Aarex Tiaokhiao's illion numbers[dead link]
- ↑ English names of the first 10000 powers of 10 - American System without dashes
- ↑ English names of the first 10000 powers of 10 - European System without dashes
See also[]
Main article: -illion
100–109: centillion (un- · duo- · tres- · quattuor- · quin- · sex- · septen- · octo- · noven-)110–119: decicentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
120–129: viginticentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
130–139: trigintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
140–149: quadragintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
150–159: quinquagintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
160–169: sexagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
170–179: septuagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
180–189: octogintacentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
190–199: nonagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)