An uncentillion is equal to \(10^{306}\) in the short scale and \(10^{606}\) in the long scale by Conway and Guy's naming system[1][2][3][4] as it is the 101st -illion number. Jonathan Bowers called this number cenuntillion.[5] Aarex Tiaokhiao called this number cebillion.[6][dead link] It is the largest -illion expressible in the double-precision floating-point format, as it maxes out at \(2^{1,024}\).
In the long scale, \(10^{306}\) is called unquinquagintillion.
Approximations[]
For short scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{306}\) | |
Arrow notation | \(10\uparrow306\) | |
Steinhaus-Moser Notation | 142[3] | 143[3] |
Copy notation | 9[306] | 1[307] |
Taro's multivariable Ackermann function | A(3,1013) | A(3,1014) |
Pound-Star Notation | #*((437))*11 | #*((438))*11 |
BEAF | {10,306} | |
Hyper-E notation | E306 | |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)[60429] | (0)(0)(0)(0)(0)(0)[60430] |
Hyperfactorial array notation | 169! | 170! |
Fast-growing hierarchy | \(f_2(1\,006)\) | \(f_2(1\,007)\) |
Hardy hierarchy | \(H_{\omega^2}(1\,006)\) | \(H_{\omega^2}(1\,007)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^23+6}}(10)\) |
For long scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{606}\) | |
Arrow notation | \(10\uparrow606\) | |
Steinhaus-Moser Notation | 252[3] | 253[3] |
Copy notation | 9[606] | 1[607] |
Taro's multivariable Ackermann function | A(3,2010) | A(3,2011) |
Pound-Star Notation | #*((187))*15 | #*((188))*15 |
BEAF | {10,606} | |
Hyper-E notation | E606 | |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)[54246] | (0)(0)(0)(0)(0)(0)(0)[54247] |
Hyperfactorial array notation | 296! | 297! |
Fast-growing hierarchy | \(f_2(2\,002)\) | \(f_2(2\,003)\) |
Hardy hierarchy | \(H_{\omega^2}(2\,002)\) | \(H_{\omega^2}(2\,003)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^26+6}}(10)\) |
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
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-)