An octocentillion is equal to \(10^{327}\) in the short scale and \(10^{648}\) in the long scale by Conway and Guy's naming system[1][2][3][4] as it is the 108th -illion number.
In the long scale, \(10^{327}\) is called quattuorquinquagintilliard.
Aarex Tiaokhiao gave the name cennillion, referring to the short-scale value of this number.[5][dead link]
Approximations[]
For short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{327}\) | |
| Arrow notation | \(10\uparrow327\) | |
| Steinhaus-Moser Notation | 150[3] | 151[3] |
| Copy notation | 9[327] | 10[164] |
| Taro's multivariable Ackermann function | A(3,1083) | A(3,1084) |
| Pound-Star Notation | #*((4375))*11 | #*((4376))*11 |
| BEAF | {10,327} | |
| Hyper-E notation | E327 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)[358] | (0)(0)(0)(0)(0)(0)(0)[359] |
| Hyperfactorial array notation | 178! | 179! |
| Fast-growing hierarchy | \(f_2(1076)\) | \(f_2(1077)\) |
| Hardy hierarchy | \(H_{\omega^2}(1076)\) | \(H_{\omega^2}(1077)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^23+\omega2+7}}(10)\) | |
For long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{648}\) | |
| Arrow notation | \(10\uparrow648\) | |
| Steinhaus-Moser Notation | 267[3] | 268[3] |
| Copy notation | 9[648] | 1[649] |
| Taro's multivariable Ackermann function | A(3,2149) | A(3,2150) |
| Pound-Star Notation | #*((5258))*15 | #*((5259))*15 |
| BEAF | {10,648} | |
| Hyper-E notation | E648 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)(0)[339] | (0)(0)(0)(0)(0)(0)(0)(0)[340] |
| Hyperfactorial array notation | 313! | 314! |
| Fast-growing hierarchy | \(f_2(2141)\) | \(f_2(2142)\) |
| Hardy hierarchy | \(H_{\omega^2}(2141)\) | \(H_{\omega^2}(2142)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^26+\omega4+8}}(10)\) | |
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.
- ↑ 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-)