Quattuorcentillion is equal to \(10^{315}\) in the short scale and \(10^{624}\) in the long scale.[1]
The least example \(n\) of \(\pi(n) > li(n)\) must be smaller than 14 quattuorcentillion[citation needed].
In the long scale, \(10^{315}\) is called duoquinquagintilliard.
Approximations
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{315}\) | |
| Arrow notation | \(10\uparrow315\) | |
| Steinhaus-Moser Notation | 145[3] | 146[3] |
| Copy notation | 9[315] | 10[158] |
| Chained arrow notation | 10→315 | |
| H* function | H(104) | |
| Taro's multivariable Ackermann function | A(3,1043) | A(3,1044) |
| Pound-Star Notation | #*((1173))*11 | #*((1174))*11 |
| BEAF & Bird's array notation | {10,315} | |
| Hyper-E notation | E315 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)[83536] | (0)(0)(0)(0)(0)(0)[83537] |
| Hyperfactorial array notation | 173! | 174! |
| Fast-growing hierarchy | \(f_2(1\,036)\) | \(f_2(1\,037)\) |
| Hardy hierarchy | \(H_{\omega^2}(1\,036)\) | \(H_{\omega^2}(1\,037)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^23+\omega+5}}(10)\) | |
Sources
- ↑ Sbiis Saibian, 2.4.8 - Bowers' -illions - Large 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-)