A quattuorcentillion is equal to \(10^{315}\) in the short scale and \(10^{624}\) in the long scale by Conway and Guy's naming system[1][2][3][4] as it is the 104th -illion number.
The least example \(n\) of \(\pi(n) > \mathrm{li}(n)\) must be smaller than 14 quattuorcentillion.[5]
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[]
- ↑ 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.
- ↑ Y. Saouter and P. Demichel (2010) A sharp region where π(x) - li(n) is positive. Math. Comp. 79, 2395-2405. doi:10.1090/S0025-5718-10-02351-3 Theorem 6.3
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-)