A trigintacentillion is equal to \(10^{393}\) in the short scale and \(10^{780}\) in the long scale by the Conway and Guy's naming system[1][2][3][4] as it is the 130th -illion number.
In the long scale, \(10^{393}\) is called quinsexagintilliard.
Approximations[]
For the short scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{393}\) (exact) | |
Arrow notation | \(10\uparrow 393\) (exact) | |
Steinhaus-Moser Notation | 175[3] | 176[3] |
Chained arrow notation | \(10\rightarrow 393\) (exact) | |
H* function | H(130) (exact) | |
Taro's multivariable Ackermann function | A(3,1302) | A(3,1303) |
BEAF & Bird's array notation | {10,393} (exact) | |
Hyper-E notation | E393 (exact) | |
s(n) map | \(s(1)^3(\lambda x.x+1)(7)\) | \(s(1)^3(\lambda x.x+1)(8)\) |
m(n) map | m(1)(175) | m(1)(176) |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)(0)[34] | (0)(0)(0)(0)(0)(0)(0)(0)[35] |
Copy notation | 9[393] | 10[197] |
Hyperfactorial array notation | 207! | 208! |
Fast-growing hierarchy | \(f_2(1295)\) | \(f_2(1296)\) |
Hardy hierarchy | \(H_{\omega^2}(1295)\) | \(H_{\omega^2}(1296)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^2 3+\omega 9+3}}(10)\) (exact) |
For the long scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{780}\) (exact) | |
Arrow notation | \(10\uparrow 780\) (exact) | |
Steinhaus-Moser Notation | 312[3] | 313[3] |
Chained arrow notation | \(10\rightarrow 780\) (exact) | |
Taro's multivariable Ackermann function | A(3,2588) | A(3,2589) |
BEAF & Bird's array notation | {10,780} (exact) | |
Hyper-E notation | E780 (exact) | |
s(n) map | \(s(1)^3(\lambda x.x+1)(8)\) | \(s(1)^3(\lambda x.x+1)(9)\) |
m(n) map | m(1)(312) | m(1)(313) |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)(0)(0)[33] | (0)(0)(0)(0)(0)(0)(0)(0)(0)[34] |
Fast-growing hierarchy | \(f_2(2579)\) | \(f_2(2580)\) |
Hardy hierarchy | \(H_{\omega^2}(2579)\) | \(H_{\omega^2}(2580)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^2 7+\omega 8}}(10)\) (exact) |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-11.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-11.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-02-11.
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-)