A quinviginticentillion is equal to \(10^{378}\) in the short scale and \(10^{750}\) in the long scale by the Conway and Guy's naming system[1][2][3][4] as it is the 125th -illion number.
In the long scale, \(10^{378}\) is called tresexagintillion.
Approximations[]
For the short scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{378}\) (exact) | |
Arrow notation | \(10\uparrow 378\) (exact) | |
Steinhaus-Moser Notation | 169[3] | 170[3] |
Chained arrow notation | \(10\rightarrow 378\) (exact) | |
Taro's multivariable Ackermann function | A(3,1252) | A(3,1253) |
BEAF & Bird's array notation | {10,378} (exact) | |
Hyper-E notation | E378 (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)(169) | m(1)(170) |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)(0)[29] | (0)(0)(0)(0)(0)(0)(0)(0)[30] |
Fast-growing hierarchy | \(f_2(1245)\) | \(f_2(1246)\) |
Hardy hierarchy | \(H_{\omega^2}(1245)\) | \(H_{\omega^2}(1246)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^2 3+\omega 7+8}}(10)\) (exact) |
For the long scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{750}\) (exact) | |
Arrow notation | \(10\uparrow 750\) (exact) | |
Steinhaus-Moser Notation | 302[3] | 303[3] |
Chained arrow notation | \(10\rightarrow 750\) (exact) | |
Taro's multivariable Ackermann function | A(3,2488) | A(3,2489) |
BEAF & Bird's array notation | {10,750} (exact) | |
Hyper-E notation | E750 (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)(302) | m(1)(303) |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)(0)(0)[29] | (0)(0)(0)(0)(0)(0)(0)(0)(0)[30] |
Fast-growing hierarchy | \(f_2(2480)\) | \(f_2(2481)\) |
Hardy hierarchy | \(H_{\omega^2}(2480)\) | \(H_{\omega^2}(2481)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^2 7+\omega 5}}(10)\) (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-)