A quinoctogintacentillion is equal to \(10^{558}\) in the short scale and \(10^{1110}\) in the long scale by the Conway and Guy's naming system[1][2][3][4] as it is the 185th -illion number.
In the long scale, \(10^{558}\) is called trenonagintillion.
Approximations[]
For the short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{558}\) (exact) | |
| Arrow notation | \(10\uparrow 558\) (exact) | |
| Steinhaus-Moser Notation | 235[3] | 236[3] |
| Chained arrow notation | \(10\rightarrow 558\) (exact) | |
| Taro's multivariable Ackermann function | A(3,1850) | A(3,1851) |
| BEAF & Bird's array notation | {10,558} (exact) | |
| Hyper-E notation | E558 (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)(235) | m(1)(236) |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)(0)(0)[12] | (0)(0)(0)(0)(0)(0)(0)(0)(0)[13] |
| Fast-growing hierarchy | \(f_2(1842)\) | \(f_2(1843)\) |
| Hardy hierarchy | \(H_{\omega^2}(1842)\) | \(H_{\omega^2}(1843)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^2 5+\omega 5+8}}(10)\) (exact) | |
For the long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{1110}\) (exact) | |
| Arrow notation | \(10\uparrow 1110\) (exact) | |
| Steinhaus-Moser Notation | 422[3] | 423[3] |
| Chained arrow notation | \(10\rightarrow 1110\) (exact) | |
| Taro's multivariable Ackermann function | A(3,3684) | A(3,3685) |
| BEAF & Bird's array notation | {10,1110} (exact) | |
| Hyper-E notation | E1110 (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)(422) | m(1)(423) |
| Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
| Fast-growing hierarchy | \(f_2(3675)\) | \(f_2(3676)\) |
| Hardy hierarchy | \(H_{\omega^2}(3675)\) | \(H_{\omega^2}(3676)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^3+\omega^2+\omega}}(10)\) (exact) | |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-17.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-17.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-02-17.
See also[]
Main article: -illion
1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non10–19: decillion · undec · duodec · tredec · quattuordec · quindec · sexdec · septendec · octodec · novemdec
20–29: vigintillion · unvigint · duovigint · tresvigint · quattuorvigint · quinvigint · sesvigint · septemvigint · octovigint · novemvigint
30–39: trigintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
40–49: quadragintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
50–59: quinquagintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
60–69: sexagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
70–79: septuagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
80–89: octogintillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
90–99: nonagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
100–900: centillion · ducent · trecent · quadringent · quingent · sescent · septingent · octingent · nongent
1,000–1030: millillion · dumill · dumillinonagintanongent · trimill · trimilliduotrigintatrecent · trimillisexoctogintaoctingent · quadrimill · quadrimilliquattuordecicent · quinmill · sexmill · septimill · octimill · nonimill · myr · decimilliquinsexagintasescent · dumyr · unquadragintamilliunquinquagintacent · centimill · micr · nan · pic · femt · att · zept · yoct · ront · quect
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-)