A quattuoroctogintaducentillion is equal to \(10^{855}\) in the short scale and \(10^{1704}\) in the long scale by the Conway and Guy's naming system[1][2][3][4][5] as it is the 284th -illion number.
In the long scale, \(10^{855}\) is called duoquadragintacentilliard.
Approximations[]
For the short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{855}\) (exact) | |
| Arrow notation | \(10\uparrow 855\) (exact) | |
| Steinhaus-Moser Notation | 338[3] | 339[3] |
| Chained arrow notation | \(10\rightarrow 855\) (exact) | |
| Taro's multivariable Ackermann function | A(3,2837) | A(3,2838) |
| BEAF & Bird's array notation | {10,855} (exact) | |
| Hyper-E notation | E855 (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)(338) | m(1)(339) |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)(0)(0)[46] | (0)(0)(0)(0)(0)(0)(0)(0)(0)[47] |
| Fast-growing hierarchy | \(f_2(2828)\) | \(f_2(2829)\) |
| Hardy hierarchy | \(H_{\omega^2}(2828)\) | \(H_{\omega^2}(2829)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^2 8+\omega 5+5}}(10)\) (exact) | |
For the long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{1704}\) (exact) | |
| Arrow notation | \(10\uparrow 1704\) (exact) | |
| Steinhaus-Moser Notation | 611[3] | 612[3] |
| Chained arrow notation | \(10\rightarrow 1704\) (exact) | |
| Taro's multivariable Ackermann function | A(3,5657) | A(3,5658) |
| BEAF & Bird's array notation | {10,1704} (exact) | |
| Hyper-E notation | E1704 (exact) | |
| s(n) map | \(s(1)^3(\lambda x.x+1)(9)\) | \(s(1)^3(\lambda x.x+1)(10)\) |
| m(n) map | m(1)(611) | m(1)(612) |
| Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
| Fast-growing hierarchy | \(f_2(5648)\) | \(f_2(5649)\) |
| Hardy hierarchy | \(H_{\omega^2}(5648)\) | \(H_{\omega^2}(5649)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^3+\omega^2 7+4}}(10)\) (exact) | |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-27.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-27.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-02-27.
- ↑ Fish. Conway's illion converter - 10^855. Retrieved 2023-02-27.
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
200–209: ducentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)210–219: deciducentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
220–229: vigintiducentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
230–239: trigintaducentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
240–249: quadragintaducentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
250–259: quinquagintaducentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
260–269: sexagintaducentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
270–279: septuagintaducentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
280–289: octogintaducentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
290–299: nonagintaducentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)