A duotrigintaquadringentillion is equal to \(10^{1299}\) in the short scale and \(10^{2592}\) in the long scale by the Conway and Guy's naming system[1][2][3][4][5] as it is the 432nd -illion number.
In the long scale, \(10^{1299}\) is called sedeciducentilliard.[6]
Approximations[]
For the short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{1299}\) (exact) | |
| Arrow notation | \(10\uparrow 1299\) (exact) | |
| Steinhaus-Moser Notation | 483[3] | 484[3] |
| Chained arrow notation | \(10\rightarrow 1299\) (exact) | |
| Taro's multivariable Ackermann function | A(3,4312) | A(3,4313) |
| BEAF & Bird's array notation | {10,1299} (exact) | |
| Hyper-E notation | E1299 (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)(483) | m(1)(484) |
| Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
| Fast-growing hierarchy | \(f_2(4303)\) | \(f_2(4304)\) |
| Hardy hierarchy | \(H_{\omega^2}(4303)\) | \(H_{\omega^2}(4304)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^3+\omega^2 2+\omega 9+9}}(10)\) (exact) | |
For the long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{2592}\) (exact) | |
| Arrow notation | \(10\uparrow 2592\) (exact) | |
| Steinhaus-Moser Notation | 880[3] | 881[3] |
| Chained arrow notation | \(10\rightarrow 2592\) (exact) | |
| Taro's multivariable Ackermann function | A(3,8607) | A(3,8608) |
| BEAF & Bird's array notation | {10,2592} (exact) | |
| Hyper-E notation | E2592 (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)(880) | m(1)(881) |
| Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
| Fast-growing hierarchy | \(f_2(8597)\) | \(f_2(8598)\) |
| Hardy hierarchy | \(H_{\omega^2}(8597)\) | \(H_{\omega^2}(8598)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^3 2+\omega^2 5+\omega 9+2}}(10)\) (exact) | |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-03-10.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-03-10.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-03-10.
- ↑ Fish. Conway's illion converter - 10^1299. Retrieved 2023-03-10.
- ↑ Fish. Conway's illion converter - 10^1299 (long scale). Retrieved 2023-03-10.
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
1,000–1024: 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
Main article: -illion
400–409: quadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)410–419: deciquadringentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
420–429: vigintiquadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
430–439: trigintaquadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
440–449: quadragintaquadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
450–459: quinquagintaquadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
460–469: sexagintaquadringentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
470–479: septuagintaquadringentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
480–489: octogintaquadringentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
490–499: nonagintaquadringentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)