An octingentillion is equal to \(10^{2403}\) in the short scale and \(10^{4800}\) in the long scale by the Conway and Guy's naming system[1][2][3][4][5] and the Jonathan Bowers' system[6] as it is the 800th -illion number.
In the long scale, \(10^{2403}\) is called quadringentilliard.[7]
Approximations[]
For the short scale:
Notation | Lower bound | Upper bound | |||
---|---|---|---|---|---|
Scientific notation | \(1\times10^{2403}\) (exact) | ||||
Arrow notation | \(10\uparrow 2403\) (exact) | ||||
Steinhaus-Moser Notation | 824[3] | 825[3] | |||
Chained arrow notation | \(10\rightarrow 2403\) (exact) | ||||
Taro's multivariable Ackermann function | A(3,7979) | A(3,7980) | |||
BEAF & Bird's array notation | {10,2403} (exact) | ||||
Hyper-E notation | E2403 (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)(824) | m(1)(825) | |||
Bashicu matrix system | (0)(1)[3] | (0)(1)[4] | |||
Copy notation | 9[2403] | 10[1202] | |||
Pound-Star Notation | #*((2))*28 | #*((3))*28 | |||
Hyperfactorial array notation | 944! | - | Fast-growing hierarchy | \(f_2(7969)\) | \(f_2(7970)\) |
Hardy hierarchy | \(H_{\omega^2}(7969)\) | \(H_{\omega^2}(7970)\) | |||
Slow-growing hierarchy | \(g_{\omega^{\omega^3 2+\omega^2 4+3}}(10)\) (exact) |
For the long scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{4800}\) (exact) | |
Arrow notation | \(10\uparrow 4800\) (exact) | |
Steinhaus-Moser Notation | 1509[3] | 1510[3] |
Chained arrow notation | \(10\rightarrow 4800\) (exact) | |
Taro's multivariable Ackermann function | A(3,15942) | A(3,15943) |
BEAF & Bird's array notation | {10,4800} (exact) | |
Hyper-E notation | E4800 (exact) | |
s(n) map | \(s(1)^3(\lambda x.x+1)(10)\) | \(s(1)^3(\lambda x.x+1)(11)\) |
m(n) map | m(1)(1509) | m(1)(1510) |
Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
Copy notation | 9[4800] | 1[4801] |
Pound-Star Notation | #*((3158))*37 | #*((3159))*37 |
Hyperfactorial array notation | 1713! | 1714! |
Fast-growing hierarchy | \(f_2(15931)\) | \(f_2(15932)\) |
Hardy hierarchy | \(H_{\omega^2}(15931)\) | \(H_{\omega^2}(15932)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^3 4+\omega^2 8}}(10)\) (exact) |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-06-21.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-06-21.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-06-21.
- ↑ Fish. Conway's illion converter - 10^2403. Retrieved 2023-06-21.
- ↑ Illion Numbers by Jonathan Bowers
- ↑ Fish. Conway's illion converter - 10^2403 (long scale). Retrieved 2023-06-21.
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
800–809: octingentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)810–819: decioctingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
820–829: vigintioctingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
830–839: trigintaoctingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
840–849: quadragintaoctingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
850–859: quinquagintaoctingentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
860–869: sexagintaoctingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
870–879: septuagintaoctingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
880–889: octogintaoctingentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
890–899: nonagintaoctingentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)