A septuagintasescentillion is equal to \(10^{2013}\) in the short scale and \(10^{4020}\) in the long scale by the Conway and Guy's naming system[1][2][3][4][5] as it is the 670th -illion number.
In the long scale, \(10^{2013}\) is called quintrigintatrecentilliard.[6]
Sbiis Saibian calls this number septuagintisescentillion.[7]
Decimal expansion[]
Written out in decimal form septuagintisescentillion (in the short scale) is:
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In long scale:
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Approximations[]
For the short scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{2013}\) (exact) | |
Arrow notation | \(10\uparrow 2013\) (exact) | |
Steinhaus-Moser Notation | 706[3] | 707[3] |
Chained arrow notation | \(10\rightarrow 2013\) (exact) | |
Taro's multivariable Ackermann function | A(3,6684) | A(3,6685) |
BEAF & Bird's array notation | {10,2013} (exact) | |
Hyper-E notation | E2013 (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)(706) | m(1)(707) |
Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
Copy notation | 9[2013] | 10[1007] |
Pound-Star Notation | #*((5348))*25 | #*((5349))*25 |
Hyperfactorial array notation | 812! | 813! |
Fast-growing hierarchy | \(f_2(6674)\) | \(f_2(6675)\) |
Hardy hierarchy | \(H_{\omega^2}(6674)\) | \(H_{\omega^2}(6675)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^3 2+\omega+3}}(10)\) (exact) |
For the long scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{4020}\) (exact) | |
Arrow notation | \(10\uparrow 4020\) (exact) | |
Steinhaus-Moser Notation | 1292[3] | 1293[3] |
Chained arrow notation | \(10\rightarrow 4020\) (exact) | |
Taro's multivariable Ackermann function | A(3,13351) | A(3,13352) |
BEAF & Bird's array notation | {10,4020} (exact) | |
Hyper-E notation | E4020 (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)(1292) | m(1)(1293) |
Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
Copy notation | 9[4020] | 1[4021] |
Pound-Star Notation | #*((1))*35 | #*((2))*35 |
Hyperfactorial array notation | 1,470! | 1,471! |
Fast-growing hierarchy | \(f_2(13340)\) | \(f_2(13341)\) |
Hardy hierarchy | \(H_{\omega^2}(13340)\) | \(H_{\omega^2}(13341)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^3 4+\omega 2}}(10)\) (exact) |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-04-16.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-04-16.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-04-16.
- ↑ Fish. Conway's illion converter - 10^2013. Retrieved 2023-04-16.
- ↑ Fish. Conway's illion converter - 10^2013 (long scale). Retrieved 2023-04-16.
- ↑ Saibian, Sbiis. 2-4-8: Bowers' -illions - Large Numbers
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
600–609: sescentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)610–619: decisescentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
620–629: vigintisescentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
630–639: trigintasescentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
640–649: quadragintasescentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
650–659: quinquagintasescentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
660–669: sexagintasescentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
670–679: septuagintasescentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
680–689: octogintasescentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
690–699: nonagintasescentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)