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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:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

In long scale:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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[]

  1. Conway and Guy. (1995) "The book of Numbers" Copernicus
  2. Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-04-16.
  3. Olsen, Steve. Big-Ass Numbers. Retrieved 2023-04-16.
  4. Fish. Conway's zillion numbers. Retrieved 2023-04-16.
  5. Fish. Conway's illion converter - 10^2013. Retrieved 2023-04-16.
  6. Fish. Conway's illion converter - 10^2013 (long scale). Retrieved 2023-04-16.
  7. Saibian, Sbiis. 2-4-8: Bowers' -illions - Large Numbers

See also[]

Main article: -illion
1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non
10–19: 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-)
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