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septuagintacentillion is equal to \(10^{513}\) in the short scale and \(10^{1020}\) in the long scale by the Conway and Guy's naming system[1][2][3][4] as it is the 170th -illion number. It is septuaginticentillion in Cookie fonster's extension of the Jonathan Bowers system.[5]

In the long scale, \(10^{513}\) is called quinoctogintilliard.

Approximations[]

For the short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{513}\) (exact)
Arrow notation \(10\uparrow 513\) (exact)
Steinhaus-Moser Notation 219[3] 220[3]
Chained arrow notation \(10\rightarrow 513\) (exact)
Taro's multivariable Ackermann function A(3,1701) A(3,1702)
BEAF & Bird's array notation {10,513} (exact)
Hyper-E notation E513 (exact)
s(n) map \(s(1)^3(\lambda x.x+1)(7)\) \(s(1)^3(\lambda x.x+1)(8)\)
m(n) map m(1)(219) m(1)(220)
Copy notation 9[423] 10[212]
H* function H(170)
Bashicu matrix system (0)(0)(0)(0)(0)(0)(0)(0)(0)[10] (0)(0)(0)(0)(0)(0)(0)(0)(0)[11]
Fast-growing hierarchy \(f_2(1693)\) \(f_2(1694)\)
Hardy hierarchy \(H_{\omega^2}(1693)\) \(H_{\omega^2}(1694)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2 5+\omega+3}}(10)\) (exact)

For the long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{1020}\) (exact)
Arrow notation \(10\uparrow 1020\) (exact)
Steinhaus-Moser Notation 393[3] 394[3]
Chained arrow notation \(10\rightarrow 1020\) (exact)
Taro's multivariable Ackermann function A(3,3385) A(3,3386)
BEAF & Bird's array notation {10,1020} (exact)
Hyper-E notation E1020 (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)(393) m(1)(394)
Bashicu matrix system (0)(1)[3] (0)(1)[4]
Fast-growing hierarchy \(f_2(3376)\) \(f_2(3377)\)
Hardy hierarchy \(H_{\omega^2}(3376)\) \(H_{\omega^2}(3377)\)
Slow-growing hierarchy \(g_{\omega^{\omega^3+\omega 2}}(10)\) (exact)

Sources[]

  1. Conway and Guy. (1995) "The book of Numbers" Copernicus
  2. Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-15.
  3. Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-15.
  4. Fish. Conway's zillion numbers. Retrieved 2023-02-15.
  5. 1.8. Extensions to the -illions II: Jonathan Bowers' -illions

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
100–109: centillion (un- · duo- · tres- · quattuor- · quin- · sex- · septen- · octo- · noven-)
110–119: decicentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
120–129: viginticentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
130–139: trigintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
140–149: quadragintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
150–159: quinquagintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
160–169: sexagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
170–179: septuagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
180–189: octogintacentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
190–199: nonagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
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