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septentrigintacentillion is equal to \(10^{414}\) in the short scale and \(10^{822}\) in the long scale by the Conway and Guy's naming system[1][2][3][4] as it is the 137th -illion number.

In the long scale, \(10^{414}\) is called novensexagintillion.

Approximations[]

For the short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{414}\) (exact)
Arrow notation \(10\uparrow 414\) (exact)
Steinhaus-Moser Notation 182[3] 183[3]
Chained arrow notation \(10\rightarrow 414\) (exact)
Taro's multivariable Ackermann function A(3,1372) A(3,1373)
BEAF & Bird's array notation {10,414} (exact)
Hyper-E notation E414 (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)(182) m(1)(183)
Bashicu matrix system (0)(0)(0)(0)(0)(0)(0)(0)[41] (0)(0)(0)(0)(0)(0)(0)(0)[42]
Fast-growing hierarchy \(f_2(1364)\) \(f_2(1365)\)
Hardy hierarchy \(H_{\omega^2}(1364)\) \(H_{\omega^2}(1365)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2 4+\omega+4}}(10)\) (exact)

For the long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{822}\) (exact)
Arrow notation \(10\uparrow 822\) (exact)
Steinhaus-Moser Notation 326[3] 327[3]
Chained arrow notation \(10\rightarrow 822\) (exact)
Taro's multivariable Ackermann function A(3,2727) A(3,2728)
BEAF & Bird's array notation {10,822} (exact)
Hyper-E notation E822 (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)(326) m(1)(327)
Bashicu matrix system (0)(0)(0)(0)(0)(0)(0)(0)(0)[40] (0)(0)(0)(0)(0)(0)(0)(0)(0)[41]
Fast-growing hierarchy \(f_2(2719)\) \(f_2(2720)\)
Hardy hierarchy \(H_{\omega^2}(2719)\) \(H_{\omega^2}(2720)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2 8+\omega 2+2}}(10)\) (exact)

Sources[]

  1. Conway and Guy. (1995) "The book of Numbers" Copernicus
  2. Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-12.
  3. Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-12.
  4. Fish. Conway's zillion numbers. Retrieved 2023-02-12.

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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