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A quattuorquadragintillion is equal to 10135 in the short scale, or \(10^{264}\) in the long scaleby Conway-Wechsler system[1][2][3][4] or Jonathan Bowers system.[5]

In the long scale which is commonly used in France and Germany, \(10^{135}\) is called duovigintilliard.

Decimal expansion

In short scale:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

In long scale:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Approximations

For short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{135}\)
Arrow notation \(10\uparrow135\)
Steinhaus-Moser Notation 72[3] 73[3]
Copy notation 9[135] 10[68]
Taro's multivariable Ackermann function A(3,445) A(3,446)
Pound-Star Notation #*(1,14,10,5,0,9,2,1)*10 #*(9,5,13,6,3,0,3)*12
BEAF {10,135}
Hyper-E notation E135
Bashicu matrix system (0)(0)(0)(0)(0)[16548] (0)(0)(0)(0)(0)[16549]
Hyperfactorial array notation 88! 89!
Fast-growing hierarchy \(f_2(439)\) \(f_2(440)\)
Hardy hierarchy \(H_{\omega^2}(439)\) \(H_{\omega^2}(440)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2+\omega3+5}}(10)\)

For long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{264}\)
Arrow notation \(10\uparrow264\)
Steinhaus-Moser Notation 125[3] 126[3]
Copy notation 9[264] 1[265]
Taro's multivariable Ackermann function A(3,873) A(3,874)
Pound-Star Notation #*((3432))*10 #*((3433))*10
BEAF {10,264}
Hyper-E notation E264
Bashicu matrix system (0)(0)(0)(0)(0)(0)[13335] (0)(0)(0)(0)(0)(0)[13336]
Hyperfactorial array notation 150! 151!
Fast-growing hierarchy \(f_2(867)\) \(f_2(868)\)
Hardy hierarchy \(H_{\omega^2}(867)\) \(H_{\omega^2}(868)\)
Slow-growing hierarchy \(g_{\omega^{\omega^22+\omega6+4}}(10)\)

List of prefixed numbers derived from quadragintillion

Name Short scale Long scale
unquadragintillion 10126 10246
duoquadragintillion 10129 10252
trequadragintillion 10132 10258
quattuorquadragintillion 10135 10264
quinquadragintillion 10138 10270
sexquadragintillion 10141 10276
septenquadragintillion 10144 10282
octoquadragintillion 10147 10288
novemquadragintillion 10150 10294

Sources

  1. Conway and Guy. (1995) "The book of Numbers" Copernicus
  2. The Conway-Wechsler System
  3. Extensions to the -illions I: Henkle, Conway, and Rowlett
  4. Fish. Conway's zillion numbers, July 25, 2021
  5. Saibian, Sbiis. 2.4.8 Bowers' -illions - Large Numbers. Retrieved 2021-08-01.

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 · trevigint · quattuorvigint · quinvigint · sexvigint · septenvigint · octovigint · novemvigint
30–39: trigintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
40–49: quadragintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
50–59: quinquagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
60–69: sexagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
70–79: septuagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
80–89: octogintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
90–99: nonagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
100–900: centillion · unviginticent · unsexagintacent · ducent · trecent · duotrigintatrecent · quadringent · quingent · sescent · septuagintisescent · 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
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