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An unquadragintillion is equal to 10126 in the short scale, or \(10^{246}\) in the long scale by Conway and Guy's naming system[1][2][3][4] and Jonathan Bowers system.[5]

In the long scale which is commonly used in France and Germany, \(10^{126}\) is called unvigintillion.

10126 was called kathana in Pali language of the 1st century B.C.[6]

Approximations[]

For short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{126}\)
Arrow notation \(10\uparrow126\)
Steinhaus-Moser Notation 68[3] 69[3]
Copy notation 9[126] 1[127]
Taro's multivariable Ackermann function A(3,415) A(3,416)
Pound-Star Notation #*(0,11,3,10,10,4,8,1)*9 #*(1,11,3,10,10,4,8,1)*9
BEAF {10,126}
Hyper-E notation E126
Bashicu matrix system (0)(0)(0)(0)(0)[8659] (0)(0)(0)(0)(0)[8660]
Hyperfactorial array notation 83! 84!
Fast-growing hierarchy \(f_2(409)\) \(f_2(410)\)
Hardy hierarchy \(H_{\omega^2}(409)\) \(H_{\omega^2}(410)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2+\omega2+6}}(10)\)

For long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{246}\)
Arrow notation \(10\uparrow246\)
Steinhaus-Moser Notation 118[3] 119[3]
Copy notation 9[246] 1[247]
Taro's multivariable Ackermann function A(3,814) A(3,815)
Pound-Star Notation #*((387))*10 #*((388))*10
BEAF {10,246}
Hyper-E notation E246
Bashicu matrix system (0)(0)(0)(0)(0)(0)[6978] (0)(0)(0)(0)(0)(0)[6979]
Hyperfactorial array notation 142! 143!
Fast-growing hierarchy \(f_2(807)\) \(f_2(808)\)
Hardy hierarchy \(H_{\omega^2}(807)\) \(H_{\omega^2}(808)\)
Slow-growing hierarchy \(g_{\omega^{\omega^22+\omega4+6}}(10)\)

List of prefixed numbers derived from quadragintillion[]

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

Sources[]

  1. Conway and Guy. (1995) "The book of Numbers" Copernicus
  2. The Conway-Wechsler System
  3. Steve Olsen, Big-Ass Numbers
  4. Conway's zillion numbers. Retrieved 2021-07-28.
  5. Saibian, Sbiis. 2.4.8 Bowers' -illions - Large Numbers. Retrieved 2021-07-28.
  6. https://digitalcommons.butler.edu/cgi/viewcontent.cgi?article=2344&context=wordways

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
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