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For Tiaokhiao's vigintillion, see novemdecillion.

A vigintillion is equal to 1063 in the short scale, or 10120 in the long scale.[1][2] It is the largest -illion with a recognized name in the English language other than the much larger centillion, although the extended names to the -illions like unvigintillion have been recognized by many people as well.

In the long scale, 1063 is called decilliard, which is commonly used in France and Germany.

This number is also called icosihenillion in Russ Rowlett's Greek-based naming system of -illions.[3]

Aarex Tiaokhiao gave the name vigimillion, referring to the value of this number.[4]

Decimal

  • 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 - short scale
  • 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 - long scale

List of prefixed numbers derived from vigintillion

Name Short scale Long scale
unvigintillion 1066 10126
duovigintillion 1069 10132
trevigintillion 1072 10138
quattuorvigintillion 1075 10144
quinvigintillion 1078 10150
sexvigintillion 1081 10156
septenvigintillion 1084 10162
octovigintillion 1087 10168
novemvigintillion 1090 10174

Examples

  • The volume of the Virgo Super Cluster (The super cluster in which we reside) is roughly 3.54 vigintillion cubic kilometers.[5]
  • There is about 1 vigintillion possible chess combinations.
  • For prefixes that mean multipling by one vigintillion, see Prefix 10^63.
  • One vigintillion (1×1063) is Archimedes' estimate in The Sand Reckoner of the total number of grains of sand that could fit into the entire cosmos, the diameter of which he estimated in stadia to be what we call 2 light years.

Approximations

For short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{63}\)
Arrow notation \(10\uparrow63\)
Steinhaus-Moser Notation 39[3] 40[3]
Copy notation 9[63] 10[32]
Taro's multivariable Ackermann function A(3,206) A(3,207)
Pound-Star Notation #*(1,9,0,6)*12 #*(5,2,0,2,4,2)*7
BEAF {10,63}
Hyper-E notation E63
Bashicu matrix system (0)(0)(0)(0)[8659] (0)(0)(0)(0)[8660]
Hyperfactorial array notation 49! 50!
Fast-growing hierarchy \(f_2(201)\) \(f_2(202)\)
Hardy hierarchy \(H_{\omega^2}(201)\) \(H_{\omega^2}(202)\)
Slow-growing hierarchy \(g_{\omega^{\omega6+3}}(10)\)

For long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{120}\)
Arrow notation \(10\uparrow120\)
Steinhaus-Moser Notation 65[3] 66[3]
Copy notation 9[120] 1[121]
Taro's multivariable Ackermann function A(3,395) A(3,396)
Pound-Star Notation #*(9,5,5,10,4,5,6,4)*8 #*(10,5,5,10,4,5,6,4)*8
BEAF {10,120}
Hyper-E notation E120
Bashicu matrix system (0)(0)(0)(0)(0)[5623] (0)(0)(0)(0)(0)[5624]
Hyperfactorial array notation 80! 81!
Fast-growing hierarchy \(f_2(390)\) \(f_2(391)\)
Hardy hierarchy \(H_{\omega^2}(390)\) \(H_{\omega^2}(391)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2+\omega2}}(10)\)

Sources

  1. Vigintillion at Wolfram MathWorld
  2. Illion Numbers by Jonathan Bowers
  3. Names for Large Numbers
  4. Aarex Tiaokhiao's illion numbers
  5. Saibian, Sbiis. Larger numbers in science.

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 · primo-vigesimo-cent · ducent · trecent · duotrigintatrecent · quadringent · quingent · sescent · septuagintisescent · septingent · octingent · nongent
1000–1024: millillion · dumill · trimill · quadrimill · quinmill · sexmill · septimill · octimill · nonimill · myr · centimill · micr · nan · pic · femt · att · zept · yoct