A vigintillion is equal to 1063 in the short scale, or 10120 in the long scale.[1][2][3][4][5][6] 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. It is also the second-largest -illion number found in most major English dictionaries, and is the fourth-largest largest number found in most major English dictionaries (after googol, centillion, and googolplex). It is 64 digits long in short scale, and 121 digits long in long scale.
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.[7]
Aarex Tiaokhiao gave the name vigimillion, referring to the value of this number.[8]
BlankEntity calls this number Voogol.[9]
Decimal expansion[]
- 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
Examples[]
- The volume of the Virgo Super Cluster (The super cluster in which we reside) is roughly 3.54 vigintillion cubic kilometers.[10]
- 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.
List of prefixed numbers derived from vigintillion[]
| Name | Short scale | Long scale |
|---|---|---|
| unvigintillion | 1066 | 10126 |
| duovigintillion | 1069 | 10132 |
| tresvigintillion | 1072 | 10138 |
| quattuorvigintillion | 1075 | 10144 |
| quinvigintillion | 1078 | 10150 |
| sesvigintillion | 1081 | 10156 |
| septemvigintillion | 1084 | 10162 |
| octovigintillion | 1087 | 10168 |
| novemvigintillion | 1090 | 10174 |
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 | |
| s(n) map | \(s(1)^2(\lambda x.x+1)(201)\) | \(s(1)^2(\lambda x.x+1)(202)\) |
| m(n) map | m(1)(39) | m(1)(40) |
| 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 | |
| s(n) map | \(s(1)^2(\lambda x.x+1)(390)\) | \(s(1)^2(\lambda x.x+1)(391)\) |
| m(n) map | m(1)(65) | m(1)(66) |
| 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[]
- ↑ Merriam-Webster Dictionary Vigintillion
- ↑ Conway and Guy. The Book of Numbers. Copernicus. 1995. ISBN 978-0387979939 p.16
- ↑ Vigintillion at Wolfram MathWorld
- ↑ Illion Numbers by Jonathan Bowers
- ↑ Conway and Guy (1995) "The book of Numbers" Copernicus
- ↑ Fish, Conway's zillion numbers, 2022/02/20.
- ↑ Russ Rowlett Names for Large Numbers Archived 2006-01-10.
- ↑ Aarex Tiaokhiao's illion numbers[dead link]
- ↑ BlankEntity's Googology Site
- ↑ Saibian, Sbiis. Larger numbers in science.
See also[]
Main article: -illion
1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non10–19: 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
1,000–1030: 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 · ront · quect