A septuagintillion is equal to 10213 in short scale, or 10420 in the long scale by Conway and Guy's naming system[1][2][3][4] or Jonathan Bowers system.[5] This number has 214 digits.
In the long scale which is commonly used in France and Germany, 10213 is called quintrigintilliard.
Contents
Approximations
For short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times 10^{213}\) | |
| Arrow notation | \(10\uparrow 213\) | |
| Steinhaus-Moser Notation | 105[3] | 106[3] |
| Copy notation | 9[213] | 10[107] |
| Taro's multivariable Ackermann function | A(3,704) | A(3,705) |
| Pound-Star Notation | #*((4913))*9 | #*((4914))*9 |
| BEAF | {10,213} | |
| Hyper-E notation | E213 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)[2128] | (0)(0)(0)(0)(0)(0)[2129] |
| Hyperfactorial array notation | 126! | 127! |
| Fast-growing hierarchy | \(f_2(698)\) | \(f_2(699)\) |
| Hardy hierarchy | \(H_{\omega^2}(698)\) | \(H_{\omega^2}(699)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^22+\omega+3}}(10)\) | |
For long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{420}\) | |
| Arrow notation | \(10\uparrow420\) | |
| Steinhaus-Moser Notation | 185[3] | 186[3] |
| Copy notation | 9[420] | 1[421] |
| Taro's multivariable Ackermann function | A(3,1392) | A(3,1393) |
| Pound-Star Notation | #*((39))*13 | #*((40))*13 |
| BEAF | {10,420} | |
| Hyper-E notation | E420 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)[1910] | (0)(0)(0)(0)(0)(0)(0)[1911] |
| Hyperfactorial array notation | 219! | 220! |
| Fast-growing hierarchy | \(f_2(1\,384)\) | \(f_2(1\,385)\) |
| Hardy hierarchy | \(H_{\omega^2}(1\,384)\) | \(H_{\omega^2}(1\,385)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^24+\omega2}}(10)\) | |
List of prefixed numbers derived from septuagintillion
| Name | Short scale | Long scale |
|---|---|---|
| unseptuagintillion | 10216 | 10426 |
| duoseptuagintillion | 10219 | 10432 |
| treseptuagintillion | 10222 | 10438 |
| quattuorseptuagintillion | 10225 | 10444 |
| quinseptuagintillion | 10228 | 10450 |
| sexseptuagintillion | 10231 | 10456 |
| septenseptuagintillion | 10234 | 10462 |
| octoseptuagintillion | 10237 | 10468 |
| novemseptuagintillion | 10240 | 10474 |
Sources
- ↑ Big-Ass Numbers
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ The Conway-Wechsler System
- ↑ Conway's zillion numbers. Retrieved 2021-08-01.
- ↑ Bowers, Jonathan. Illion Numbers. Retrieved 2021-08-01.
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 · 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
