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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.

## 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

1. Big-Ass Numbers
2. Conway and Guy. (1995) "The book of Numbers" Copernicus
3. The Conway-Wechsler System
4. Conway's zillion numbers. Retrieved 2021-08-01.
5. Bowers, Jonathan. Illion Numbers. Retrieved 2021-08-01.