Largest Integer Expressible by 3 Digits
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Theorem
The largest integer that can be represented using no more than $3$ digits, with no additional symbols, is:
- $9^{9^9} = 9^{387 \, 420 \, 489}$
and (at $369 \, 693 \, 100$ digits, is too large to be calculated on a conventional calculator.
Note that this does not include the notation for tetration: ${}^9 9$.
Logarithm Base 10
- $\map {\log_{10} } {9^{9^9} } \approx 369 \, 693 \,099 \cdotp 63157 \, 03685 \, 87876 \, 1$
Number of Digits
- $9^{9^9}$ has $369 \, 693 \, 100$ digits when expressed in decimal notation.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $9^{9^9}$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $9^{9^9}$