Factorial/Examples/1,000,000

Example of Factorial

The factorial of $1 \, 000 \, 000$ has $5 \, 569 \, 709$ digits.

Proof

Let $d$ be the number of digits in $1 \, 000 \, 000!$

From Number of Digits in Factorial:

$d = 1 + \floor {\paren {n + \dfrac 1 2} \log_{10} n - 0.43429 \ 4481 \, n + 0.39908 \ 9934}$

from which the result can be calculated by setting $n = 1 \, 000 \, 000$.

$\blacksquare$

Historical Note

The factorial of $1\,000\,000$ was calculated in its entirety by Harry Lewis Nelson and David Slowinski.

The computer printout was $5$ inches high.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $24$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $24$