So one night, I got bored, so, as you do, I made a depressingly inefficient python formula to calculate the density of the digits in a text file with a billion digits of pi in it. As I expected, it came out to roughly 10% per digit, and the precision increased proportionately to the number of digits I put in (so a billion digits was around a thousand times closer than a million was). Is there a way to prove this distribution approaches equality?
2026-03-27 05:37:44.1774589864
The Distribution of Pi’s Binary Digits
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