Mind Blown

P(d)

log10(1+1/d): digit 1 -> 30.1%, 2 -> 17.6%, ... 9 -> 4.6%. Holds across many independent real-world datasets.

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Real Numbers Start With 1 Too OftenMind Blown

More terms from this board

Leading digitthe first non-zero digit (the '3' in 342 or 0.0389). Benford predicts how often each 1-9 appears.
Scale invariancethe pattern looks the same in dollars, euros, or feet — a hallmark of log-distributed data.