30% of natural numbers start with 1 · log scale makes it obvious · scale-invariant distributions · runs locally
n = 1,000
P(leading digit = d) = log₁₀(1 + 1/d) · d=1: 30.1% · d=9: 4.6% · why: a scale-invariant distribution must be uniform on a log scale, giving each log-width equal probability · used in fraud detection: fabricated numbers violate benford