Benford's law


A set of numbers satisfies Benford’s law if the leading digits of these numbers occur with a probability logarithmically decreasing with the digit. More precisely, for \(d \in \{1, \ldots, 9\}\),

\[ P(d) = \log_{10} \left(1 + \frac{1}{d} \right) \]

Many sequence that span multiple orders of magnitude satisfy Benford’s law, including the Fibonacci sequence (Washington 1981).

The law has been proposed for use in fraud detection, because artificial uniformly distributed fake numbers would not follow the law.


  1. . . "Benford's Law for Fibonacci and Lucas Numbers". The Fibonacci Quarterly 2 (19):175–77.
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