  The uneven distribution of digits in numerical data, known as Benford's law,
was discovered in 1881. Since then, this law has been shown to be correct in
copious numerical data relating to economics, physics and even prime numbers.
Although it attracts considerable attention, there is no a priori probabilistic
criterion when a data set should or should not obey the law. Here a general
criterion is suggested, namely that any file of digits in the Shannon limit
(namely, having maximum entropy) has a Benford's law distribution of digits.

Discrete Mathematics;Data Analysis, Statistics and Probability