Benford's law is a neat piece of mathematics which essentially states that given a large data set with a large distribution, the numbers with leading digit as 1 occurs about 30% of the time. Now this is obviously counter intuitive; given a set of numbers, the probability of a number starting with 0-9 should be equal for all the numbers.

A set of numbers is said to satisfy Benford's law if the leading digit $(d\\in{1,\\ldots,9})$ occurs with probability

$$P(d)=log_{10}(d+1)-log_{10}(d)=log_{10}(1+\\frac{1}{d})$$