Aku's dump

Benford's law states that the leading digit d (d ∈ {1, …, b − 1} ) in base b (b ≥ 2) occurs with probability proportional to logb(d + 1) − logbd = logb((d + 1)/d). This quantity is exactly the space between d and d + 1 in a log scale.

In base 10, the leading digits have the following distribution by Benford's law, where d is the leading digit and p the probability:

d	p
1	30.1%
2	17.6%
3	12.5%
4	9.7%
5	7.9%
6	6.7%
7	5.8%
8	5.1%
9	4.6%