On the Distribution of Numbers

The main purpose of this paper is to examine, from the computing machine's point of view, the well-known (to comparatively few people) unequal distribution of the "mantissas" of "naturally occurring" sets of numbers. The observed probability density distributions are often close to the reciprocal density distribution r(t) = (1/6 ^ t^ 1), 1609 (1) 1610 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1970 where b is the number base (usually 2, 8, 10, or 16). The corresponding cumulative probability distribution is _ hi t + In b In b where, of course, R(/b) = 0 and R{ 1) = 1.