The recent discussion of the density of a subset S of the positive integers defines the density of S to be d if number of elements in S that are <= n ----------------------------------------- approaches d as n --> infinity. n This is usually called the "natural" density. Two problems with this are 1) the limit may not exist 2) the limit can be hard to compute. Number theorists tend to work with another type of density, called Dirichlet density. This is often easier to compute. When both densities exist, they are equal. Sometimes the Dirichlet density exists when the above natural density does not. An example of such a case is S = {set of primes whose first digit is 1}. It follows easily from the prime number theorem (according to Serre's "A course in arithmetic") that the natural density does not exist. Can anyone explain why this is so? Gary McGuire