Definition
If A is a subset of the prime numbers, the Dirichlet density of A is the limit
if the limit exists. This expression is usually the order of the "pole" of
at s = 1, (though in general it is not really a pole as it has non-integral order), at least if the function on the right is a holomorphic function times a (real) power of s−1 near s = 1. For example, if A is the set of all primes, the function on the right is the Riemann zeta function which has a pole of order 1 at 0, so the set of all primes has Dirichlet density 1.
More generally, one can define the Dirichlet density of a sequence of primes (or prime powers), possibly with repetitions, in the same way.
Read more about this topic: Dirichlet Density
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