Abstract
Just as we studied the distribution of prime numbers in the sequence of natural numbers, we can pose and solve the problem of the distribution of prime numbers in an arithmetic progression with difference k≥ 1 and initial term l, where 1≤ l≤ k and(l,k)=1. This problem is important not only because it generalizes a classical result, but also because it has exceptional importance for the solution of many additive problems in prime number theory (for example, the Goldbach conjecture, discussed in Chapter X).
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