Abstract
This paper presents the theoretical elements that support the calculation of the prime number counting function, π(x), based on properties of the sequences (6n-1) and (6n+1), n ≥ 1. As a result, Sufficient primality criteria are exposed for the terms of both sequences that support a deterministic computational algorithm that reduces the number of operations in calculating the function π(x) by exonerating all multiples of 3 from the analysis. In analyzing the primality of a particular term, the divisions by factor 3 are excluded. Such an algorithm can be applied to the search for prime numbers in each sequence separately, a possibility that allows approximately half the time of number search in practical applications.
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