Application of the Inclusion-Exclusion Principle to Prime Number Subsequences (European Journal of Pure and Applied Mathematics, 2024)
We apply the Inclusion-Exclusion Principle to a unique pair of prime number subsequences to determine whether these subsequences form a small set or a large set and thus whether the infinite sum of the inverse of their terms converges or diverges. In this paper, we analyze the complementary prime number subsequences P′ and P′′ as well as revisit the twin prime subsequence P2.
Keywords: Prime numbers; Higher-order prime number sequences; Inclusion-Exclusion Principle; Sums over prime reciprocals; Prime density; Sieves