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Sum of reciprocals of primes in a range is < 2

Source: St Petersburg 2021 11.5

December 23, 2021
number theory

Problem Statement

A natural number nn is given. Prove that ∑n≤p≤n21p<2\sum_{n \le p \le n^2} \frac{1}{p} < 2 where the sum is across all primes pp in the range [n,n2][n, n^2]
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