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Sum of reciprocals of primes in a range is less than 4

Source: St Petersburg 2021 9.7

December 23, 2021
Saint Petersburgnumber theory

Problem Statement

For a positive integer nn, prove that ∑n≤p≤n41p<4\sum_{n \le p \le n^4} \frac{1}{p} < 4 where the sum is taken across primes pp in the range [n,n4][n, n^4]
N. Filonov
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