Further results on a generalization of Bertrand's postulate
Let \(d(k)\) be the least positive integer \(n\) for which \(p_{n+1} < 2p_n-k\). The prime number theorem implies that \(d(k)\) is equivalent to \(k/ \log k\). It is proved in this paper, among other things, that \(d(k) < k/(\log k-2.531)\) for \(k \geq 286664\).
scientific article; zbMATH DE number 844405