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Erdős problem 1138

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Erdős Problem 1138. Let x/2<y<xx/2 < y < x and C>1C > 1. If d=max⁡pn<x(pn+1−pn)d = \max_{p_n < x}(p_{n+1} - p_n), where pnp_n denotes the nn-th prime, then is it true that π(y+Cd)−π(y)∼Cdlog⁡y\pi(y + Cd) - \pi(y) \sim \frac{Cd}{\log y}?

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