We show that equation*∑_pₙ≤ x\\ pₙ₊₁-pₙ≥√pₙ(pₙ₊₁-pₙ) ε x3/5+εequation*or any fixed ε>0. This improves a result of Matomäki, in which the exponent was $2/3$.
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D. R. Heath‐Brown (2019) studied this question.
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