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Abstract For c > 1 we denote by πc(x) the number of integers n ≤ x such that ⌊n c ⌋ is prime. In 1953, Piatetski-Shapiro has proved that holds for c < 12/11. Many authors have extended this range, which measures our progress in exponential sums techniques. In this article we obtain c < 1.16117….
Rivat et al. (Sun,) studied this question.
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