On the distribution of prime numbers of the form [nc]

A. KUMCHEV

doi:10.1017/S0017089599970477

Abstract

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Let πc(x) be the number of the integers n≤x such that [nc] is prime. We shall prove that $$π_{c}\tfrm{(}x\tfrm{)&2_Gt;}{x\over \log x}$$ for 1<c<45/38. This improves the former range 1<c<13/11.

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On the distribution of prime numbers of the form [nc]

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