On the Pjateckii-Šapiro prime number theorem. (English) Zbl 0772.11032

I. I. Piatetski-Shapiro [Mat. Sb., Nov. Ser. 33, 559-566 (1953; Zbl 0053.027)] proved the extraordinary result that, for any positive \(c<12/11\), the number of integers \(n\leq x\) for which the integer part of \(n^ c\) is prime, is asymptotically \(x/c\log x\). There have been various papers which show this result for larger and larger values of \(c\), and herein the authors show it for any \(c<15/13\), a new record.


11N05 Distribution of primes


Zbl 0053.027
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