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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.

##### MSC:
 11N05 Distribution of primes
##### Keywords:
Piatetski-Shapiro problem
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