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Piatetski-Shapiro primes from almost primes

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Abstract

Let \(\left\lfloor \cdot \right\rfloor \) be the floor function. In this paper, we show that for any fixed \(c\in \left( 1,\frac{77}{76}\right) \) there are infinitely many primes of the form \(p=\left\lfloor n^c\right\rfloor \), where \(n\) is a natural number with at most eight prime factors (counted with multiplicity).

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Authors and Affiliations

  1. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA

    Roger C. Baker

  2. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    William D. Banks & Zhenyu V. Guo

  3. Department of Mathematics, Oklahoma State University, Stillwater, OK, 74078, USA

    Aaron M. Yeager

Authors
  1. Roger C. Baker
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  2. William D. Banks
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  3. Zhenyu V. Guo
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  4. Aaron M. Yeager
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Correspondence to William D. Banks.

Additional information

Communicated by J. Schoißengeier.

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Baker, R.C., Banks, W.D., Guo, Z.V. et al. Piatetski-Shapiro primes from almost primes. Monatsh Math 174, 357–370 (2014). https://doi.org/10.1007/s00605-013-0552-8

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  • DOI: https://doi.org/10.1007/s00605-013-0552-8

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