On a Pillai’s Conjecture and gaps between consecutive primes

Rafael Jakimczuk
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 3, Pages 60—72
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Authors and affiliations

Rafael Jakimczuk
División Matemática, Universidad Nacional de Luján
Buenos Aires, Argentina


In this article we show that the following Pillai’s conjecture pn is the n-th prime number)

can be established in terms of gaps between consecutive primes. We also study general sequences that have this property. We call these sequences Pillai sequences. We prove that the sequence of perfect powers is a Pillai-sequence.


  • Pillai’s conjecture
  • Gaps between consecutive primes
  • General sequences
  • Sequence of perfect powers

AMS Classification

  • 11A99
  • 11B99


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Cite this paper

Jakimczuk, R. (2017). On a Pillai’s Conjecture and Gaps between Consecutive Primes. Notes on Number Theory and Discrete Mathematics, 23(3), 60-72.

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