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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
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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.