Bounded gaps and perfect power gaps in sequences of consecutive primes

Abstract We study whether several consecutive prime gaps can all be relatively large at the same time, or is it possible that all are squares or perfect powers, or perhaps none of them are squares? A few related results and problems are also presented.

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Publication Details

Journal
Analysis Mathematica
Published
2026-08-14
DOI
https://doi.org/10.1007/s10476-026-00179-9
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
0.00

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article

Bounded gaps and perfect power gaps in sequences of consecutive primes

Katalin Gyarmati
Analysis Mathematica
Analytic Number Theory Research
article

Bounded gaps and perfect power gaps in sequences of consecutive primes

Katalin Gyarmati
article en

Abstract

Abstract We study whether several consecutive prime gaps can all be relatively large at the same time, or is it possible that all are squares or perfect powers, or perhaps none of them are squares? A few related results and problems are also presented.

Analysis Mathematica
Eötvös Loránd University (HU)
Eötvös Loránd Tudományegyetem
Openalex Percentile: Top 76%
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Bounded gaps and perfect power gaps in sequences of consecutive primes — Katalin Gyarmati · Analysis Mathematica (2026) | TGRS Research Map | TGRS