Bounded gaps and perfect power gaps in sequences of consecutive primes

Katalin Gyarmati

doi:10.1007/s10476-026-00179-9

August 14, 2026Analysis MathematicaOpen Access

Bounded gaps and perfect power gaps in sequences of consecutive primes

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Key Points

To examine whether multiple consecutive prime gaps can simultaneously be large, perfect powers, squares, or entirely non-squares.
Applied analytic number-theoretic methods to evaluate sequences of gaps between consecutive prime numbers.
Analyzed constraints on the algebraic properties and magnitudes of simultaneous differences across consecutive primes.
Established theoretical results regarding the simultaneous occurrence of square and perfect power gap lengths between consecutive primes.
Identified open problems and structural bounds governing the distribution and behavior of multiple adjacent prime gaps.

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Implication

Mathematical analysis investigates prime gap distributions across consecutive primes, revealing constraints on consecutive perfect power gaps.

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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Katalin Gyarmati (2026) studied this question.

synapsesocial.com/papers/6a8178fcf2fb91fc834ac2fa https://doi.org/10.1007/s10476-026-00179-9

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Bounded gaps and perfect power gaps in sequences of consecutive primes

Key Points

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Implication

Abstract

Discussion

Cite This Study

Bounded gaps and perfect power gaps in sequences of consecutive primes

Key Points

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Implication

Abstract

Discussion

Cite This Study

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