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August 16, 2026Analysis MathematicaOpen Access

Bounded gaps and perfect power gaps in sequences of consecutive primes

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Authors

KGKatalin Gyarmati

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Overview

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

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.

Cite This Study

Katalin Gyarmati (2026) studied this question.

synapsesocial.com/papers/6a8178fcf2fb91fc834ac2fahttps://doi.org/10.1007/s10476-026-00179-9
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