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May 4, 2026Open Access

On the maximal gap between consecutive primes: an 𝑂 (ln 𝑝) bound via additive basis properties of K-indices with 4π‘˜ Β± 1 prime

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Authors

AFAndrei Fedotkin

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Overview

Derives an upper bound for the maximal gap between consecutive primes using K-indices, suggesting implications for classical conjectures.

Key Points

  • The goal is to derive an upper bound for the maximal gap between consecutive primes using properties of K-indices.
  • Established the generating set K of primes as an additive basis of order 2.
  • Analyzed contradictions assuming gaps exceed C ln ki to conclude all gaps in K are O(ln ki).
  • Linked findings on K-indices to prime gaps via the form p = 4k Β± 1.
  • Proven that the maximal gap between consecutive primes, gn(pn) = pn+1 - pn, is O(ln pn).
  • Confirmed that every sufficiently large gap satisfies pn+1 - pn ≀ C ln pn with C > 0.
  • Showed improvements over classical conjectures and best-known analytic results.

Cite This Study

Andrei Fedotkin (2026) studied this question.

synapsesocial.com/papers/69f837c23ed186a739981ff5https://doi.org/10.5281/zenodo.19987891
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1On the Gap Between Perfect Squares and the Nearest Prime Below: A Logarithmic Bound Conjecture2026
  2. 2Explicit lower bound for large gaps between some consecutive primes2024
  3. 3On the frequency of small gaps between the primes2025
  4. 4The golden vein: Generating sets K are complete additive bases of order 2. On the representation of natural numbers as sums of pairs of indices of primes2026 Β· 9 citations
  5. 5A Note on Oppermann's Conjecture2024