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December 21, 2025Open Access

On the frequency of small gaps between the primes

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Authors

AMAkos MagyarJPJanos Pintz

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Overview

The analysis reveals unconditional insights on prime gaps, suggesting implications for divergence in sums of reciprocals.

Key Points

  • To provide answers regarding the size of gaps between consecutive primes and their relationship to the divergence of reciprocal sums.
  • Exploration of prime gaps and their properties based on existing hypotheses regarding prime distribution.
  • Focus on a weaker formulation of a previously studied problem without requiring specific hypotheses.
  • Establishes an unconditional approach to understanding gaps between consecutive primes.
  • Provides insights into the conditions under which the sum of reciprocals of primes diverges.

Cite This Study

Magyar et al. (2025) studied this question.

synapsesocial.com/papers/69473b64db9c958d0dfca9aahttps://doi.org/10.48550/arxiv.2505.07630
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Also Consider

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

  1. 1Rough numbers between consecutive primes2025
  2. 2On the maximal gap between consecutive primes: an 𝑂 (ln 𝑝) bound via additive basis properties of K-indices with 4𝑘 ± 1 prime2026 · 3 citations
  3. 3Pseudorandomness of primes at large scales2024
  4. 4Note for the Small Gaps2024
  5. 5Bounded gaps and perfect power gaps in sequences of consecutive primes2026