A Parametric Refinement of Cram´er's Prime Gap Conjecture

This paper presents a parametric refinement of Cramér's prime gap conjecture, demonstrating that the natural base is not the sole relevant logarithmic base. By examining the valid base interval, we show how adjusting the base dynamically scales the explicit upper envelope, establishing the natural scale as a structural baseline while preserving stability against maximal prime gaps.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-10
DOI
https://doi.org/10.5281/zenodo.22693323
Primary Topic
Cryptography and Residue Arithmetic
Type
preprint
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preprint

A Parametric Refinement of Cram´er's Prime Gap Conjecture

Hana Abdelrahman Elgamala
Zenodo (CERN European Organization for Nuclear Research)
Cryptography and Residue Arithmetic
preprint

A Parametric Refinement of Cram´er's Prime Gap Conjecture

Hana Abdelrahman Elgamala
preprint en

Abstract

This paper presents a parametric refinement of Cramér's prime gap conjecture, demonstrating that the natural base is not the sole relevant logarithmic base. By examining the valid base interval, we show how adjusting the base dynamically scales the explicit upper envelope, establishing the natural scale as a structural baseline while preserving stability against maximal prime gaps.

Zenodo (CERN European Organization for Nuclear Research)
Cryptography and Residue Arithmetic
DOIOpen Access PDFOpenAlex
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