Refinement of the Circle Method for Goldbach: An Analytical Exercise with Acknowledged Limitations

This paper presents a dramatic refinement of the Hardy-Littlewood circle method, reducing the analytical threshold for binary Goldbach from the previous n ≥ 10²⁰ down to an unprecedented n ≥ 10¹⁸. Combined with existing computational verification up to 4×10¹⁸, this closes the gap entirely, potentially solving a 280-year-old conjecture.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-07-19
DOI
https://doi.org/10.5281/zenodo.16161227
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
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article

Refinement of the Circle Method for Goldbach: An Analytical Exercise with Acknowledged Limitations

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
article

Refinement of the Circle Method for Goldbach: An Analytical Exercise with Acknowledged Limitations

article en

Abstract

This paper presents a dramatic refinement of the Hardy-Littlewood circle method, reducing the analytical threshold for binary Goldbach from the previous n ≥ 10²⁰ down to an unprecedented n ≥ 10¹⁸. Combined with existing computational verification up to 4×10¹⁸, this closes the gap entirely, potentially solving a 280-year-old conjecture.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 50%
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Refinement of the Circle Method for Goldbach: An Analytical Exercise with Acknowledged Limitations · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS