March 3, 2026Open Access

Exact Angular Counting for Prime Gaps under Gap-Dependent Encoding, with Ramanujan-Based Diagnostics

Ask AI

Bookmark

Authors

Discussion

Analysis reveals exact counting laws and transfer principles for prime gaps, suggesting new methodologies for exploration.

Exact counting laws are derived from a novel angular encoding of integers within prime gaps, demonstrating structural regularities.
A short-window sieve bridge effectively transfers information from prime pairs to consecutive gaps, clarifying existing multiplicative corrections.
Variance-reduced smoothing via a helical roughness weight enhances numerical stability while providing conceptual clarity on divisibility properties.
Independent checks validate the framework, ensuring reproducibility and modular application for future research in prime gap analysis.

Maisara Shoeib (2025) studied this question.

Ask AI

Bookmark

March 3, 2026Open Access

Ask AI

Bookmark

Authors

Analysis reveals exact counting laws and transfer principles for prime gaps, suggesting new methodologies for exploration.

Exact counting laws are derived from a novel angular encoding of integers within prime gaps, demonstrating structural regularities.
A short-window sieve bridge effectively transfers information from prime pairs to consecutive gaps, clarifying existing multiplicative corrections.
Variance-reduced smoothing via a helical roughness weight enhances numerical stability while providing conceptual clarity on divisibility properties.
Independent checks validate the framework, ensuring reproducibility and modular application for future research in prime gap analysis.