The Turkish Sieve Methodology: Deterministic Computation of Twin and Cousin Prime Pairs Using an N/6 Bit Data Structure

The Twin Prime Conjecture via prime-gap persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Legendre's Conjecture via short-interval prime persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

This repository provides a constructive supplement to the Littlewood Conjecture using prime density and asymptotic analysis. 本リポジトリは、リトルウッド予想に対して、6n±1型構成と素数密度の漸近解析に基づく構成的補完を提示します。

Investigates deterministic prime-gap interiors using the Divisor Normalization Identity (DNI). Establishes the Gap Winner Rule (GWR) the raw-Z maximizer is always the leftmost min-d(n) carrier. Validates the No-Later-Simpler-Composite Theorem with zero violations through 10^18. Documents hierarchical first-arrival laws and square-phase terminal.

Closed-form nth-prime estimator built on invariant-normalization logic, with deterministic refinement and exact benchmarks across a contract grid spanning n = 10^2 to 10^24.