Hassan Prime Suite : A Modular Computational Framework For Prime Distribution Via Residue Classes

The Hasani Prime Suite is a modular C++ software framework designed to analyze prime number distribution through residue-based arithmetic sequences. It implements the Hasani Sieve computationally, generating candidate sequences of the form \( S_r = r + mk \) for \( \gcd(r, m) = 1 \), and provides analytical tools for density estimation, fluctuation modeling, and comparative residue analysis. The suite includes:- Candidate generation modules (`sieve_generator`)- Prime density analysis (`density_analyzer`)- Goldbach decomposition testing (`GoldbachAnalyzer`)- Structural pattern recognition (`pattern_analysis`)- CSV export for academic reporting (`pattern_exporter`)- A bilingual interface supporting Arabic-English publishing Empirical results confirm that residues \( r = 1 \) and \( r = 5 \) modulo 6 are prime-rich, validating the modular generative hypothesis. The suite also supports extended Goldbach-type representations involving semiprimes. This software complements the theoretical framework presented in *Hasani Sieve and Modular Prime Distribution* (DOI: [10.5281/zenodo.17456649](https://doi.org/10.5281/zenodo.17456649)), forming a complete research ecosystem for modular prime analysis. Presented in both English and Arabic, the suite supports bilingual mathematical publishing and global accessibility.