| Description: |
This paper presents a computational framework for Goldbach Conjecture verification based on a structural decomposition of the problem using residue class constraints modulo 6. This approach partitions the verification task into three distinct, computationally cheaper subproblems. A direct serial benchmark shows our optimized Python implementation achieves a speedup of over 1.6x over a conventional baseline algorithm. When fully parallelized, our method successfully verifies the conjecture for all 4,999,999,999 even integers up to 10^10, processing at a sustained rate of over 11.2 million verifications per second and completing the task in under 13 minutes. Key contributions include: * A formal framework for decomposing the Goldbach verification problem using residue classes modulo 6.* An optimized, open-source Python implementation achieving a serial speedup of over 1.6x compared to a conventional baseline.* Complete verification of the conjecture for all even integers up to 10^10, completed in under 13 minutes on a single machine.* A fully transparent and reproducible research package, including the source code, performance data, and environment specifications. This work provides a transparent, reproducible, and efficient methodology for large-scale empirical tests of the Goldbach Conjecture. The complete source code and performance data are provided to ensure full reproducibility. Keywords: Goldbach conjecture, computational number theory, algorithmic optimization, residue classes, open science, reproducible research, prime numbers, empirical verification, Python, Numba Files in this upload: This upload contains the following files: Venkat2025_GoldbachVerification.pdf - The complete research paper with methodology, benchmarks, and discussion. goldbach_verifier.py - The complete, commented Python script used to run the verification and benchmarks. verification_results.txt - A text file containing the summary output and performance metrics from the full 10^10 verification run. requirements.txt - A file listing the necessary Python packages to replicate the software environment. Licensing: Source code (goldbach_verifier.py): MIT License All other files (paper, text files): Creative Commons Attribution 4.0 International |