Digit Transitions of Twin Primes in Bases 6, 12, 18, 30, and 10: An Experimental Study

This is version 3.0.0 of the dataset and code accompanying the paper: "Digit Transitions of Twin Primes in Bases 6, 12, 18, 30, and 10: An Experimental Study" This release includes all materials necessary to reproduce the analysis: 📁 code/ - Python script for analyzing last digits of twin primes📁 data/ - Complete dataset of 3,424,506 twin prime pairs up to 10⁹📁 latex/ - LaTeX source files for the paper📁 results/ - Co-occurrence matrices in CSV format📁 figures/ - Heatmaps generated from the analysis📄 paper1.pdf - Final PDF version of the article Key updates in this version:- Added the complete twin prime dataset (gemelos_1bi.txt)- Included the analysis script (twin_prime_analysis_paper1.py)- Added documentation (README.md, requirements.txt)- Organized all supplementary materials in a structured ZIP The analysis confirms that twin primes exhibit perfect modular structure:- Base 6: 5→1 (3,424,505 times)- Base 12: 5→7 and 11→1 (≈1.71M each)- Base 18: 5→7, 11→13, 17→1 (≈1.14M each)- Base 30: 11→13, 17→19, 29→1 (≈1.14M each)- Base 10: 1→3, 7→9, 9→1 (≈1.14M each) All observed transitions match exactly those predicted by the condition that both primes must be coprime to the base. For citation, please use the following DOI: 10.5281/zenodo.18912775