Code for: Structural Analysis and Computational Verification of the Totient Triple φ(5186)=φ(5187)=φ(5188)=2592

Complete computational implementation for the research paper "Structural Analysis and Computational Verification of the Totient Triple φ(5186)=φ(5187)=φ(5188)=2592". This repository contains all code used to verify the unique consecutive totient triple and search for additional triples up to 10¹³. Includes: • totient_research_pro.c - Main search engine with checkpointing and parallel processing• euler_triple_analyzer.c - Educational tool for totient pattern analysis• phi_pairs_analyzer.py - Statistical analysis of consecutive totient pairs• totient_triple_research.py - Complete Python research suite• quick_verify.py - Instant verification of the known triple Key features:- Optimized search to 10¹³ (36.5 hours on standard hardware)- Checkpointing system for resumable long searches- Parallel processing with OpenMP- Analysis of 17 parametric families- Verification of algebraic structure All code is released under MIT License.

Keywords

computational mathematics, number theory, prime numbers, totient function, consecutive integers, Euler phi function

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