Twin Prime XOR Law: Computational Validation Dataset and Source Code

This dataset provides computational validation for the Twin Prime XOR Identity theorem, which establishes that for any twin prime pair (p, p+2) with p > 3, the bitwise XOR operation yields: p XOR (p+2) = 2^(v_2(p+1)+1) - 2, where v_2 denotes the 2-adic valuation. The repository contains:- High-performance C++ implementation for twin prime mining (deterministic Miller-Rabin)- Validator with OpenMP parallelization- Verification of 1+ billion twin prime pairs (p < 10^12)- 100% validation rate with chi-squared test (chi-squared = 20.40, df=14, p < 0.05) Statistical results confirm geometric distribution P(k) = 2^(-k) for k-values derived from 2-adic valuations. Related publication: "Binary Structure of Twin Primes and Connection to Iwasawa Lambda-Invariants"

Keywords

binary structure, computational number theory, prime gaps, elliptic curves, twin primes, 2-adic valuation, XOR operation, Iwasawa theory, Miller-Rabin primality test

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