Published November 17, 2025 | Version v1
Dataset Restricted

Twin Prime XOR Law: Computational Validation Dataset and Source Code

Authors/Creators

Description

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"

Files

Restricted

The record is publicly accessible, but files are restricted to users with access.

Additional details

Identifiers

URL
https://github.com/thiagomassensini/twin-prime-xor-law

Related works

Is supplemented by
Dataset: https://github.com/thiagomassensini/twin-prime-xor-law (URL)

Dates

Copyrighted
2025-11-17
Twin Prime XOR

Software

Repository URL
https://github.com/thiagomassensini/twin-prime-xor-law
Programming language
C++
Development Status
Active

References

  • Hardy, G. H., & Wright, E. M. (2008). An Introduction to the Theory of Numbers (6th ed.). Oxford University Press.
  • Crandall, R., & Pomerance, C. (2005). Prime Numbers: A Computational Perspective (2nd ed.). Springer.