Primes decomposition via novel additive identities

This project introduces and investigates two novel additive identities involving prime numbers. The first identity expresses every odd number ≥ 9 as O = 2P + Q, and the second expresses every prime number ≥ 11 as P = 2Q + R, where P, Q, and R are prime numbers (with P ≠ 2 and Q ≠ 2). These identities are explored computationally and structurally to examine their ability to cover all prime numbers through valid combinations. The archive includes:- The full research paper (PDF format)- Python code files for generating and verifying all valid combinations for given ranges- A README file for usage notes and citation- A license file (CC BY 4.0) All results have been verified up to a range of 100,000. The Python scripts allow for reproducibility and further exploration of prime decomposition behavior. Author: Usman Shabbir ([e-mail])