Analytic Resolution of the Twin Prime Conjecture using Discrete Operators: Research by Ayoub Teymornejad

This paper presents a novel approach to the Twin Prime Conjecture by introducing discrete anti-derivative operators and a discontinuity principle for prime detection. The proposed framework achieves strong agreement with the Hardy–Littlewood conjecture and shows numerical convergence up to 10^6. The method is extensible to prime n-tuples and offers a new computational and analytic path in number theory. Authored by Ayoub Teymornejad (ORCID: https://orcid.org/0009-0006-5276-1153).