The Teymornejad Conjecture and Its Implications in Number Theory

This paper provides a detailed study of the Teymornejad Conjecture, which asserts that for every integer n with |n| ≥ 2, there exists a natural number d ≥ 0 such that both n - d and n + d are prime numbers. This conjecture is a natural generalization of Goldbach's conjecture and establishes deep connections with prime number distribution. In this work, we present a precise mathematical formulation, extend the conjecture to Gaussian integers, and analyze its implications in cryptography and quantum physics. A new theorem regarding the asymptotic behavior of d is also proven and supported by strong computational evidence.