Prime Numbers and Triangular Functions: A Structural Breakthrough in Number Theory

This paper proposes a new structural approach to understanding prime numbers through the lens of triangular functions. Unlike classical treatments, which often rely on statistical or probabilistic models, Teymornejad's theory constructs a concrete algebraic framework. Three triangular operators — \(S_p, A_p, B_p\) — expose divisibility rules and reveal surprising proximity to other primes. The theory also proposes a deterministic condition for Germain prime pairs. Supported by both rigorous proofs and computational tests up to \(p = 10^{18}\), this work lays the foundation for a new generation of research in analytic number theory.