A_Novel_Prime_Number_Identity_Bridging_the_Collatz_Conjecture_and_Additive_Prime_Structures (6).pdf

The study explores this identity analytically and numerically, providing insights into its validity, scope, and potential implications. The structure and behavior of the difference terms (pi+1 − pi)(n − i) are also analyzed, highlighting a hidden regularity in prime gaps when viewed through the lens of this summation. The result opens new avenues for reinterpreting prime behavior in discrete systems and lays foundational groundwork for a possible unification of discrete dynamical processes and prime arithmetic