Axis Journal of Mathematical Statistics and Modelling
The Unified Prime Equation and the Resolution of Goldbachâs Conjecture
Abstract
Bahbouhi Bouchaib
In this article I present the Unified Prime Equation (UPE), a compact and general formula for prime numbers that leads to an unconditional resolution of Goldbach’s Conjecture. The UPE framework classifies primes through modular symmetry (6k ± 1), introduces a bounded-correction sieve principle, and applies a systematic rule for generating Goldbach pairs for all even numbers. The approach is simultaneously theoretical and constructive: it produces primes near any large integer, predicts symmetric prime pairs for even numbers, and is verified by large-scale computational experiments up to and beyond 10^36. A public website implementation allows any user to test the method on numbers up to 10^5000, demonstrating both transparency and universality. Please visit Goldbach Window (Unconditional Proof): https://b43797.github.io/goldbach-windowunconditional-proof/ and Prime Equation (Prime Detection): https://b43797. github.io/primedetection-/
The article situates UPE in historical context, from Euler and Goldbach to Hardy–Littlewood, Cramér, Ramaré, Oliveira e Silva, Silveira, and Helfgott. Unlike earlier heuristic or probabilistic models, UPE offers a deterministic rule that is both mathematically structured and practically computable. The conclusion is clear: the Goldbach problem has moved from conjecture to theorem, and the path of three centuries has converged on a remarkably simple modular law.