Gokul's Prime Matrix Conjecture A Structural Unification Tool for Goldbach Conjecture and the Least Prime in Arithmetic Progressions

We introduce a structural framework for prime distribution: arranging integers 1,2,...,n2 into an n × n square matrix, where n is a prime number. Conjecture. Every row and every column of this prime matrix contains at least one prime. This holds for all prime dimension: n = 2,3,5,7,11,13,... up to infinity (∞) suggesting a universal structural law. This conjecture offers a unified diagnostic for two classical problems: ensuring prime presence in short intervals (Goldbach Conjecture) and in residue classes (least prime in Arithmetic Progression)