The MBM Coprime Composite Sum Conjecture

This paper is aimed at presenting a novel MBM Coprime Composite Sum Conjecture, that reveals an interesting connection between primes and coprimes, asserting that for every composite integer n, there exist composite integers a, b $>$ n such that gcd(a, b) $=$ 1 and a+b is a prime number. This conjecture sheds light on three inevitable constraints---compositeness, coprimality, and an unbounded lower threshold. Such connection between coprimes and primes has not been studied extensively in maths literature as Goldbach's conjecture and similar problem. We shall expound on formal definitions, verification algorithms, computational evidence reported up to n≤ 10⁶, and probabilistic heuristics that has been substantiated by the Prime Number Theorem and Cram\'er's random model to make the foundation of your claim rocksolid. We have also elaborated on generalization of conjecture to k pairwise-coprime composite summands and stronger case pertaining to our conjecture is also proposed, also heuristic density estimates hints at infinitely many valid solutions. The conjecture claim, while its proof remains open, has been substantiated by both numerical evidence and analytic heuristics which predicts support the plausibility of the conjecture to be true.