Goldbach Conjecture and the Trichotomy Law

This paper asserts that the falsity of Goldbach Conjecture results in the breakdown of Trichotomy Law. Assuming that Goldbach Conjecture breaks down at an even integer 2n, where n ≥ 3, we note that the differences of 2n with the odd primes in the interval (1, n) are composite integers. We form a product δ of the collection of the least prime factors of these composite integers. We show that for a base case this product breaks Trichotomy Law. With the inductive hypothesis that such is the case with 2n, we prove that for all even integers the breakdown of Goldbach Conjecture entails the breakdown of Trichotomy Law.