A Heuristic Approach to the Strong Goldbach Conjecture Based on a Minimum Additive Prime Product Principle

This paper presents a heuristic exploration of the Strong Goldbach Conjecture from an optimization principle perspective. We postulate that the representation of an even number n as a sum of primes pi is governed by an "additive effort," defined as the sum of the natural logarithms of its prime components, E = ∑ ln(pi). This metric is mathematically equivalent to minimizing the product of these primes. An exhaustive computational analysis was performed for all even numbers in the range 4 < n ≤ 10, 000. Within this range, it was verified that, for n ≥ 8, the Goldbach partition (n = p1 + p2) consistently minimizes this effort function. A unique exception was identified at n = 6, where the minimum effort is achieved with the partition 2 + 2 + 2. This work does not constitute a formal proof but offers a conceptual framework and numerical evidence suggesting that the two-prime solution is not only possible but optimal under this minimization principle for most even numbers.