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

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Ricardo Adonis Caraccioli Abrego ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.20944/preprints202507.1523.v1

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.

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Goldbach's Conjecture

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Goldbach's conjecture Prime (order theory) Heuristic Product (mathematics) Conjecture Mathematics Combinatorics Computer science Mathematical optimization Geometry

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Type: preprint
Language: en
Landing Page: https://doi.org/10.20944/preprints202507.1523.v1
PDF: https://www.preprints.org/frontend/manuscript/7bc78385d3e6d39a248d8364bd68c8b2/download_pub
OA Status: green
References: 3
Related Works: 10
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DOI: https://doi.org/10.20944/preprints202507.1523.v1

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

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-07-18

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Authors: Ricardo Adonis Caraccioli Abrego

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Landing page: https://doi.org/10.20944/preprints202507.1523.v1

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PDF URL: https://www.preprints.org/frontend/manuscript/7bc78385d3e6d39a248d8364bd68c8b2/download_pub

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Concepts: Goldbach's conjecture, Prime (order theory), Heuristic, Product (mathematics), Conjecture, Mathematics, Combinatorics, Computer science, Mathematical optimization, Geometry

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