Nguyen's Evidence for Goldbach's Conjecture: Prime is Odd A Structural Explanation for Why Every Even Number is the Sum of Two Primes
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2025
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| _version_ | 1866901233874239488 |
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| author | Nguyen, Van Laurie |
| author_facet | Nguyen, Van Laurie |
| contents | <p>Goldbach's Conjecture, proposed in 1742, states that every even</p> <p>number greater than 2 can be expressed as the sum of two prime</p> <p>numbers. Despite verification up to 4 × 10^18, no formal proof has been</p> <p>accepted. This paper proposes that the conjecture resists proof because</p> <p>mathematicians have focused on finding prime pairs (verification) rather</p> <p>than understanding why the structure guarantees their existence</p> <p>(explanation). We demonstrate that Goldbach's Conjecture is a</p> <p>necessary consequence of three established facts: (1) all primes except</p> <p>2 are odd, (2) odd + odd = even, and (3) infinite primes exist. The</p> <p>"mystery" dissolves when we recognize that two primes is the minimum</p> <p>required to "fold" hidden values (odd, prime) into a visible surface</p> <p>(even). This framework, consistent with the author's prior work on P</p> <p>versus NP as dimensional layers, positions Goldbach not as an</p> <p>unsolved problem but as a structural inevitability.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17994584 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Nguyen's Evidence for Goldbach's Conjecture: Prime is Odd A Structural Explanation for Why Every Even Number is the Sum of Two Primes Nguyen, Van Laurie <p>Goldbach's Conjecture, proposed in 1742, states that every even</p> <p>number greater than 2 can be expressed as the sum of two prime</p> <p>numbers. Despite verification up to 4 × 10^18, no formal proof has been</p> <p>accepted. This paper proposes that the conjecture resists proof because</p> <p>mathematicians have focused on finding prime pairs (verification) rather</p> <p>than understanding why the structure guarantees their existence</p> <p>(explanation). We demonstrate that Goldbach's Conjecture is a</p> <p>necessary consequence of three established facts: (1) all primes except</p> <p>2 are odd, (2) odd + odd = even, and (3) infinite primes exist. The</p> <p>"mystery" dissolves when we recognize that two primes is the minimum</p> <p>required to "fold" hidden values (odd, prime) into a visible surface</p> <p>(even). This framework, consistent with the author's prior work on P</p> <p>versus NP as dimensional layers, positions Goldbach not as an</p> <p>unsolved problem but as a structural inevitability.</p> |
| title | Nguyen's Evidence for Goldbach's Conjecture: Prime is Odd A Structural Explanation for Why Every Even Number is the Sum of Two Primes |
| url | https://doi.org/10.5281/zenodo.17994584 |