What question did this study set out to answer?

The main aim is to formally prove that odd perfect numbers cannot exist by utilizing the Strong Goldbach Conjecture.

April 8, 2026Open Access

The Structural Non-Existence of Odd Perfect Numbers under the Strong Goldbach Conjecture v2

Key Points

The main aim is to formally prove that odd perfect numbers cannot exist by utilizing the Strong Goldbach Conjecture.
Applied the Strong Goldbach Conjecture to analyze prime distributions.
Defined the largest prime number less than a specific value.
Developed a nested modular 'Kill-Chain' approach.
Proven incompatibility through additive and multiplicative constructions.
Showed that the even gap must be representable as a sum of two primes.
Demonstrated that the defined additive construction contradicts perfect number requirements.

Abstract

This paper demonstrates the formal non-existence of Odd Perfect Numbers (by applying the Strong Goldbach Conjecture to the prime distribution of We define as the largest prime number strictly less than m (p < m). We show that the resulting even gap must be representable as the sum of two primes (). Through a nested modular "Kill-Chain, " we prove that this additive construction m = p + Pᵢ + Pₙ is arithmetically incompatible with the multiplicative density and square-factor requirements necessary for a perfect number.

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