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Arturo´s criterion for additive prime blocks: A necessary condition based on local density for finite Goldbach closure

Year: 2026

Type: article

Abstract: A necessary condition is presented for the set of odd primes p ≤ n to generate all even numbers up to 2n via sums, without using primes greater than n. We prove that the additive block "closes" only when n is the largest of a prime quadruple, i.e., n ≡ 9 (mod 10). As an application, the largest known prime M = 2^136279841 - 1 does not satisfy the closure property. This avoids over-induction in finite versions of the Goldbach Conjecture.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.19799938

Author: GOMEZ RODRIGUEZ, ARTURO

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7155683851

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