The Spring Conjecture: An Extremal Observable for the Even Goldbach Problem
Year: 2026
Type: preprint
Abstract: This paper introduces an extremal observable for the even Goldbach problem. Let R be the upper bound of the prime pool. Even numbers within this pool that cannot be decomposed into a sum of two primes are called failed even numbers, and their count is denoted C(R). The supremum of the minimal outward pairing amount is denoted D(R), based on which the Spring Conjecture is proposed. Fifty groups of numerical experiments with R ranging from 97 to 4999 yield an empirical upper bound D = O(\ln^2(2R)), with the tightest coefficient being 2.52. Multi-parameter formulations are also provided, and an unconditional lower bound is derived from the large prime gap theorem. The finiteness of D(R) together with D/R \to 0 implies the Goldbach conjecture. This paper does not claim a proof; it only presents intermediate propositions that are numerically verifiable.
Author: Kong, Shi
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225821405
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