基于双行奇数空间模型与反证概率法，探究哥德巴赫猜想Investigating the Goldbach Conjecture Based on a Dual-Row Odd-Number Space Model and a Proof-by-Contradiction Probability Method
Year: 2026
Type: preprint
Abstract: 本文针对哥德巴赫猜想构建每列和恒定的双行奇数空间模型：将大偶数2m拆成两个奇数之和，把所有这样的奇数分别按升序、降序排列，同列相加为2m。记单行素数占比为p。本文采用放缩法：解除列和约束、打乱上下行排列，在"有放回、独立抽取"的宽松模型中推得单列不出现素数对的概率为1-p²，m-2列全部不出现的总概率为(1-p²)^(m-2)；基于集合论与概率原理，该放松模型构成了真实约束的"全集"，公式概率必然构成真实概率的严格上界。据此提出"反证概率法"：反例是确定性事件，若存在则其概率必须等于1；由于真实概率受限于严格小于1且单调递减趋近于0的公式概率上界，故绝无可能突破至1。依据柯尔莫哥洛夫公理与排中律，反例不存在。此外，反向推导亦表明，若假设反例存在，将迫使公式概率违反概率公理并得出代数矛盾。双重验证表明，哥德巴赫猜想成立。文末讨论了该方法对确定性命题判定的推广意义。This paper constructs a dual-row odd-number space model with a constant column sum to investigate the Goldbach Conjecture. A large even number, 2m, is decomposed into the sum of two odd numbers, and all such odd numbers are arranged in ascending and descending order in two rows, respectively. The sum of the numbers in each column is always 2m. Let p denote the proportion of primes in a single row. This paper adopts a relaxation method: by relaxing the column-sum constraint and shuffling the arrangement of the upper and lower rows, a relaxed model of "independent sampling with replacement" is established. In this model, the probability that a single column does not contain a prime pair is derived to be 1-p², and the total probability that none of the m-2 columns contain a prime pair is (1-p²)^(m-2). Based on set theory and probability principles, this relaxed model constitutes a "universal set" for the real constraints. Therefore, the formula probability must constitute a strict upper bound for the real probability. Accordingly, the "Proof-by-Contradiction Probability Method" is proposed. A counterexample is a deterministic event; if it exists, its probability must equal 1. Since the real probability is strictly bounded by the upper bound of the formula probability—which is strictly less than 1 and monotonically decreases toward 0—it is absolutely impossible to break through to 1. According to Kolmogorov's axioms and the law of excluded middle, the counterexample does not exist. Furthermore, the reverse derivation demonstrates that assuming the existence of a counterexample would force the formula probability to violate the probability axioms and lead to an algebraic contradiction. This dual verification establishes that the Goldbach Conjecture holds. The paper concludes by discussing the broader implications of this method for determining deterministic propositions.
Source: Figshare
Author: Yunzhi Tian
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225742530
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