基于双行网格与反证概率法，探究哥德巴赫猜想Investigating the Goldbach Conjecture Based on the Double-Row Grid and the Proof-by-Contradiction Probability Method

This paper constructs a double-row odd-number spatial 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 respectively, with the sum of the numbers in the same column equaling 2m. Letting p denote the proportion of primes in a single row, this paper adopts the relaxation method: by removing the column sum constraint and shuffling 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). Substituting the computational verification bound 2m = 4×10¹⁸ yields a probability of approximately 10^(−1.88×10¹⁵), and it is proven that the limit approaches 0 as m→∞. Based on this, the "Proof-by-Contradiction Probability Method" is proposed: a counterexample is a deterministic event; if it exists, its probability must equal 1. The above derivation demonstrates that the survival probability of a counterexample is strictly less than 1. According to Kolmogorov's axioms and the Law of Excluded Middle, a counterexample cannot exist, and the Goldbach Conjecture holds. The generalization significance of this method for determining deterministic propositions is discussed at the end of the paper.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)；代入验证边界2m = 4×10¹⁸得该概率约为10^(−1.88×10¹⁵)，并证得m→∞时其极限为0。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；而上述推导表明反例存活概率严格小于1，依据柯尔莫哥洛夫公理与排中律，反例不存在，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。