哥德巴赫猜想的确定性证明
综合数学
2025-08-12 v7
摘要
哥德巴赫猜想指出，每个大于 2 的偶数都可以表示为两个素数之和。该猜想由德国数学家 Christian Goldbach 于 1742 年首次提出，尽管显然为真，却一直未被证明。本文证明了：在所有不被小于其平方根的素数整除的偶数 n 的集合中，素数对的数量相对最少。我们推导出一个方程，用以近似这些 n 值对应的素数对数量。随后证明该方程对任意 n 均不为零，且随着 n 增大，素数对数量亦增加，从而验证了哥德巴赫猜想。通过误差分析表明，该近似值与实际素数对数量之差足够小，使得对所有 n > 622，n 的素数对数量大于 1，由此证明了哥德巴赫猜想。
引用
@article{arxiv.1811.02415,
title = {Definitive Proof of Goldbach's conjecture},
author = {Kenneth A. Watanabe},
journal= {arXiv preprint arXiv:1811.02415},
year = {2025}
}
备注
27 pages, 6 figures. The following modifications were made from the previous version - the W(n) function was simplified to be the fraction of prime pairs less than n, proof was modified to take into account the new W(n) function, error analysis was performed to confirm deviation from actual prime pair counting function was small, figures were added to further explain proof