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arXiv 1811.02415math.GM
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哥德巴赫猜想的确定性证明

Definitive Proof of Goldbach's conjecture

Kenneth A. Watanabe

AI总结:

本文通过推导近似素数对数量的方程并进行误差分析,证明对于所有n > 622的偶数素数对数量大于1,从而确定性证明了哥德巴赫猜想。

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,尽管显然成立,但一直未被证明。本文证明了,所有不被小于其平方根的素数整除的偶数n的集合,具有相对最少的素数对数量。推导出了一个近似这些n值的素数对数量的方程。随后证明了该方程对于任何n都不会变为零,并且随着n的增加,素数对数量也增加,从而验证了哥德巴赫猜想。进行了误差分析,表明该近似值与实际素数对数量之间的差异足够小,使得对于所有n > 622,n的素数对数量大于1,从而证明了哥德巴赫猜想。

英文摘要:

The Goldbach conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers. This conjecture was first proposed by German mathematician Christian Goldbach in 1742 and, despite being obviously true, has remained unproven. In this paper, it is shown that the set of all even integers n that are not divisible by a prime number less than the square root of n has the relatively fewest number of prime pairs. An equation was derived that approximates the number of prime pairs for these values of n. It was then proven that this equation never goes to zero for any n, and as n increases, the number of prime pairs also increases, thus validating Goldbach's conjecture. Error analysis was performed to show that the difference between this approximation and the actual number of prime pairs is small enough so that for all n > 622, the number of prime pairs of n is greater than 1, thus proving Goldbach's conjecture.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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