Mertens定理的Mertens证明
Mertens' Proof of Mertens' Theorem
摘要：
我们提出了一个独立的小学和详细的阐述梅尔滕斯自己的证明他的定理的分歧系列的倒数的素数和比较它与现代的证据。他的证明包含明确的数值误差估计和计算的梅尔滕斯“常数”，这两个都是失踪的现代博览会。由于他的策略和技术与今天的方法大不相同，他的原始方法值得更好地了解。
英文摘要：
We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit numerical error estimates and computations of the Mertens "constant," both of which are missing from modern expositions. In as much as his strategy and techniques are quite different from today's methods, his original methods deserve to be better known.
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。
