The Riemann's Hypothesis, the Prime Numbers Theorem (PNT), and the Error

Ing Mg Carlos A Correa*

In this simple paper, a small refinement to the Prime Number Theorem (PNT) is proposed, which allows us to limit the error with which said theorem predicts the value of the Prime-counting function π(x); and, in this way, endorse the veracity of the Riemann Hypothesis.

Many people know that the Riemann Hypothesis is a difficult mathematical problem - even to understand - without a certain background in mathematics. Many techniques have been used, for more than 150 years, to try to solve it. Among them is the one that establishes that, if the Riemann hypothesis is true, then the error term that appears in the prime number theorem can be bounded in the best possible way. Specifically, Helge von Koch demonstrated in 1901 that it should be:

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Published on: Aug 31, 2024 Pages: 242-245

Full Text PDF Full Text HTML DOI: 10.17352/amp.000129
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