期刊名称：Computational Methods in Science and Technology
印刷版ISSN：1505-0602
出版年度：2014
卷号：20
期号：2
页码：39-47
DOI：10.12921/cmst.2014.20.02.39-47
出版社：Poznan Supercomputing and Networking Center
摘要：In this paper we are going to describe the results of the computer experiment, which in principle can rule out validity of the Riemann Hypothesis (RH). We use the sequence ck appearing in the Báez-Duarte criterion for the RH and compare two formulas for these numbers. We describe the mechanism of possible violation of the Riemann Hypothesis. Next we calculate c100000 with a thousand digits of accuracy using two different formulas for ck with the aim to disprove the Riemann Hypothesis in the case these two numbers will differ. We found the discrepancy only on the 996th decimal place (accuracy of 10−996 ). The computer experiment reported herein can be of interest for developers of Mathematica and PARI/GP.
