Failed attempt to disproof the Riemann Hypothesis

2009/10/08 by Marek Wolf, Wolf, Marek
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Number Theory (math.NT) #math.GM #math.NT

paper · pdf · doi:10.48550/arxiv.0910.1534

16 pages, 2 figures

arxiv created 2009/10/08 · arxiv updated 2009/12/01

Abstract

In this paper we are going to describe the results of the computer experiment, which in principle can rule out the Riemann Hypothesis. We use the sequence c_k appearing in the \BD criterion for the RH. Namely we calculate c₁₀₀₀₀₀ with thousand digits of accuracy using two different formulas for c_k with the aim to disproof the Riemann Hypothesis in the case these two numbers will differ. We found the discrepancy only on the 996 decimal place (accuracy of 10^-996). The reported here experiment can be of interest for developers of Mathematica and PARI/GP.

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