Download PDFOpen PDF in browserCurrent versionThe Complete Proof of the Riemann HypothesisEasyChair Preprint 6710, version 119 pages•Date: September 27, 2021AbstractRobin criterion states that the Riemann Hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all $n > 5040$, where $\sigma(n)$ is the sumofdivisors function and $\gamma \approx 0.57721$ is the EulerMascheroni constant. We prove that the Robin inequality is true for all $n > 5040$ which are not divisible by any prime number between $2$ and $953$. Using this result, we show there is a contradiction just assuming the possible smallest counterexample $n > 5040$ of the Robin inequality. In this way, we prove that the Robin inequality is true for all $n > 5040$ and thus, the Riemann Hypothesis is true. Keyphrases: Riemann hypothesis, Robin inequality, prime numbers, sumofdivisors function
