Download PDFOpen PDF in browserProof of the Riemann HypothesisEasyChair Preprint 715910 pages•Date: December 6, 2021AbstractThe Riemann hypothesis has been considered the most important unsolved problem in mathematics. Robin 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 natural numbers $n > 5040$, where $\sigma(n)$ is the sumofdivisors function of $n$ and $\gamma \approx 0.57721$ is the EulerMascheroni constant. We show that the Robin inequality is true for all natural numbers $n > 5040$ which are not divisible by the prime $3$. Moreover, we prove that the Robin inequality is true for all natural numbers $n > 5040$ which are divisible by the prime $3$. Consequently, the Robin inequality is true for all natural numbers $n > 5040$ and thus, the Riemann hypothesis is true. Keyphrases: Riemann hypothesis, Riemann zeta function, Robin inequality, prime numbers, sumofdivisors function
