Download PDFOpen PDF in browserCurrent versionThe Riemann HypothesisEasyChair Preprint 3708, version 4Versions: 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152→history 4 pages•Date: July 27, 2020AbstractIn mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. Many consider it to be the most important unsolved problem in pure mathematics. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. The Robin's inequality is true for every natural number $n > 5040$ if and only if the Riemann hypothesis is true. We demonstrate the Robin's inequality is possible to be true for every natural number $n > 5040$ which is not divisible by $2$, $3$ or $5$ under a computational evidence. Indeed, we have checked this for every number $10^{1875} \geq n > 5040$ which is not divisible by $2$, $3$ or $5$. In this way, if there is a counterexample for the Robin's inequality, then this should be for some natural number $n > 5040$ which is divisible by $2$, $3$ or $5$. Keyphrases: Divisor, inequality, number theory
