# What are some practical attempts to disprove Riemann Hypothesis?

Most people believe Riemann Hypothesis is true. Since RH has not been proved yet, so it is not completely insane to disprove RH.

Among the ways to disprove RH, straightforward ways, such as: try to find a zero not on critical line, or to find a number n which Mertens function M ( n ) not satisfy "square root error term" condition, those approaches seems not practical. Because we know, even if such a root or a number exist, they will be very big.

What are some practical attempts to disprove Riemann Hypothesis ?

The only 'practical' attempt I know to disprove RH is to prove De Bruijn–Newman constant Λ > 0.

In additional to above attempt, is there any other 'practical' attempt to disprove RH ?

• prove it undecideable is pretty practical I think , i.e. link it to godel's theorem some how and show that it could be true or not true given our axioms. – shai horowitz May 23 '16 at 19:16
• "disprove", not "disapprove" – BrianO May 23 '16 at 19:33
• Not a single counter example found so far, right? – Narasimham May 23 '16 at 20:29
• I am not able to read $Ivic'$ article, and I don't know if the article is concerning in your words practical attempts to drisprove. But I undertand for example that if you find an integer $n$ or know how build it such that doesn't satisfy Nicolas, Robin or Lagarias condition then you have a counterexample. I don't know what you means 'practical'. I tell you this, from a divulgative viewpoint. – user243301 May 28 '16 at 12:51
• @shaihorowitz The Riemann hypothesis cannot be DISPROVED by showing that it is undecideable. Because a disprove implies that there is at least one counterexample, and the existence of this counterexample would be proveable, hence the Riemann hypothesis could not be false. – Peter Aug 24 '18 at 7:49