Critical Line
The line ![R[s]=1/2](http://mathworld.wolfram.com/images/equations/CriticalLine/Inline1.gif)
in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first few zeros of the Riemann zeta function, with the critical line shown in red. The zeros with ![I[s]=0](http://mathworld.wolfram.com/images/equations/CriticalLine/Inline2.gif)
and ![R[s]<0](http://mathworld.wolfram.com/images/equations/CriticalLine/Inline3.gif)
that do not line on the critical line are the trivial zeros of 
at 
, 
, .... Although it is known that an infinite number of zeros lie on the critical line and that these comprise at least 40% of all zeros, the Riemann hypothesis is still unproven.
in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first few zeros of the Riemann zeta function, with the critical line shown in red. The zeros with and that do not line on the critical line are the trivial zeros of at , , .... Although it is known that an infinite number of zeros lie on the critical line and that these comprise at least 40% of all zeros, the Riemann hypothesis is still unproven.
In the Season 1 episode "Prime Suspect" (2005) of the television crime drama NUMB3RS, math genius Charlie Eppes discusses the critical line after realizing that character Ethan's daughter has been kidnapped because he is close to solving theRiemann hypothesis, which allegedly would allow the perpetrators to break essentially all internet security.
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