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Study Riemann's Prime Counting Function Near the Origin
The analytic function RiemannR approximates the prime-counting function PrimePi. Its first zero occurs at about 1.83×10-14828.
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LogPlot[Abs[RiemannR[10^x]], {x, -45000, 2}, Frame -> True, 

 Axes -> False, MaxRecursion -> 4]
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