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RiemannR

RiemannR[x]
gives the Riemann prime counting function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For , the Riemann prime counting function is given by .
  • RiemannR[z] has a branch cut discontinuity in the complex z plane running from to .
  • RiemannR can be evaluated to arbitrary numerical precision.
  • RiemannR automatically threads over lists.
Evaluate numerically:
Evaluate numerically:
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Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
RiemannR threads element-wise over lists:
TraditionalForm formatting:
The behavior of RiemannR near the origin:
The largest root of the Riemann prime counting function:
The second largest root:
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