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PrimeZetaP

PrimeZetaP[s]
gives prime zeta function P(s).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • P(s) is defined by Sigma_(p in P)p^(-s) for Re(s)>1 and by analytic continuation for 0<Re(s)<=1.
  • PrimeZetaP can be evaluated to arbitrary numerical precision.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Evaluate to high precision:
Evaluate to high precision:
In[1]:=
Click for copyable input
Out[1]=
 
In[1]:=
Click for copyable input
Out[1]=
Scope   (5)
Evaluate for machine precision:
Evaluate for complex arguments:
The precision of the output tracks the precision of the input:
PrimeZetaP threads element-wise over lists:
TraditionalForm formatting:
Applications   (2)
Compute Artin's constant:
Compute the first Mertens' constant:
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