PrimeZetaP[s]
gives prime zeta function .


PrimeZetaP
PrimeZetaP[s]
gives prime zeta function .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
is defined by
for
and by analytic continuation for
.
- PrimeZetaP can be evaluated to arbitrary numerical precision.
- PrimeZetaP automatically threads over lists. »
Examples
open all close allScope (14)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate efficiently at high precision:
Compute the elementwise values of an array:
Or compute the matrix PrimeZetaP function using MatrixFunction:
Compute average-case statistical intervals using Around:
Specific Values (3)
Simple exact values are generated automatically:
Some singular points of PrimeZetaP:
Find a value of s for which Re[PrimeZetaP[s]]=-2:
Visualization (2)
Plot the real and imaginary parts of PrimeZetaP function:
Plot the real part of PrimeZetaP function:
Function Properties (3)
Related Guides
History
Text
Wolfram Research (2008), PrimeZetaP, Wolfram Language function, https://reference.wolfram.com/language/ref/PrimeZetaP.html.
CMS
Wolfram Language. 2008. "PrimeZetaP." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PrimeZetaP.html.
APA
Wolfram Language. (2008). PrimeZetaP. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PrimeZetaP.html
BibTeX
@misc{reference.wolfram_2025_primezetap, author="Wolfram Research", title="{PrimeZetaP}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/PrimeZetaP.html}", note=[Accessed: 08-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_primezetap, organization={Wolfram Research}, title={PrimeZetaP}, year={2008}, url={https://reference.wolfram.com/language/ref/PrimeZetaP.html}, note=[Accessed: 08-August-2025]}