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PrimeNu—Wolfram Documentation

PrimeNu[n]

gives the number of distinct primes in n.

Details and Options

Examples

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Basic Examples  (2)

Compute PrimeNu at 24:

Plot the PrimeNu sequence for the first 100 numbers:

Scope  (9)

Numerical Evaluation  (4)

PrimeNu works over integers:

Gaussian integers:

Compute for large integers:

PrimeNu threads over lists:

Symbolic Manipulation  (5)

Options  (1)

GaussianIntegers  (1)

Compute PrimeNu over integers:

Gaussian integers:

Applications  (7)

Basic Applications  (2)

Table of the values of PrimeNu for the integers up to 100:

Histogram of the values of PrimeNu:

Number Theory  (5)

Properties & Relations  (6)

Possible Issues  (1)

Neat Examples  (2)

Plot the arguments of the Fourier transform of PrimeNu:

Plot the Ulam spiral of PrimeNu:

Wolfram Research (2008), PrimeNu, Wolfram Language function, https://reference.wolfram.com/language/ref/PrimeNu.html.

Text

Wolfram Research (2008), PrimeNu, Wolfram Language function, https://reference.wolfram.com/language/ref/PrimeNu.html.

CMS

Wolfram Language. 2008. "PrimeNu." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PrimeNu.html.

APA

Wolfram Language. (2008). PrimeNu. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PrimeNu.html

BibTeX

@misc{reference.wolfram_2025_primenu, author="Wolfram Research", title="{PrimeNu}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/PrimeNu.html}", note=[Accessed: 23-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_primenu, organization={Wolfram Research}, title={PrimeNu}, year={2008}, url={https://reference.wolfram.com/language/ref/PrimeNu.html}, note=[Accessed: 23-February-2026]}