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DOCUMENTATION CENTER SEARCH
Mathematica
>
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>
Prime Numbers
>
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Prime Numbers
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Built-in
Mathematica
Symbol
Integer and Number Theoretic Functions
Tutorials »
|
Prime
NextPrime
RiemannR
Zeta
ZetaZero
See Also »
|
Analytic Number Theory
Mathematical Functions
Multiplicative Number Theory
Number Theoretic Functions
Number Theory
Prime Numbers
More About »
PrimePi
PrimePi
[
x
]
gives the number of primes
(
x
)
less than or equal to
x
.
MORE INFORMATION
Integer mathematical function, suitable for both symbolic and numerical manipulation.
The argument of
PrimePi
can be any positive real number.
PrimePi
[1]
gives
0
.
PrimePi
automatically threads over lists.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
The number of primes up to a billion:
In[1]:=
Out[1]=
PrimePi
increases every time there is a prime:
In[1]:=
Out[1]=
Scope
(2)
Applications
(3)
Properties & Relations
(2)
SEE ALSO
Prime
NextPrime
RiemannR
Zeta
ZetaZero
TUTORIALS
Integer and Number Theoretic Functions
RELATED LINKS
Demonstrations with PrimePi
(
Wolfram Demonstrations Project
)
Implementation notes: Numerical and Related Functions
MathWorld
The Wolfram Functions Site
NKS|Online
(
A New Kind of Science
)
MORE ABOUT
Analytic Number Theory
Mathematical Functions
Multiplicative Number Theory
Number Theoretic Functions
Number Theory
Prime Numbers
New in 2
(x) less than or equal to x.
EXAMPLES
Basic Examples 
Scope 