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Stephen Wolfram
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE
DOCUMENTATION CENTER
FOR THE LATEST INFORMATION.
Mathematica
>
Prime Numbers
>
Built-in
Mathematica
Symbol
Integer and Number Theoretic Functions
Tutorials »
|
Prime
NextPrime
Zeta
ZetaZero
See Also »
|
Mathematical Functions
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
(2)
Properties & Relations
(2)
SEE ALSO
Prime
NextPrime
Zeta
ZetaZero
TUTORIALS
Integer and Number Theoretic Functions
RELATED LINKS
Implementation notes: Numerical and Related Functions
MathWorld
The Wolfram Functions Site
NKS|Online
(
A New Kind of Science
)
MORE ABOUT
Mathematical Functions
Number Theoretic Functions
Number Theory
Prime Numbers
New in 2
© 2013 Wolfram Research, Inc.
(x) less than or equal to x.
EXAMPLES
Basic Examples 
Scope 