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PrimePi

PrimePi[x]
gives the number of primes 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 automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (2)
The number of primes up to a billion:
PrimePi increases every time there is a prime:
The number of primes up to a billion:
In[1]:=
Click for copyable input
Out[1]=
 
PrimePi increases every time there is a prime:
In[1]:=
Click for copyable input
Out[1]=
Scope   (2)
PrimePi takes continuous arguments, but gives integer values:
TraditionalForm formatting:
Applications   (3)
Plot PrimePi compared with estimates:
Compute PrimePi based on the Hardy-Wright formula:
Properties & Relations   (2)
For primes, Prime is effectively the inverse of PrimePi:
Integrate :
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