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Prime

Prime[n]
gives the n^(th) prime number.
  • Prime automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (3)
The first 20 primes:
The billionth prime:
Plot the sequence:
The first 20 primes:
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The billionth prime:
In[1]:=
Click for copyable input
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Plot the sequence:
In[1]:=
Click for copyable input
Out[1]=
Scope   (2)
Some symbolic operations can be done with Prime[n]:
TraditionalForm formatting:
Applications   (3)
Differences between the first 100 primes:
The n^(th) prime compared with an estimate:
An approximation to the zeta function:
Properties & Relations   (1)
PrimePi is effectively the inverse of Prime:
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