Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[PrimeCounting] instead.

The function pi(n) computes the number of prime numbers less than or equal to the given integer n.

$\mathrm{with}\left(\mathrm{numtheory}\right)\:$

$\mathrm{pi}\left(10\right)$

$4$

$\mathrm{pi}\left(100\right)$

$25$

$\mathrm{pi}\left(1000\right)$

$168$

$\mathrm{pi}\left(10000\right)$

$1229$

$\mathrm{nops}\left(\mathrm{select}\left(\mathrm{isprime}\,\left[\mathrm{`\$`}\left(2..10000\right)\right]\right)\right)$

$1229$

$\mathrm{Li}\left(10000.0\right)$

$1246.137216$

$\frac{10000.0}{\ln \left(10000.0\right)}$

$1085.736205$