The PrimeCounting(x) command computes the number of prime numbers less than or equal to x.

pi is an alias of PrimeCounting.

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

$\mathrm{PrimeCounting}\left(1\right)$

$0$

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

$2$

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

$1229$

$\mathrm{numelems}\left(\mathrm{select}\left(\mathrm{isprime}\,\left[\mathrm{seq}\left(1..10000\right)\right]\right)\right)$

$1229$

$\mathrm{plot}\left(\left[\mathrm{PrimeCounting}\left(x\right)\,\mathrm{Li}\left(x\right)\,\frac{x}{\ln \left(x\right)}\right]\,x=1..500\,\mathrm{legend}=\left[\mathrm{pi}\left(x\right)\,\mathrm{Li}\left(x\right)\,\frac{x}{\ln \left(x\right)}\right]\right)$

The NumberTheory[PrimeCounting] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.