Prime-Counting Function/Examples

Definition

The values of the prime-counting ($\pi$) function for the first few integers are as follows:

$n$	$\map \pi n$
$1$	$0$
$2$	$1$
$3$	$2$
$4$	$2$
$5$	$3$
$6$	$3$
$7$	$4$
$8$	$4$

This sequence is A000720 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

16

The value of the prime-counting ($\pi$) function for $16$ is determined as follows.

The prime numbers less than $16$ are:

$2, 3, 5, 7, 11, 13$

Hence:

$\map \pi {16} = 6$

Sources

• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions: Example $2.1.1$