Sieve Of Eratosthenes is a computer algorithm to find out prime numbers upto a specified integer starting from 2.
The time complexity of a unfaithful sieve is Θ(n2/(log n)2) ( regardless of what wikipedia might say )

I tried the program in PhP ( for all the php enthusiast ). There is a cool animation ( I found ) for proper understanding:

Sieve of Eratosthenes in PHP

/**
* Nishchay Shah                    August 10 2008
*
* Program: To find prime numbers
* Algorithm: Sieve of Eratosthenes
*
* Memory And Time Cost:
*        09552  bytes for 20 numbers        ( 250 to 380 usec )
*        49920 bytes for 100 numbers        ( 1600 to 2500 usec )
*        114.1 K bytes for 500 numbers    ( 230 to 350 msec )
*
*
*/
echo"
<pre>;"; // for browser output
$max = 10;   // find prime numbers till this value. [ Change it for the higher limit. Please dont go crazy.]

/// Populate the scan array
for($i=2;$i&lt;$max;$i++){
$scan[]= $i;
}
/// Call the function
primeNumber($scan);

/// Function to find prime numbers
function primeNumber($scan){
$tempFound = array(); // declare array,save memory
global $primeNumbers;
$number = current($scan); // current data pointer

foreach($scan as $remainingNumber) {
if(!fmod($remainingNumber,$number)){
$tempFound[] = $remainingNumber; //make list of multiples
} // end of if mod = 0
} // end foreach

$scan = array_diff($scan, $tempFound);     // remove the multiples from the list
$primeNumbers[] =  current($scan);
if(count($scan) !=1){
primeNumber($scan);
} // end if count is not 1
else{
return;
}
} // end of function primeNumber

/// Add 2 in the beginning ..
$primeNumbers = array_pad($primeNumbers, -(count($primeNumbers)+2), 0);
$primeNumbers= array(2) + $primeNumbers;
/// Output
print_r($primeNumbers);</pre>