A sieve of Eratosthenes in PHP

sieve.php

<?php
    define( 'N', 10000 );

    // upper bound for our prime number
    $estimate = floor( N * log( N ) + N * log( log( N ) ) );
    $primes = array( 2, 3, 5, 7, 11, 13 );
    $primeCount = 6;
    $lastPrime = 13;
    for ( $i = 17; $primeCount <= N; $i += 2 ) {
        $prime = true;
        for ( $j = 0; $j < $primeCount; ++$j ) {
            if ( $primes[ $j ] * $primes[ $j ] > $i ) {
                break;
            }
            if ( $i % $primes[ $j ] == 0 ) {
                $prime = false;
                break;
            }
        }
        if ( $prime ) {
            if ( $i * $i <= $estimate ) {
                $primes[] = $i;
            }
            $lastPrime = $i;
            ++$primeCount;
        }
    }
    echo $lastPrime . "\n";
    echo "Used " . memory_get_peak_usage() . " bytes of memory.\n";
?>