PHPで素数の和を求めるプログラム

PHPで素数の和を求めるプログラムを作ってみました。

$max = 100;

for ($i = 1; $i <= $max; $i++) {
    for ($j = 1,$count = 0; $j <= $i; $j++) {
        if ($i % $j === 0) {
            $count += 1;
        }
    }
    if ($count === 2) {
        $primeNumbers[] = $i;
    }
}

$total = 0;

foreach ($primeNumbers as $value) {
    $total += $value;
}

print_r($primeNumbers);
echo $max, 'までの素数の合計：', $total;

Array
(
    [0] => 2
    [1] => 3
    [2] => 5
    [3] => 7
    [4] => 11
    [5] => 13
    [6] => 17
    [7] => 19
    [8] => 23
    [9] => 29
    [10] => 31
    [11] => 37
    [12] => 41
    [13] => 43
    [14] => 47
    [15] => 53
    [16] => 59
    [17] => 61
    [18] => 67
    [19] => 71
    [20] => 73
    [21] => 79
    [22] => 83
    [23] => 89
    [24] => 97
)
100までの素数の合計：1060

没案（見苦しい）

$max = 100;
$primeNumbers = array(2);

for ($i = 2; $i <= $max; $i++) {
	for($j = 2; $j < $i; $j++) {
		if($i % $j === 0) {
			break;
		}
		if($i === $j + 1){
			$primeNumbers[] = $i;
		}
	}
}

$total = 0;

foreach ($primeNumbers as $value) {
	$total += $value;
}

print_r($primeNumbers);
echo $max, 'までの素数の合計：', $total;

Array
(
    [0] => 2
    [1] => 3
    [2] => 5
    [3] => 7
    [4] => 11
    [5] => 13
    [6] => 17
    [7] => 19
    [8] => 23
    [9] => 29
    [10] => 31
    [11] => 37
    [12] => 41
    [13] => 43
    [14] => 47
    [15] => 53
    [16] => 59
    [17] => 61
    [18] => 67
    [19] => 71
    [20] => 73
    [21] => 79
    [22] => 83
    [23] => 89
    [24] => 97
)
100までの素数の合計：1060