Note: there is a new update make it 650 times faster
A HUGE success from Mgccl the great
500*500 prime spiral can easily use more than 60 seconds with the previous code about spiral generation, but this one, only 12!
As a tradition, I have to introduce to you the "how" did I make it so fast so it produce the picture below:

1. Find all the primes with the PHP implementation of sieve of Eratosthenes
2. For each prime number, find where the a number locates1
3. Draw the point.

one and three are simple, 2 is HELL lot of work.
I first use some of my precious spear time2 on checking how to divide the spiral into pieces that I can operate on. Soon, I got it where all the perfect squares are going to locate, and the number's relationship to it.

So now I successfully divide the board into small half rings.
Then, I further break the half rings into two smaller pieces, one with the same x position, the other with the same y position. To find the difference, which is where the number lay related to the origin (0,0) point (where 1 is). I have to find each piece's point that lay on either x axis or y axis, so I can use simple add and subtraction to get the relative coordinates, which is the location we wanted

$size = 500;
$x_adj = ~ $size & 1;
$prime = esprime($size*$size+1);
$image = imagecreate($size,$size);
imagecolorallocate($image,255,255,255);
$color = imagecolorallocate($image,0,0,0);
$size2=$size/2;
 
$n = 2;$t = true;$sn=4;
 
$midu=2;$midl=4;$midd=6;$midr=8;
 
while($n<=$size){
	if($prime[0]<=$sn){
		$p = array_shift($prime);
		if($t){//even
			if($p <= $sn-$n){
				$x = $n/2;
				$y = $midu - $p;
			}else{
				$x = $midl -$p;
				$y = -$n/2;
			}
		}else{//odd
			if($p <= $sn-$n){
				$x = (-$n/2)+0.5;
				$y = $p - $midd;
			}else{
				$x = $p - $midr;
				$y = ($n/2)-0.5;
			}
		}
		imagesetpixel($image,$x+$size2-$x_adj,$y+$size2,$color);
	}else{
		++$n;
		$sn = $n * $n;
		$t = !$t;
		if($t){
			$midu = $sn-$n*1.5+1;
			$midl = $sn-$n*0.5+1;
 
		}else{
			$midd = $sn-$n*1.5+1.5;
			$midr = $sn-$n*0.5+0.5;
		}
	}
}
header("Content-type: image/png");
imagepng($image);

1. 1. This is the inverse of the Number Spiral algorithm from Steve Krenzel, where it find the number in a particular location.
2. 2. Every minute of my day...