#!/usr/local/bin/perl 

use strict; 
use warnings;

use Tk; 

my $NumOfPrimes = 0;
my ($colr, $counter);
my($o, $s) = (250, 20); 
my($pi, $x, $y) = (3.1415926, 0, 0);
print "type the maximum number for the prime spiral \n";
my $lastnumber = <>;
print "please wait \n"; 
my $mw = MainWindow->new; 
my $c = $mw->Canvas(-width => 500, -height => 500); 
$c->pack; 
$c->createLine(50, 250, 450, 250); 
$c->createText(10, 250, -fill => 'blue', -text => 'X'); 
$c->createLine(250, 50, 250, 450); 
$c->createText(250, 10, -fill => 'blue', -text => 'Y'); 

my $num      = 0;
my $order    = 0;
my $pnts     = 0;
my $pntcycle = 0;
OUTER: 
    for (my $i= 1; $i <= 250; $i += 1) {
        $order=$order+1;
        if ($order == 5) {$order = 1;}
        ++$pntcycle;
        if ($pntcycle == 3) {
            $pntcycle = 1;
            ++$pnts;
        }
        $counter = 0;
        while ($counter <= $pnts) {
            $counter++;
            ++$num;     # This is the more common way to increment a number
            if ($num == $lastnumber + 1) { last OUTER }

            my $b = is_prime($num);
            if ($b != 0) {$colr = "white"; $NumOfPrimes = $NumOfPrimes + 1;}
            if ($b == 0) {$colr = "black";}

            if ($order == 1) {$x = $x + 1;}
            elsif ($order == 2) {$y = $y - 1;}
            elsif ($order == 3) {$x = $x - 1; }
            elsif ($order == 4) {$y = $y + 1; }

            $c->createText( $x+$o, $y+$o, -fill => "$colr", -text => '.'); 
        } 
    }
MainLoop;

BEGIN {
    # Cache primes for future use, but using a *hash*, NOT an array!
    # Start with the value "2", which lets us avoid 
    my %primes = ( 2 => 1 );

    sub is_prime {
        my ($num) = @_;

        if (exists($primes{$num})) {
            return $primes{$num};
        }

        # Only need to calculate up to sqrt($num).
        # This is VERY important, especially with larger numbers.
        # If N is divisible by some factor $f, less than sqrt($N),
        # then it's also divisible by some other factor $k = $N/$f
        # which MUST be larger than sqrt($N), and vice versa.
        my $sqrt = int(sqrt($num));

        # Check for division by 2 (special-case)
        ($num % 2) or return 0;

        # We've tried 2 as a factor, so any other factors must be odd
        # (and prime, for that matter).
        for (my $j = 3; $j <= $sqrt; $j += 2) {
            if (0 == $num % $j) {
                # It's NOT a prime.
                return 0;
            }
        }
        # Cache the prime number and return '1'
        return $primes{$num} = 1;
    }
}