Solution to Project Euler Problem 3 - Finding prime numbers till trillion and largest prime factors for a large number (over 6 billion)

http://projecteuler.net/problem=3

I wrote the most processing power consuming script of my life. It's running from last 7 hours, till not completed !!! 

What you will know in this script? 

A optimized (to best of my knowledge) perl function to generate prime numbers.
Perl module to find square root.

How to find prime factors for a given number.

How to screw up your CPU :)

Question:

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

Solution:

#!/usr/bin/perl -w
use strict;
use Math::Complex;
my (@primes,$ulimit);
$ulimit=600851475143;
generate_prime();
prime_factors($ulimit);


sub prime_factors {
        my ($num)=@_;
        my (@prime_factors,@sorted);
        print "Prime factors of $num are \n";
        foreach(@primes) {
                if ( $_ > $num ) {
                        last;
                } else {
                        if ( ($num%$_) == 0 ) {
                                push(@prime_factors,$_);
                        }
                }
        }
        @sorted = sort { $a <=> $b } @prime_factors;
        print "@sorted \n";
        print "The largest prime factor of $num is: $sorted[$#sorted] \n";
}


sub generate_prime {
        my ($i,$j,$prime,$squareroot);
        @primes=(2,3,5,7);  # Initializing known prime numbers
        #We know only 2 is the even prime numbers, hence skip all even numbers
        for ($i=9;$i<=$ulimit; $i+=2) {
                $prime=0;
                #Divide the number by all the prime numbers less than the square root
                $squareroot=sqrt($i);
                foreach $j (@primes) {
                        if ( $j > $squareroot ) {
                                last;
                        }
                        print "$i: $i%$j\n";
                        if (($i%$j) == 0) {
                                $prime=1;
                                last;
                        }
                }
                if ($prime == 0 ) {
                        print "$i \n";
                        push(@primes,$i);
                }
        }
        print "@primes \n";
        open (FH, ">prime-numbers.txt") || die "Cant create prime-numbers.txt $!";
        print FH "@primes\n";
        my $len=@primes;
        print "Total number of prime numbers from 1 to $ulimit= $len \n";
}