I would approach the problem of programming this as follows: (I understand you have your random number generator already written from previous posting?)

1. Start by using warning and strict
2. Look up the perl data stucture called a 'array of arrays' (LoL) perldsc
3. Crate your LoL  my @lori (lori acronym for lists of random integer)
4. Populate the array items in each array in the LoL using your random integer generator

   (probably use something like

    for $i ( 1 .. 1000) {
        $AoA[$i] = [ somefunc($i) ];
    }
   [download]

   taken from ARRAYS OF ARRAYS

5. Create a scalar to hold the results of your analysis(where you apply your gcd(x, y) = 1) my $result=0;
6. Examine each pair of random integers in the LoL for meeting the gcd(x, y) = 1 criteria and increment $result when true

    foreach my @pair (@lori) {
        if( my_gcd_func(@pair) = 2) {
              $result++;
        };
   }
   [download]

7. Check that value in $result against the 6/(Pi^2) .

   if( $result = 6/(3.1415926 * 3.141596) ) {
         do whatever you need to do to meet assignment requirements
   }
   [download]

The code shown here is not tested, and there are parts which are obviously missing, but those will become obvious as you work your way through the above sequence I think. Perldocs are your friend in this endeavor I think. The basic foreach loop and if statement covered in perldoc along with the other noted perl docs above should give you a place to start.

It seems to me that your main issue is that you're new to programming and sitting fine in your understanding of the theory. I have zero understanding of the theory which is probably reflected in the way I approached it above, but that is not really important to you right now. So I hope that the basic breakdown above gets you started in the direction that you want to go on the programming end. Best of luck to you on that assignment.