That should take seconds, not minutes.

#!/usr/bin/perl
use strict;
my $t0 = time;
my @f = map{ sprintf 'product_%04d',$_ } 1..2083;
my $count = 0;
open OUT,'>','pairs.txt' or die "$!";
while (my $x = shift @f){
  for my $y (@f){
    ++$count;
    print OUT "$count\t$x\t$y\n";
  }
}
close OUT;
my $dur = time-$t0;
print "$count in $dur s\n"; # 19s on raspberryPI
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