I seem to have $Config{randbits} = 48 and  $Config{longsize} = 4. But using $seed = int(rand(2**$Config{randbits} - 1)); produced very poor results. Even when the seed was different, I would get the same series random numbers using my $pick = int(rand(1e9))+1;

In any case, it's not important because I am now using Math::Random::MT, and its srand() function takes unsigned 32-bit integers. Thus I have to produce my seed between 0 and 2**32-1.

It worked quite well, but I noticed that I would get the same seed when my program was called several times in a short time frame. So I had to seed the PRNG with a fast-moving seed first before I could produce my actual random seed.

use Math::Random::MT qw(srand rand); I'm quite happy now with the result. I appreciate your advices GrandFather. The final code looks like this:

use Math::Random::MT qw(srand rand);
sub seed_prng {
  # Seed the pseudo random number generator with a random or specified
+ seed
  # Returns what seed value is used
  my ($seed) = shift;
  if (not defined $seed) {
    # Want to produce an random unsigned 32-bit integer to feed to
    # Math::Random::MT::srand(). That means, first seed srand() with a
+ temporary
    # seed that varies quickly in time so we don't get twice the same 
+seed if we
    # request several seeds in a short interval of time.
    my $tmp_seed = time ^ ($$ + ($$ << 15)); # shown in srand's doc
    srand($tmp_seed);
    my $max = int(2**32-1); # Largest unsigned 32-bit integer
    $seed = int(rand($max+1)); # An integer between 0 and $max
  }
  srand($seed);
  return $seed;
}
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