Sinister variable caching problem with rand()

In one of my programs I started to receive database errors for not having a
unique id. I generate unique ids for each of the mysql lines that I add to
the database. I realized that the perl variable $idNum was keeping the same
random string for multiple executions.

I created a test program to demonstrate the principle of what is happening.

I have shown that the $count variable will function properly, I understand
why and expect $idNum to work the same way. However, when $idNum =
rand(99999999999) is used it misbehaves and starts to show the same numbers
after enough refreshes.

The code stores the random numbers in a file so I can detect them over
multiple sessions. Within the same session a random key has never been
generated twice.

Please help, I have been working on this for 2 days and it is killing my
progress at work.

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use strict;

my $idNum=0;
my $count=0;
for(1..10){
my %hash;
open(data,"<keys.txt");
while(<data>){
chomp;
$hash{$_}=$_;
}
close(data);

$idNum = rand(9999999999999);
$count++;
open(data2,">>keys.txt");
print data2 "$idNum\n";
close(data2);

if ($hash{$idNum}){ print "DUPLICATE - $idNum<br>\n";}else{ print "UNIQUE
$idNum<br>\n"; }

}

print "$count";