Assuming the order of the occurrences doesn't matter, the easiest way would be to store the digits as keys in a hash. Keys are always unique. You could use any value as your hash-value;

$file = "project.txt";
open(FILE,"$file");
my %hash = ();
while(my $a=<FILE>) { 
    if($a=~/\tCM+(\d*)/io) { print "$1\n"; $hash{$1}=undef; }
} 
close FILE; 
open(OUTPUT,">> project.out");
while(my $key = each %hash) {
    print OUTPUT "$key\n";
}
close OUTPUT;
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Or how I would probably write it:

my %done=();
open INPUT, "<$inputfile";
open OUTPUT, ">>$outputfile";
while(<INPUT>) {
    next unless /\tCM+(\d+)/io;
    next if exists $done{$1};
    print OUTPUT, "$1\n";
    $done{$1}=undef;
)
close INPUT;
close OUTPUT;
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Haven't tested it, but it should work, and be fast... The <HANDLE> operator and regular expressions have the useful property that they both use the default variable ($_) if you supply none. This way you can bypass the use of $a.