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$num = 12345;
$dir = "/some/dir/";
...
$num++ while -e "$dir/$num";

open(F, ">$dir/$num") or die ...

use Fcntl;
use FileHandle;
...
$num++ while !sysopen(F, "$dir/$num", O_EXCL|O_CREAT, 0777) && $! eq "
+File exists";

die "$dir/$num: $!" if $!;