I've had this problem for a while. I would open the port on my router page but it wouldn't open. I got new internet recently and I still have this problem. On my old router, if I scanned my public ip with nmap it said 4444 was filtered. Now on my new internet it says all 1000 scanned ports are filtered.
Here's what it looks like:
It's a BT smart hub 6
EDIT: What I've learned is that naturally all my ports are closed but if I open up a program (that uses it I would think) it becomes open. For example canyouseeme says my port 80 is closed but if I run Skype it says its open. So basically I think I need to trigger this somehow?