Port 4567: Sinatra / ISP management
Port 4567 is the default for Ruby's Sinatra web framework and is also used for ISP remote management on some routers.
What runs on port 4567
Sinatra development servers listen on TCP 4567 by default, and Galera database clusters use 4567 for replication. Some ISP-supplied routers, notably certain Verizon Fios models, have been seen with 4567 open on the WAN side for the provider's remote management.
On a home network
If you see 4567 open on your router from outside, it is most likely your ISP's management interface. Developers' machines running a Sinatra app will show it on the LAN.
If port 4567 is reachable from the internet
An ISP management port is usually restricted to the provider's own servers, but it is still a remotely reachable service on your router, and its safety depends on the ISP keeping firmware current. A development server on 4567 should not be exposed.
How to check whether it is open on your network
Scan your public address from outside to see if 4567 answers, and if it does and your router is ISP-supplied, ask the ISP what it is. RECON's Shodan lookup can show whether it has been indexed.
To find out whether port 4567 is open on something in your home, and whether the internet can reach it, the app scans your Wi-Fi from your phone and checks your public address from the outside. It says what it checked and what it could not. Get RECON for iPhone — one-time purchase, no account, nothing leaves the device.