Can any computer connect to a SSH server running on an android phone connected to a wireless mobile network? I run a ssh server on an Android phone using SimpleSSHD. 

When the phone is connected to a wifi network, I can connect to the SSH server from a computer in the same wifi network.

When  the phone is connected to a carrier's wireless mobile network, I found an IP address on the android phone in "Settings-> About Phone -> Status". How can I find out if the IP address is a public IP address for the phone's network interface, or shared by many devices in the same LAN? Can any computer connected to the Internet connect to the SSH server using the phone's IP address?
It seems that I can't, and I was wondering why?

$ ssh -p 2222 11.22.333.444
ssh: connect to host 11.22.333.444 port 2222: Connection timed out


Thanks.
For running a SSH server on a Smartphone connected via mobile data to the Internet you need a public IP address on the mobile network interface.

You can simple check if your IP is a public one: Enable mobile data and disable Wifi on your phone and check the IP address you have (Phone status in Android settings). If the IP address starts with 10.x.x.x or 192.168.x.x it is obviously a private IP address. If not open your web browser on the phone and go to https://www.whatismyip.com. Compare the IP address shown there with the one one in your phone settings. If they match your IP is a public one.

Unless you have a special mobile data plan, the majority of mobile network operators (MSO) will not assign your device a public IP address. Instead you are getting a private IP address that needs to pass a NAT gateway running in the MNO's network. The main reason for this situation is that the IPv4 addresses are rare - most MNOs don't have enough IPv4 addresses to assign every mobile device a public IPv4 address. 

Some MNO offer special data plans with a public IP address - usually only for business customers and with higher prices.

The whole situation is similar to a Smartphone connected to a Wifi in a network with a NAT router that is connected via DSL/cable to the Internet. But in difference the NAT router is not accessible so that nobody can open up ports (port forwarding) to make a service accessible running on a system in the network behind the NAT router.