The SharePoint Central Administration Web Application port is a global setting to the server farm. When changing the port, ...

The SharePoint Central Administration Web Application port is a global setting to the server farm.  When changing the port, a SharePoint Timer service job will be dispatched to synchronize the port for all SharePoint Central Administration Web Applications in the server farm.  If a port is not specified, the port used for existing SharePoint Central Administration Web Applications in the server farm will be used.  If a SharePoint Central Administration Web Application has not been provisioned in the server farm, then the default port chosen will be random if a port is not specified.