The WPS number shouldn't be required. My Galaxy Note connects fine, it's just the SP3 that's having issues even though my TV is updated to version 2123 as of yesterday's update and the SP3 has all updates as well.
If you swipe in from right and click "Device" then "Project" then "Add a wireless device" you should see..."Searching for devices..." at which point the [Samsung TV] should appear in the list. It's at that point after clicking the name that the SP3 tries to connect to the TV (provided the TV is in Mirror Screen mode) but eventually times out. My Android tablet connects almost immediately as AllShare works just fine.
Now, if you click "Add a device" while on the Add Devices page then the TV may also show up in a list (maybe even twice) and asks for a WPS pin. I believe this is similar to trying to connect a device to your router via the WPS feature, but that's not what we are trying to do as you know. The WPS pin is something you would get from the router for easy setup.
So,there's some sort of disconnect between both devices - specifically the TV when trying to connect directly, as Microsoft's $60!!! wireless display adapter (Miracast) works just fine.