American/German F-31

Does anyone know anything about the American/German F-31? I’ve never heard of this aircraft, it was mentioned on another forum that was discussing Technology demonstrators. Taking about the Su-47 Berkut a poster said Like the American/German F-31 it as built purposely for being a test bed only for the Russian Pak-Fa fighter and future fighters. Does anyone have any pictures on knowledge?
This got me thinking are there any other aircraft or technology demonstrator’s that were significant but were not built in any number’s? Most American fighters follow number’s in sequence but why is there a big jump from F-22 to F-35? F-23 would have been Northrop Grumman’s X-23 if it was built and F21 was the Israeli Kfir. I think it’s simply that they were not assigned. I still don’t get why they missed out all the designations when doing the F-35. Will the next US aircraft be called F-36 or F24?
I much prefer the UK way of doing it and giving the aircraft names. The US planes do often end up with names but the UK letters and number’s mean something and give an indication to what the aircraft does. Tornado F3 F=fighter 3=version. Tornado GR1=ground reconissance 1. Sea Harrier FRS1=Fighter reconnaissance strike 1. sea harrier FA-2= fighter attack version 2.
Any guesses on the F-35 lightening 2? Will the RAF stick with Lightening 2 and what will be after the name on the first versions? I’m going for FA1 or FRS1. Fighter attack 1 or fighter reconnaissance strike 1.
Actually will it have a recon ability?