Beethoven - Five Piano Concerti, or Six??

The Five Piano Concerti of Beethoven are as well-known, perhaps, as any of the piano concerti ever written.
But he DID write another piano concerto, which is almost never heard. I remember hearing it only once, as a child; sadly, I cannot recall the performer's name.
After his violin concerto, which many consider the reigning concerto for that instrument, Beethoven did indeed write a piano version of the violin masterpiece, which, as I recall, is listed as Opus 61A.
Beethoven almost always envisioned the piano when he wrote; one of the reasons, perhaps, that resulted in the palpable difficulties encountered by the soloists in that first performance of his 9th symphony. Some of the singers complained to the composer that at times the singing was impossible, whereupon Beethoven, at times not too mildly, reminded the singer or singers that their voices were instruments, like all others.
The piano transcriptions by Liszt of the 9 symphonies of Beethoven demonstrate the innate 'pianism' in so much of Beethoven's music. As difficult as they are for the piano, they work wonderfully on the instrument, almost as if it were Beethoven himself who wrote these for the keyboard. I feel quite confident that Beethoven would have embraced Liszt's creations.
Some of you may disagree; however, it seems to me that the sublimity of Beethoven's conceptualization as regards the piano propels us into the process realized by what we now know about the piano and its veritably illimitable powers of dimension.