There are multiple pieces I have played that have either Presto or Prestissimo as the tempo. Haydn and Mozart Prestos are generally easier for me because the tempo is slower, around 160-170 BPM, which I would normally consider to be Molto Allegro. But for example, Beethoven has some seriously fast Prestos. So do Chopin and a lot of other composers. These are just a few pieces that I either learned or am learning that are seriously fast Prestos or Prestissimo:
Song Without Words op. 102 no. 3, Mendelssohn
Solfeggio in C minor, CPE Bach
Grande Valse Brilliante, op. 18, Chopin
Presto Agitato of Moonlight Sonata, Beethoven
Bagatelle in C minor, Beethoven ->This piece in particular has a motif very similar to that in Beethoven's fifth symphony
And I find that as I am learning these pieces, going from Andante to Allegro is easy. But the speed up to Presto is hard. I could be playing the piece at Allegro for months and be no closer to Presto.
I find that instead of just playing the piece over and over for months, hoping that I reach a Presto tempo, that I instead play it at Allegro until it is in my muscle memory. Then, instead of thinking in terms of quarter note beats, I think in terms of eighth note beats. And I find that this helps me overcome that obstacle and reach a Presto tempo. And the sixteenths, if there are any, I think of them as being at trill speed.
But why is that? Why is it that when I think of a faster beat such as eighth notes, but play it with the same note speed as before, I can within a couple of weeks, reach a Presto tempo instead of being stuck at Allegro for months or years like I would if I was thinking in quarter note beats?