The 
– added in FC most probably in pencil – lowering c
2 to c2 is a later addition of H. Scholtz. It should be emphasized that it is highly unlikely that Chopin could have overlooked that – such an oversight of an accidental defining the sound of a newly introduced key is absolutely uncommon in Chopin's music, let alone in the discussed place, since Chopin took care of precise notation by signalizing the return of g1 with a cautionary sharp, as it was g1 that was present in a few previous bars. Scholtz introduced the version with c2 – completely arbitrary – in the edition of the Preludes that he edited (Peters, Leipzig 1879); it was also popularized by certain later collective editions, e.g. edited by one of Chopin's pupils, Karol Mikuli (Kistner, Leipzig 1879) as well as by a few 20th-century urtexts (!). The reason could have been to avoid the cross-relation of c2 in b. 23 with c1 in b. 24; however, according to us, it is too weak an argument to interfere with the Chopinesque notation to such an extent. See also the note in the next bar.
Compare the passage in the sources»
category imprint: Source & stylistic information
issues: Foreign hand additions in manuscripts
notation: Pitch