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.
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category imprint: Source & stylistic information
issues: Foreign hand additions in manuscripts
notation: Pitch