In this paper we continue, from [2], the development of provably recursive analysis, that is, the study of real numbers defined by programs which can be proven to be correct in some fixed axiom system $\mathbf{S}$. In particular we develop the provable analogue of an effective operator on the set $\mathscr{C}$ of recursive real numbers, namely, a provably correct operator on the set $\mathscr{P}$ of provably recursive real numbers. In Theorems 1 and 2 we exhibit a provably correct operator on $\mathscr{P}$ which is discontinuous at 0; we thus disprove the analogue of the Ceitin-Moschovakis theorem of recursive analysis, which states that every effective operator on $\mathscr{C}$ is (effectively) continuous. Our final theorems show, however, that no provably correct operator on $\mathscr{P}$ can be proven (in $\mathbf{S}$) to be discontinuous.