[en] Explicit sets of spinor nth derivatives of the Riemann curvature spinor for a general spacetime are specified for each n so that they contain the minimal number of components enabling all derivatives of order m to be expressed algebraically in terms of these sets for n <=m. The minimal sets are defined recursively in a manner convenient for use in the procedures for resolving the 'equivalence problem' of the local isometry of two given spacetimes. The actual numbers of quantities to be calculated are given and the reductions in these arising in special cases such as vacuum and conformally flat spacetimes, and spacetimes with vanishing Bach tensor, are discussed. Finally, the possible relevance of the present results to analytic and numerical methods of solving the Einstein equations are commented on. (author)