Purpose: Proton minibeam radiotherapy using submillimeter beam dimensions allows to enhance tissue sparing in the entrance channel by spatial fractionation additionally to advantageous proton depth dose distribution. In the entrance channel, spatial fractionation leads to reduced side effects compared to conventional proton therapy. The submillimeter sized beams widen with depth due to small angle scattering and enable therefore, in contrary to x-ray microbeam radiation therapy (MRT), the homogeneous irradiation of a tumor. Proton minibeams can either be applied as planar minibeams or pencil shaped with an additional possibility to vary between a quadratic and a hexagonal arrangement for pencil minibeams. The purpose of this work is to deduce interbeam distances to achieve a homogeneous dose distribution for different tumor depths and tumor thicknesses. Furthermore, we aim for a better understanding of the sparing effect on the basis of surviving cells calculated by the linear-quadratic model. Methods: Two-dimensional dose distributions are calculated for proton minibeams of different shapes and arrangements. For a tumor in 10-15 cm depth, treatment plans are calculated with initial beam size of σ₀ = 0.2 mm in a water phantom. Proton minibeam depth dose distributions are finally converted into cell survival using a linear-quadratic model. Results: Inter proton beam distances are maximized under the constraint of dose homogeneity in the tumor for tumor depths ranging from 4 to 15 cm and thickness ranging from 0.5 to 10 cm. Cell survival calculations for a 5 cm thick tumor covered by 10 cm healthy tissue show less cell death by up to 85%, especially in the superficial layers, while keeping the cell death in the tumor as in conventional therapy. In the entrance channel, the pencil minibeams result in higher cell survival in comparison to the planar minibeams while all proton minibeam irradiations show higher cell survival than conventional broadbeam irradiation. Conclusion: The deduced constraints for interbeam distances simplify treatment planning for proton minibeam radiotherapy applications in future studies. The cell survival results indicate that proton minibeam radiotherapy reduces side effects but keeps tumor control as in conventional proton therapy. It makes proton minibeam, especially pencil minibeam radiotherapy a potentially attractive new approach for radiation therapy.