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Although the standard Λ+cold dark matter (ΛCDM) model is well tested on large scales, the primordial power spectrum may deviate from the ΛCDM spectrum on small scales due to specific dark matter properties or alternative inflationary models. These deviations affect the formation of dark matter structure, which subsequently leads to different observable properties of galaxies. In this work, we study the impact of a blue and red tilted power spectrum on the central density of dwarf galaxies. To do this, we model densities of dwarf galaxies using a combination of high-resolution numerical simulations and galaxy formation model. The model galaxies in ΛCDM are consistent with observations of 41 faint dwarf satellite galaxies of the Milky Way. The deviations from the ΛCDM power spectrum are constrained by the central matter densities of dwarf galaxies, which set stringent constraints on the possible small-scale tilt of the primordial power spectrum, improving on the current limits. Moreover, similar analysis can be applied to test any feature in the power spectrum at small scales between k∼10–100 Mpc-1.