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First-principles electronic structure methods are used to predict the piezoresistance of n-type Si1-xGex at various alloy compositions and strain configurations. We report very large gauge factors, G = dρ/dϵ/ρ, where ρ is resistivity and ϵ is strain: for compositions x ≃ 0.90 under uniaxial strain in the 〈111〉 direction, G >; 500. These gauge factors are over three times larger than the best values for single crystalline bulk Si. This large change in resistance due to strain is explained by the change in the occupancy of the higher-conductance L valley relative to the lower-conductance Δ valley, coupled to a change in inter-valley alloy and phonon scattering.