A method to numerically solve the Euler equations for fluids with general equations of state is presented. It is based on a formulation solving the conservation equations for either pressure primitive variables or entropy variables, instead of the commonly used conservation variables. We use a space-time discontinuous Galerkin finite-element discretization, which yields a highly local, potentially higher-order scheme. The algorithm is applied to test cases for compressible fluids to demonstrate its capabilities and the performance of the different variable sets.