For the description of double hard interactions, double parton distributions (DPDs) are of major importance. We relate their Mellin Moments to the correlation functions of two local currents which we calculate on the lattice. We calculate all the Wick contractions for the first moment for the nucleon, considering both polarisation and flavor interference. We furthermore compare our results to the SU(6) quark model. Finally, we test whether DPDs can be factorized into a convolution of generalized parton distributions (GPDs).