In this work, the authors describe the confinement of singularities of the discrete Korteweg-de Vries (dKdV) equation in terms of the irreducibility and coprimeness of the terms. They are able to formulate the confinement of singularities for nonlinear partial difference equations in terms of algebraic and analytic relations between adjacent terms. This is possible since they use a combination of results, starting with the Laurent property, which essentially detect if a solution of a PDE with a given initial data can be expressed in terms of Laurent polynomials in this given initial condition. The other properties used in this work to approach the confinement of singularities are the irreducibility and coprimeness of the distinct terms. They prove that the coprimeness is the mathematical reinterpretation of the confinement of singularities for partial difference equations, and in particular for the dKdV in both bilinear and nonlinear forms. The main result of this work states that the distinct terms of the nonlinear dKdV equation do not have common factors other than monomials if they are separated by more than one cell. From this result, the authors are able to describe how the singularities are confined for the dKdV equation.