Prefabricated module for a pitched roof element and pitched roof element for a building roof

A prefabricated module for a pitched roof element comprising a frame made of at least two first beams being arranged in a distance to each other and running parallel to each other and two second beams running perpendicular to the first beams and being connected to ends of the first beams forming a compartment into which a first layer of an insulation made of mineral fibers and a binding agent is inserted and comprising a second layer of the insulation being arranged above the first layer of the insulation, covering the frame and being fixed at least to the first and/or the second beams, whereby the second layer of the insulation has a higher bulk density than the first layer of the insulation and whereby the first beams have a length being at least equal to an extension of a roof between a ridge purlin and an inferior purlin, wherein the second layer of the insulation is a dual density board made of mineral fibers and a binding agent, the dual density board having two layers of different bulk densities, wherein the layer with the lower bulk density is oriented to the first layer of the insulation and to upper narrow surfaces of the first and the second beams.