The prosthesis part (1) has a conical protrusion (10) connected to another prosthesis part (3) having a complementary conical bore (30). The protrusion comprises a lateral recess for engagement of a securing element (40) i.e. headless screw, where the lateral recess is formed as a circulating recess or blind hole. The protrusion is provided with a removable cone attachment part, which includes a lateral recess (21) for engagement of the securing element. A symmetry axis of the cone attachment part coincides in an assembled state of the prosthesis part with axes of the protrusion. An independent claim is also included for a prosthesis comprising a securing element.