The pillbox comprises a pill receptacle comprising a number of pill compartments and a cover sheet attached to the pill receptacle that has a number defined by borders above each pill compartment. Tearable tab tearing lines are provided on the sealing sheet to form tearable tabs, and each comprises main portion side segments that define a tearable tab main portion therebetween tongue portion side segments that define a tearable tab tongue portion therebetween, the tearable tab tongue portion linking the tearable tab main portion to one of the cell borders and a main portion end segment that links the main portion side segments to each other spacedly from the tongue portion. The tearable tabs can be torn away from the remainder of the sealing sheet to allow access to the pill compartments, the tearing of the tearable tab being initiated by either one of grasping the tearable tab tongue portion and peeling the tearable tab away along the tearable tab tongue portion side segments and the tearable tab main portion side segments and punching the tearable tab in by applying pressure on the tearable tab main portion, with the sealing sheet then tearing along at least one of the tearable tab main portion side segments and the tearable tab main portion end segment. When the tearable tab is punched in, the sealing sheet can alternately tear along a tearable tab intermediate segment in addition to or instead of at least one of the tearable tab main portion side segments and the tearable tab main portion end segment.