Abstract: A vacuum pump includes first, second, third and fourth pump stages. Each pump stage has a trochoidal-shaped cavity and a rotor that rotates within the respective cavity. Each cavity has a volume determined by the depth of the cavity and a generally corresponding thickness of the rotor. The fourth stage has a largest volume and receives gas at an input pressure. The fourth stage outputs the gas to the third stage at a second pressure higher than the input pressure. The cavity of each successive stage (third, second and first) has a smaller volume and outputs the gas at a higher pressure than the previous stage. The last (first) stage outputs the gas to the atmosphere. The rotors in the stages rotate about a common pump shaft. Each rotor has a multiple vertices that follow the inner perimeter surface of the respective cavity without contact and without requiring additional seals.