The design, manufacture and support of the primary mirror segments for the GMT build on the successful primary mirror systems of the MMT, Magellan and Large Binocular telescopes. The mirror segment and its support system are based on a proven design, and the experience gained in the existing telescopes has led to significant refinements that will provide even better performance in the GMT. The first 8.4 m segment has been cast at the Steward Observatory Mirror Lab, and optical processing is underway. Measurement of the off-axis surface is the greatest challenge in the manufacture of the segments. A set of tests that meets the requirements has been defined and the concepts have been developed in some detail. The most critical parts of the tests have been demonstrated in the measurement of a 1.7 m off-axis prototype. The principal optical test is a full-aperture, high-resolution null test in which a hybrid reflective- diffractive null corrector compensates for the 14 mm aspheric departure of the off-axis segment. The mirror support uses the same synthetic floatation principle as the MMT, Magellan, and LBT mirrors. Refinements for GMT include 3-axis actuators to accommodate the varying orientations of segments in the telescope.