B737 pilot reported during a test flight while conducting a functionality test of the positive pressure relief valves; they received a cabin altitude warning light and horn. Flight crew descended and regained normal pressurization.

Narrative

The flight was a Functional Check post heavy maintenance test flight. Using the Company Flight Test manual for the 737NG aircraft; I was conducting test that tests functionality of the positive pressure relief valves. The test calls for setting the Pressurization Mode Select switch in MANUAL and manually closing the outflow valve until achieving a 1500 feet per minute (FPM) cabin descent rate. This drives up the Delta-P (Differential Pressure) toward the limit of 9.1 PSI pressure differential. As the maximum Delta-P is neared; indication of the first outflow valve relieving cabin pressure is a decrease in the cabin descent rate to approximately 1000 FPM. Observing this; the procedure calls for closing the outflow valve a little bit more to keep the descent rate at approximately 1000 FPM. Indication of the second pressure relief valve opening is when the cabin rate begins decreasing again to a positive (slight climb) indication; indicating that the cabin altitude is increasing and the Delta-P is decreasing. During the test; just after indication of the first valve opening; I was just starting to manually control the valve toward closed to keep the descent rate going while watching for indication that the second valve opened. Suddenly the cabin altimeter rapidly rotated clockwise; and pegged full scale at over a 4000 FPM climb rate and the Delta-P quickly decreased to zero. The cabin altitude rapidly rose to 25000 ft and the cabin altitude warning light and horn came on. Masks in the cabin also dropped.Both pilots quickly donned our oxygen masks; established crew and ATC communication and executed an emergency descent. I [requested priority handling] with ATC. Upon reaching 9000 ft MSL; the cabin altitude was now below 10000 ft; so we removed our masks and recovered at ZZZ via normal procedures.