The hobbing machine of recent years has positively introduced a computer numerical control (CNC) system, but many traditional hobbing machines with gear trains are still being used to produce gears. These traditional machines generally prepare many indexing change gears for gear cutting. But when we cut the gear of a prime number of teeth, the indexing change gear is not prepared for more than about 100 teeth of the gear. In such a case, we have to correct the indexing of the number of teeth using a differential gear to cut a helical gear, but when we apply the prime number of teeth on the helical gear, we cannot choose an arbitrary feed speed. Therefore, in this paper, we report on a new indexing mechanism for the prime number of gear teeth using a double differential gear device, which reduces the number of indexes the change gear must go through.