Sannin isn't what the description in the users/groups area says it is.
Sannin was a title given to Jiraiya, Tsunade, and Orochimaru for surviving a huge battle in amegakure. It has nothing to do with being trained by a hokage, and when they were trained, it was by a former hokage, since the 4th was ruling at that time. Sannin simply means legendary three ninja, and was actually given when the three were chuunin, not jounin anyways.
Sannin was a title given to Jiraiya, Tsunade, and Orochimaru for surviving a huge battle in amegakure. It has nothing to do with being trained by a hokage, and when they were trained, it was by a former hokage, since the 4th was ruling at that time. Sannin simply means legendary three ninja, and was actually given when the three were chuunin, not jounin anyways.