Rav Yosef became head of the yeshiva in Pumbedita from year 4498 for 9 years until year 4507 [(Tzemach David). And in Yuchsin in the letter of Rash"b, after Rav Yehuda, Rav Yosef ruled in year 1050, which is year 4460 (and in Shada"k page 36b it says he died in year 4469), and after him ruled Rav Shmuel bar Rav Mar in year 1059, which is year 4507].