Mar Rav Ivumai Gaon bar Sherira [(brother of his father Mar Avraham Gaon, Rash"b)] was head of the yeshiva in Pumbedita in year 4569 for 6 years. And in his days they stood in Sura for three years without a Gaon from year 4572 until year 4575 [(Tzemach David). In Shada"k page 36, after Rav Yosef bar Shila was Rav Mordechai HaKohen (see above year 4560), and after him Rav Achuna'i who died in year 4580, and he was a great and perfect pious man, and Elijah was in his yeshiva.
After him was Rav Avraham. His intention is Rav Avumai because Yuchsin does not mention Rav Achuna'i, but he erred when he wrote Elijah was in his yeshiva - in my opinion it refers to Rav Yosef as I will write below nearby. Rash"b Yuchsin wrote:] And his father's brother was Mar Aharon [(see above year 4687)] Kamui who was the father of the house, and he was more learned and superior than him.
Nevertheless, through a dream they told him about Mar Yosef Gaon, who was a good pious man and an elder of one hundred, and Elijah the Prophet would sit in his yeshiva during the days of Hillul [(see Me'or Einayim chapter 27: Rav Yosef Gaon, a complete righteous man, and Elijah would always be in his yeshiva)]. And Avi Gaon was his scribe and stood for all the needs of the yeshiva before him all his days.
On the day he departed there was great anger and the earth shook, and he was troubled - a good soul on learning was writing. And Mar Rav Shenui, a great Rabbi Gaon, blessed him and said: May you merit that your nation be praised, and you shall rule for twelve years. And afterwards came Mar Rav Avraham bar Rav Sherira in year 4679 and ruled for 12 years [(see above year 4575)], and Mar Rav Yosef was the father of the house, and in the dispute that was Daniel's he was the Exilarch.
They called Mar Rav Yosef Gaon, and in the end they were appeased with Mar Rav Avraham and they said: Let both Mar Rav Yosef and Mar Rav Avraham be called Geonim.
Nevertheless, when his father's brother died, they settled that Mar Rav Avraham and Mar Rav Yosef sit before him, etc. Rav Yosef departed from being Gaon and returned to being the father of the house and Mar Rav Avraham blessed him. After Mar Avraham, Mar Rav Yosef ruled in year 4577 for 6 years. And afterwards Mar Rav Yitzchak bar Mar Rav Chananin in year 1140 of the Seleucid era [(see above year 4586)], and his brother is the great Mar Rav Yosef bar Rav Mordechai who was the Rabbi in the days of Rav Yosef bar Mar Chiya, and he was the grandson of Mar Rav Ava Gaon [(see above year 4629)], his grandfather.
And Mar Rav Yitzchak was older than him. And thus Semikha's son Huna the Exilarch supported Mar Rav Yitzchak, the elder. Mar Yosef was the judge, and they asked Rav Yitzchak Luti'a and he said: This judge should not be difficult for you. They were like Rabba and Rav Yosef.
And he said: You are guaranteed that you will be and merit Torah. And Rav Yosef agreed and accepted, and they made him before him head of the yeshiva. He ruled for six years. And afterwards Mar Rav Yosef the above for three years in year 1120, end quote. [This is year 4698 (see above year 4697)].