The most significant Jewish, Torah based population was in Bavel and/or Persia from 11 years before Churban Bayis Rishon (Hecharash v’hamasger) until roughly the time that Rabbeinu Gershom left and went to Europe. The greatest gedolim and biggest yeshivos were mostly (but not completely) in Bavel. Rabbeinu Gershom, upon moving to Europe about 50-100 years before the birth of Rashi, became the first Gadol Hador to live there. Rav Hai Gaon was probably the last of the Gedolei Hador to live and die in that area.