By the 1st century, Babylonia, to which Jews migrated to after the Babylonian conquest as well as after the Bar Kokhba revolt in 135 CE, already held a speedily growing population of an estimated 1,000,000 Jews, which increased to an estimated 2 million  between the years 200 CE – 500 CE, both by natural growth and by immigration of more Jews from the Land of Israel, making up about 1/6 of the world Jewish population at that era. At times conversion has accounted for a part of Jewish population growth. Some have claimed that in the 1st century of the Christian era, for example, the population more than doubled, from four to 8–10 million within the confines of the Roman Empire, in good part as a result of a wave of conversion.
What was happening to the Jewish population in the 1st century?
speedily growing