Prime Minister Ariel Sharon likes to quote a theory developed by his close friend, attorney Dov Weissglas, that had the Jews not been expelled by the Romans and suffered nearly 2,000 years of persecution, there would be between 500-800 million Jews living in the world today.

Prof. Sergio Della Pergola of Hebrew University, among the most prominent experts on Jewish demography, calls this estimate "back of an envelope arithmetic," but admits that he too indulges in this occasionally.

Della Pergola himself estimates that given the ideal hypothetical scenario, without anti-Semitism, persecution, and assimilation, there would be no more than 100-120 million Jews in the world today. This estimate is based on the assessment that at its height, on the eve of the great Jewish revolt against the Romans, the Jewish population totaled 2 percent of the ancient world's population.

"On the one hand, there's no doubt that expulsions, persecution and destruction have led to the number of Jews today being far lower than the growth potential," Della Pergola says. "On the other hand, you need to remember that a great many lovely peoples like the Jews disappeared completely over the course of history, so that the Jews need not feel disadvantaged."

The Jewish Agency's education department recently published a new study program that tries to provide answers to various questions concerning Jewish demography. The pamphlet contains estimates of the number of Jews who lived in the world during various historic periods, from the era of the Patriarchs to the present.

For example, the program determines that at the high point of Solomon's kingdom, around 1000 B.C.E., some two million Jews lived in the Land of Israel. On the eve of the destruction of the Second Temple, the number of Jews reached a peak of about 4.5 million - a record broken only in the 19th century. During the Middle Ages, the global Jewish population remained stable, at around one million. The all-time high, 16.5 million Jews, was recorded right before the Holocaust. In recent decades, the number of Jews has remained steady at around 13 million, with the demographic growth in Israel offset by the ongoing decrease in the number of Diaspora Jews.

Della Pergola, the program's scientific consultant, repeatedly emphasizes that the estimates for the ancient and Medieval periods are not scientifically substantiated and are merely intended to illustrate demographic trends in the Jewish people.

He collected the numeric data from known written sources, the credibility of which is in some cases in doubt, to say the least. One striking case concerns the 13th century B.C.E., for which the estimate of 600,000 refers to the biblical figure related in the account of the Exodus from Egypt, which many scholars say never took place. Della Pergola says that setting aside the question of its historic truth, the biblical text contains an internal statistical logic.

"The bible speaks of 70 men who went down to Egypt with Jacob and of 600,000 men who left it 430 years later," he says. "That estimate is certainly possible demographically, if you take as a given that the average life span was 40 years and the number of children per household was six."

A relatively large number of estimates have been published on the size of the Jewish population in the first century, in the period before the destruction of the second Temple. These estimates are based on written sources such as Flavius Josephus and Roman populace commanders.

Columbia University's Prof. Salo Baron, considered among the most important researchers of Judaism in that period, estimated the number of Jews in the world at that time at 8 million. More cautious researchers like Israel's Dr. Magen Broshi put it closer to 2 million.

Della Pergola averaged the various estimates to reach his estimate of 4.5 million. His main source for the Middle Ages was the diary of Binyamin of Tudela, who traveled throughout Europe and the Middle East in 1170.

"Tudela's estimates are fairly credible regarding the places he himself visited," Della Pergola says. "But when he relies on other sources, his estimates sound pretty implausible."

The demographic trends described by the program are less controversial than the numeric data. One of the intersting phenomena touched on is that the spread of Jews in the Middle Ages largely overlapped with the Arab conquests: From present-day Iraq and the Arabian Peninsula, the Jewish core moved to North Africa and Spain. Another direction for expansion was from the south of France northward into Germany and central Europe - the region that became known as Ashkenaz.

Another remarkable phenomena was the rise of Eastern Europe as the largest Jewish center from the 16th-20th centuries. In Tudela's time, there were very few Jews living in Eastern Europe. Della Pergola says Tudela himself notes the scant Jewish presence and observes that it was cold there. The Jews who reached Eastern Europe from Ashkenaz and from the Black Sea and the Balkans multiplied at an astonishing rate, mostly thanks to natural growth. Within a few centuries, Eastern Europe was home to two-thirds of all Jews.

Looking ahead to the future, Della Pergola sees Israel continuing to become the largest Jewish population center, replacing the United States. The most recent survey of U.S. Jewry, for 2000-2001, indicated a decrease of about half a million in the number of Jews, from 5.7 million to 5.25 million, as a result of low fertility rates and an intermarriage rate of nearly 50 percent.

However, Della Pergola says the U.S. figure rises to almost 9 million if you include all members of a household in which there is at least one Jew.

"Even that expansionist estimate is minimalist compared to the number of those living in the United States who are entitled to immigrate to Israel under the Law of Return. This number apparently exceeds 10 million," he says.