On Some Arguments Regarding the Number of Israelites During the Exodus and Their Relevance

Abstract

The traditionally accepted figure of 600,000 men departing Egypt during the Exodus is widely regarded as highly implausible by non-fundamentalist readers of the Torah. Biblical scholars have proposed alternative interpretations, beginning with W. M. Flinders Petrie, who argued in 1906 that the term elef, as used in passages enumerating potential soldiers leaving Egypt, should be understood not as “thousand” but rather as “a group.” This paper introduces two relatively underexplored considerations and examines their relevance for contemporary believers. First, a mathematical argument is presented that refines Petrie’s approach, providing further support for the improbability of a literal reading of these figures. Second, an additional calculation—based on the number of midwives mentioned in the Torah, also noted by Petrie—suggests that the population of Israelites may have been closer to 20,000. It should be emphasized that no argument of this kind can definitively establish any thesis regarding these numbers; rather, arguments can only render a given thesis more probable, depending on the assumptions employed to perform the calculations. Finally, the paper addresses the theological relevance of belief in the literal truth of the Exodus narrative. Drawing on the Buberian concept of saga and the approach of such thinkers as Louis Jacobs, it argues that, despite reinterpretations, it remains important for Jewish and other adherents to preserve belief in a kernel of historical truth within the Biblical narratives. At the same time, this residual core of literally true historical facts has been diminishing over time and remains subject to unpredictable further revision.

1. Presenting the Problem

In the Book of Numbers (1:46), the total number of males over twenty years of age—those “able to go forth to war” (1:20)—among those who left Egypt is given as 603,550. A slightly different figure from the second census, 601,730, appears in Numbers 26:51. These figures imply a total Israelite population well exceeding two million.

The striking improbability of such numbers, together with the absence of corroborating evidence in Egyptian sources, has led many biblical scholars who no longer accept the traditional view to adopt one of two positions. Some treat the Exodus narrative as fictional or at least regard the numerical data contained in the Torah as later projections or rhetorical “Eastern” exaggerations intended to magnify the significance of the event.

Others seek to reinterpret the figures. While accepting that some form of Exodus occurred, they argue that the numerical terminology in Numbers 1 and 26, as well as Exodus 12:37, has been misunderstood. This approach departs from the textual fundamentalism dominant in pre-modern interpretations—and still influential in some Orthodox Jewish and Christian circles—which treats the numbers as literally accurate and the traditional literal understanding of the Torah words as beyond doubt. At the same time, it is important to emphasize that reinterpretation allows for continued respect for the Biblical text while acknowledging the changes that the text must have undergone in the course of history. (The book Ganzel et al. 2019 is written in this spirit.)

The foundational reinterpretation was proposed by the Egyptologist Petrie (1906, 1911, pp. 42–45), who postulated that אֶלֶף (elef) occurring in the verses relating the numbers of (potential) soldiers going out of Egypt should be understood not as “thousand” but rather as “group.” Elef may refer to a clan, family, or military unit; if so, the standard reading of, say, the number of men who can be soldiers in the tribe of Reuven, that is, 46,500 (Numbers 1:21), would mean 46 troops or extended families (elef), or 500 men altogether. Applied to the remaining tribes—excluding the Levites, who are omitted from the military census and whose number raises a separate interpretive issue, alongside other numerical difficulties (see, e.g., Fouts 1997)—this reading yields 598 units and a total of 5500 men. Thus, the average would be 9 people to a unit, which seems entirely reasonable. It is also reasonable from the modern point of view, as this is roughly the number of people in an army squad. To explain why the number 603,550 appears in the Torah, it has been proposed that a later editor of the text understood all those mentions of elef as referring to a thousand, and so, adding 598,000 to 5500, obtained the figure 603,550. The numbers in chapter 26 can be treated in the same way: one obtains 596 squads numbering 5730 men rather than 601,730. Now, assuming that the number of male children, youth, and elderly was similar to that of potential soldiers over 20, and that the number of females was more or less equal to that of males, the total number of people taking part in Yetsi’at Mitsrayim would be approximately 20,000.

Petrie’s interpretation of the size of the Israelite group has been developed in a number of scholarly works, including Mendenhall (1958) and Humphreys (1998). Proponents of the reinterpretation cite such uses of elef as in Judges 6:15, where alpi (אלפי), or “my elef,” clearly means “my family” or “clan” (which, the verse says, is poor or humble in Manasseh). Some, like Clark (1955), read elef as “leader” or “captain” (alluf), and also derive relatively small numbers. Many authors have criticized this approach, either adhering to the literal, received reading, rejecting the very idea that the numbers in the Biblical text could have been adjusted, or arguing that other passages cannot be explained using Petrie-style interpretation. Notably, a recent sophisticated statistical analysis of the numbers given in the text, by Adair (2025), questions both the traditional rendering and the reinterpretations, and concludes that it is most probable that the numbers were fabricated.

The present paper does not summarize the ongoing discussion, which can be accessed readily, also via the internet, through scholarly papers such as those mentioned above or general overviews such as (Merrill et al. 2011; Bishop 2025; Katz 2015). Instead, two apparently little-known points are made below, followed by a discussion of the relevance of the issue for present-day believers. First, a mathematical argument supporting the improbability of the literal reading of the numbers in the Book of Numbers is presented (Section 2). It is somewhat more precise than that offered by Petrie. Second, and more importantly, a separate argument is presented in Section 3 to the effect that the number of Israelites may have been approximately 20,000. It is based on the number of midwives given in the Torah and was also mentioned by Petrie (1911, p. 45); the calculation is developed in slightly greater detail here. (The idea occurred to the present author during a study session in Warsaw with Rabbah Margalit Kordowicz.) It should be emphasized again that no argument proves any thesis about these numbers; considerations can only render a thesis more probable, given the assumptions necessary to perform the calculations. An attempt is made below to make those assumptions explicit. Third, a discussion is presented regarding the need to affirm the truth of the stories included in the Torah. In agreement with such authors as Jacobs (1964, [1957] 1965) and Buber (1947, 1968), and largely following Krajewski (2020), it is argued that it is important for Jews and other believers in the relevance of the Biblical account of history to retain a kernel of literal truth; however, this residual core has been shrinking and it is difficult to formulate specific statements that may be held as perpetually literally true.

2. The Traditional Number of Israelites Is Highly Improbable

The standard reading of the numbers given in the Book of Numbers presents figures that are rounded up or down to the nearest hundred, with each tribe numbering several tens of thousands and some additional hundreds. (Let us set aside the two exceptions that are not rounded to full hundreds: 650 in chapter 1 and 730 in chapter 26; difficult to interpret, they suggest a real source of data rather than an arbitrary textual construction.) It is striking that the hundreds values vary between 200 and 700, but never yield 000, 100, 800, or 900. Assuming that a count of several tens of thousands, when rounded, would be equally likely to end in any number of hundreds, one can calculate the probability of obtaining only six out of ten possible outcomes. For each of the two censuses, this probability is (0.6)¹², or approximately 0.002. If both censuses are taken together, the probability falls to approximately 0.000005.

This probability—half a percent of a per mille—is extremely slight. At the same time, it does not constitute proof that the actual numbers could not be exactly as traditionally presented; after all, any specific outcome is highly improbable. What lends even stronger support to the reinterpretation of the numbers given in the Torah is the fact that if one adopts a Petrie-style reading, according to which each tribe comprised several hundred potential soldiers, then the sizes of the (reinterpreted) numbers in the Torah make perfect sense. Zero was impossible, and one hundred was too few, since the tribes were not so small; while 800 or 900 were simply too many, since the tribes were not that large. Unsurprisingly, the most common values are 400 and 500, which is natural if a tribe comprises 1500 to 2000 people. (As mentioned above, we assume that the total number of people in a family is roughly four times the number of men over twenty who could serve as soldiers.)

Although similar calculations can be found in the literature, I have not encountered the one presented above. Katz (2015) mentions David Lerner, who provided a simpler version: the probability of obtaining a zero in the hundreds column never occurring in any of the 24 tribe totals is quite small. (It is 8%. Katz wrote mistakenly “1 in 200” because he apparently assumed that results between 900 and 1100 would round to 1000; in fact, only values between 950 and 1050 would.) I suspect that the calculation given here could easily have been made, or at least envisaged, by Petrie himself. However, the calculation presented in the next section appears to be absent from Biblical scholarship, even though it is simple enough to have been rediscovered independently on many occasions.

3. How Many Women Could Be Assisted by the Midwives?

According to the Torah (Exodus 1:15), two midwives, Shifra and Pua, served the Israelite community. Some commentators hold that they were not Jewish; others argue that they were; and in the midrash they are sometimes identified with Yocheved and Miriam. Whoever they were, our starting point is that there were only two of them. This would suggest that the Israelite population in Egypt was not very large. The tension with the received number prompted the interpretation that the two women were chief midwives overseeing many others. For example, Ibn Ezra states: “there can be no doubt that there were more than five hundred midwives. These two midwives were in charge of all the other midwives.” (Commentary to Ex 1:15, after Sefaria n.d.) The figure of 500 is given without apparent justification, presumably to indicate that a population of over two million would require a substantial midwifery infrastructure—even though no allusion to other midwives is made in the Torah. Taking the text at face value, and assuming that two midwives sufficed, we can attempt to estimate the number of women, and consequently the total Israelite population.

It is worth noting that girls and elderly women, who were before or past childbearing age, were probably roughly equinumerous with those of reproductive age. Assuming, as before, that the numbers of men and women were similar, we can conclude that the total population was approximately four times the number of women who needed midwifery assistance. This ratio happens to be roughly the same as that of men over 20 who could serve as soldiers—established above as approximately one quarter of the total Israelite population. It is therefore of interest to determine whether plausible assumptions yield a number of childbearing Israelite women close to the 5000 suggested in the previous sections.

It seems reasonable to assume that in the Biblical era women between the ages of 13 and 35 could give birth. This would mean that each woman could potentially be pregnant over a span of 23 years. We may assume that she could conceive 8 to 10 times, carry 8 pregnancies to term, and that only some of the infants and children would survive. These are, of course, average figures; individual variation must have been considerable, as it is today. Assuming further that only half of all deliveries required midwifery assistance, we can estimate that on average a woman would need one of the two midwives approximately four times in her lifetime. This is an estimate. We will examine the results of the calculation for other values of the parameter m = the average number of times a woman requires a midwife.

It seems reasonable to assume that a midwife attended one delivery per day. Travel was not easy—they presumably had to walk—and labor could be prolonged, so attending two locations in a single day would rarely have been feasible. Thus, even if the midwives worked every day, the two together could assist 730 women per year. Petrie, incidentally, assumed that “the two midwives were employed (probably one at Pithom and one at Raamses), at the rate of one birth a week…” (Petrie 1911, p. 45). His assumption would make the total population figures derived below, based on various possible values of m, seven times smaller.

We can further assume that roughly equal numbers of women enter and leave the childbearing age at any given time. Accordingly, the Israelite population remained more or less stable throughout the 23-year span during which a woman could become pregnant. Over this period, two midwives could assist in 730 × 23 = 16,790 deliveries. If the average woman requires assistance 4 times (m = 4), the number of women who might have needed assistance is 16,790 ÷ 4 ≈ 4200.

The figure of 4200 is not far from the 5000 suggested by the calculations in the previous sections. Note that if m = 3, the number of women between 13 and 35 would be 5600—almost exactly the 5550 or 5730 given in the (reinterpreted) Torah censuses. If m = 2, the number is 8400. If, on the other hand, m = 8, the number of women of childbearing age is only 2100, and the total Israelite population approximately 8400.

We can also consider the case in which an average woman requires assistance just once (m = 1), which would yield a total Israelite population of approximately 67,000; or the case in which only every second woman requires midwifery assistance and only once (m = 0.5), which would yield approximately 135,000. Either way, these are far below 2 or 3 million. The figure of 2.5 million can be reached only if we assume that a midwife was needed in exceptional cases—say, by one woman in forty (m = 0.025).

It emerges that under seemingly reasonable assumptions two midwives can serve a community of approximately 20,000 people. The figure varies between roughly 10,000 and 35,000, depending on the parameter m. This is strikingly consistent with the figures given in the Torah as interpreted according to Petrie’s proposal. (If, however, one adopts his suggestion that a midwife could assist one woman per week, the total would fall to between 2000 and 5000.) It must be emphasized once more that the above calculations offer no indisputable proof. Too many assumptions are involved that can be questioned—most notably the claim that there were only two midwives, and that an average woman required midwifery assistance at least once in her lifetime. Nevertheless, the argument lends meaningful support to the reading of elef as a squad or similar unit of approximately 10 people.

4. How Essential Is the Historical Accuracy of Biblical Accounts?

The speculative calculations presented in the previous sections assume the factual accuracy of the numerical data given in the Torah account (even if reinterpreted), and of the presence of precisely two midwives. More generally, the investigation rests on the assumption that the Torah account of the history of the Israelites is reliable to some degree. This assumption can be either (i) completely denied, as do historians who point to the absence of documentation of those events; (ii) treated as an accurate description, as do traditionalist believers; or (iii) subjected to a middle way, retaining only some basic elements as factual, as is done above. From the philosophy of religion perspective, the natural question is: What is the impact of these three options regarding the veracity of the Biblical historical account on religious commitment? Here, we limit the question to Jewish religious commitment, though a similar discussion could be conducted with respect to Christian and, to some extent, Muslim religiosity. Those two traditions face their own additional challenges, insofar as they must also determine how essential is the belief in the historical accuracy of detailed accounts of the lives of Jesus and Muhammad respectively.

From the traditional Jewish perspective, the literal interpretation of the Biblical narrative is rather natural. The image of the Exodus, including the image of 600,000 men leaving Egypt, is repeatedly recalled in the liturgy. This does not mean, however, that the fundamentalist approach is unavoidable even from a deeply Orthodox standpoint. A well-known example is the development of non-literal interpretation of Biblical anthropomorphisms; a metaphorical reading was championed by Maimonides and has been dominant among theologians since. Another example from the same thinker is even more directly relevant to the present discussion, as it concerns the historical accuracy of a Biblical narrative—namely, the story of Job. In the Guide for the Perplexed, Part 3, Chapter XXII, he wrote:

“[S]ome of our Sages clearly stated Job has never existed, and has never been created, and that he is a poetic fiction. Those who assume that he has existed, and that the book is historical, are unable to determine when and where Job lived. Some of our Sages say that he lived in the days of the Patriarchs; others hold that he was a contemporary of Moses; others place him in the days of David; and again others believe that he was one of those who returned from the Babylonian exile. This difference in opinion supports the assumption that he has never existed in reality.”

(Maimonides [c. 1190] 1904)

To be sure, Maimonides did not question the Exodus story. We may ask, however, whether his approach can be extended—perhaps in a modified form—to encompass the Exodus narrative. This is unproblematic for a detached scholar, but considerably less straightforward for a believer, since the Torah text is presented as a description of facts. Historical research, meanwhile, provides no support for literal reading. A useful summary of the problem can be found in a discussion initiated by Gellman (2012) within a group of religious Jews in the framework of the Association for the Philosophy of Judaism. According to Gellman, whose argument resembles the above-mentioned reasoning of Maimonides: “if the [Exodus] story did take place, we would have strong evidence in its favor. But none of the evidence that should exist does exist. Therefore, we have strong evidence against the truth of the story.” Gellman does not spell out why the Exodus, as described in the Torah, is archaeologically implausible. He could have cited Israel Finkelstein and Neil Silberman, historians who survey the archaeological evidence, and who maintain that the Exodus narrative reflects later monarchic or exilic concerns, especially those of the 7th century BCE. “The saga of Israel’s Exodus from Egypt is neither historical truth nor literary fiction. It is a powerful expression of memory and hope born in a world in the midst of change.” (Finkelstein and Silberman 2001, pp. 70–71) In response to Gellman’s statement, Dani Rabinowitz affirmed a traditionalist position: “Orthodox Judaism stands or falls on the historical accuracy of the Exodus Story.” In reply to this thesis, Sam Lebens argued that a faithful Jew is not obliged to adopt the fundamentalist position but may instead embrace the vision it expresses—the “conviction and trust that this narrative, and this way of viewing ourselves, is the best vehicle for perfecting ourselves and for coming closer to God Himself.” Therefore, if faith—“emunah”—is “in some or all instances, a relation to a vision rather than to a proposition, there is no immediate threat of irrationality or epistemic criminality.”

Emphasizing vision rather than propositions describing events offers a promising middle way, somewhere between literalism and its opposite—fictionalism, which treats the Bible as literature alone. Yet one must ask: what is a vision? And, more to the point, what is its relation to history?

It seems clear to many Jewish and other contemporary Biblical commentators that a path must be found between the Scylla of naïve literalism and the Charybdis of complete fictionalism. This idea can be expressed in the words of Louis Jacobs: “While Judaism stands or falls on the belief in revelation, there is no ‘official’ interpretation on the way in which God spoke to man.” (Jacobs [1957] 1965, p. 59) He also argues that “on the non-fundamentalist view faith should have no voice in matters that can be determined by the investigation of the facts.” (Jacobs [1957] 1965, pp. 466–67) This position makes the middle way possible. It also opens the door to a cultural approach to the Torah narratives. The term is associated with the work of Assmann ([1997] 2009), who argued that what truly matters is not history but cultural memory. For example, Moses is fundamentally a figure of memory rather than of history. Arguably, approaches in this vein had already been present in the works of such Jewish philosophers as Martin Buber and Franz Rosenzweig. For Buber (1947), the Exodus and above all the Sinaitic revelation is an encounter—an event preserved as a saga, that is, a legend that retains the memory of a genuine encounter even if the story has been shaped by communal tradition. For Rosenzweig, the Exodus story is the source of Israel’s covenantal life. However, the details of the Exodus seem not to have been of central importance to him, as they are barely mentioned in his theological-philosophical treatise (Rosenzweig [1921] 1985), in which revelation, paradigmatically defined by the Sinai experience, plays a central role.

The importance of narratives for religious communities seems beyond doubt. Yet the problem of historical accuracy remains, even if it is reduced to only parts of the story. While the cultural approach can be grounded in the rejection of the historical basis of the narrative—or, even more radically, in the rejection of the very need to seek such a basis—we may instead postulate the necessity of retaining that need. Following the proposal of Krajewski (2020), the kernel-of-history model is adopted here. The idea is that it is possible to preserve belief in a residual core of facts behind the Biblical narrative; to this kernel, literal truth applies. The remainder of the story is treated as fiction, or rather as metaphor—true relative to the narrative. At the same time, it is equally important to acknowledge that this core has been diminishing over time and remains subject to unpredictable further reduction as scientific research progresses. “The extent of literal truths about history seen in the Torah can change. Something must remain historically accurate, but what exactly is not predetermined.” (Krajewski 2020, p. 56) The kernel-of-truth model seems to express quite well the position of many non-fundamentalist Jewish thinkers. “These traditional tales may, of course, contain ‘kernels,’ to use a word fashionable last century, of historical veracity. In some cases they may even be used to reconstruct the real history of Israel, a real people in the Iron Age Levant. But that was not their main purpose.” (Brettler 2019, p. 232) This remark can be applied, for example, to Buber and Rosenzweig who can be seen as operating within this model: for Buber, a saga carries the spirit of the original experience; something happened that was experienced as a dialogical relation between God and Israel; for Rosenzweig, something happened that could serve as the source of revelation and the functional center of the universe defined by Creation, Revelation, and Redemption. Among more recent authors, Levenson (1993) is worth noting. He rejects as “unsound” the wholesale replacement of traditional interpretations with the historical-critical method. A completely fictional Exodus undermines Jewish covenantal theology. While the traditional narrative was expanded and shaped by later events, the tradition likely rests on historical experience.

5. The Kernel of History

To elaborate on the residual-core model, let us observe that it permits as much reduction in the literal truth of Biblical stories as scholarly progress requires. Scholars can of course be mistaken, but it is generally sounder to take established expert opinion into account than to ignore it. There is no way to predict future discoveries. It is therefore quite difficult to point to any specific fact that must be maintained forever. The boundary between what is literally true and what is true relative to the narrative is not fixed and cannot be precisely identified. We only assume that it exists, and that its contents are non-empty. Something from the Torah story remains factually and strictly true. But what exactly—that is not easy to say, and we should be aware that any specific proposal may prove mistaken. On the other hand, for those who identify with the Jewish tradition it is difficult not to form some picture of the facts that will never be overturned.

As an example of a literally true aspect of the Exodus story that will most probably remain unchallenged by future historical research, I would propose the following: at some point in the second millennium BCE, a group of ancient Hebrews was in Egypt and left it in a dramatic way, facing extreme dangers; something unprecedented happened during their journey that was later remembered as a divine revelation to the community and especially to their leader; and a sense of mission grew out of that experience. It is difficult to imagine discoveries that would contradict these statements. This is not to say that historians have confirmed them, only that they are compatible with established scholarly opinion.

To this broad picture of the core truth, one may add details presented in the Torah and not disproved by historical research. What exactly can be added is open to debate, and divergent opinions are inevitable in scholarly analysis. Yet, to return to the first sections of the present paper, it seems safe enough to include the picture of 600 families taking part in the Exodus. Somewhat more tentative, but also consistent with at least part of scholarly opinion, is the assumption of the presence of exactly two midwives serving that Hebrew community.

The concept of residual truth may appear minimalistic and may seem to force an abandonment of traditional belief. To quote a recent statement, “It is uncommon for religious exegesis to cast doubt on the historical veracity of the biblical text. Modern biblical scholarship, meanwhile, sees the text as literature based on a kernel of historical truth at the most.” (Raviv 2019, p. 534) However, the kernel-of-truth model, as presented in Krajewski (2020), involves a second step, following the first step of recognizing the fluid nature of the boundary between the residual literal truth and the metaphorical truth relative to the narrative. To be sure, the residue of factual truth has become much smaller for modern believers who have accepted the achievements of science than it was for pre-modern Jews (or Christians). Nevertheless, the second step remains available in our era: it consists in accepting the Biblical narrative in its entirety—together with its traditional ramifications—as the Jewish source of meaning. The story is accepted not as literally true, but as providing the foundation for the vision perpetuated by tradition, and in this sense as true in another register: internal, or metaphorical. Interestingly, this seems to accord with Maimonides’ statement about Job. Or, to quote Krajewski (2020, p. 57): “if we agree to use the term ‘myth’ in its noble sense, we can say, with Protestant theologian Paul Tillich, that by affirming a story in a non-naïve way we arrive at a ‘broken’ myth—understood as a myth, but not removed or replaced.” (Cf. Tillich 1957, p. 49) Applying this insight to the Exodus story, we can engage with the wealth of commentaries that remain within the mythic realm of the 600,000 men leaving Mitsrayim without actually believing in the accuracy of that number. In this way we can be both faithful and critical, expressing commitment and rationality together. The attitude of faith is focused on the message radiating from tradition and preserved through the Torah stories and their commentaries, while criticism grounded in historical research, concerning specific details, is accepted without hesitation. It seems to me that a version of this approach—perhaps in an implicit form—is very widely adopted by contemporary Jews.