Question about the number of Egyptians

What about the population growth, if each generation is twenty years, then after ten generations, isn't it so difficult to accept such a number of people?
And so a situation was created in which, dating back to the time of the Exodus, the population of the Exodus was almost a tenth of the total world population, which numbered about 50 million people.
And even at the time of the Exodus, it is not necessary that the power that was then in Egypt would be broken, it is not mandatory.
All in all, it sounds reasonable in my opinion. What is the rabbi's opinion on this?

Regarding the culture of the Jewish people, the calculation does not seem so reasonable. There is an article in the journal Hagion (I think by Eliyahu Beller) that calculates according to various models. The subject has already been discussed here on the site, and possibilities have been raised that these are typological numbers (although the Torah gives numbers that seem accurate). Search here on the site.

I searched the site and the only thing I really had difficulty with was the number of firstborns
But can it be answered that in most families the women and the elderly were born before the men who had left the army and thus they are not firstborns except for those 22 thousand firstborns in the Torah verses?
Assuming that there is no difficulty then the issue of accelerated natural reproduction is not difficult either, which in total if we claim that the population was 2.5 million then in ten generations each family should have given birth to 5.7 children on average.
What does the rabbi think, is this possible?

After all, we are talking about one son from each family, so all the potential firstborns could be in the region of 100,000 people, together with the women and the old men and old women (who are potential firstborns). Let's say there are 280,000 people in total, including the men, so the chances of firstborns are less for the men.

It seems like science fiction. Consider life expectancy, infant mortality among the slave population in Egypt, fertility and infertility, and more.

I meant that military veterans may have 100 thousand birthrights.
For women, old men and old women (who are potentially birthrights), a total of 180 thousand people will be in their favor, let's say, so that the chance of birthright will be more in their favor than for military veterans.
So it is possible to say that in fact only an eighth of military veterans received birthright.

See more here http://forum.otzar.org/viewtopic.php?f=17&t=13568#p126797 and beyond

How do we know that there was no miraculous birth through nature? Why is it so difficult to claim that every woman over the course of her 70 years of life managed to give birth to at least 6 children? - And so the issue of infertility and mortality does not affect us that much, since we will reach a few million after 10 generations anyway?
And after all, in the Bible, Exodus 20:17, it simply describes an enormous increase, so perhaps there was a natural providence?

What does the rabbi think about the assumption that the Ramban raises about the problem of firstborns, where he writes that it is possible that the firstborns are those born in the last year of the exodus from Egypt? And there he retracts it by claiming that it is impossible that so many firstborns were born in one year.
If we assume that the enormous increase is possible - then what the Ramban initially suggested about the number of firstborns per year is perhaps possible?
According to Eliyahu Beller's article, he made a comparison between "Sacred to me every firstborn, every womb" and "Under every firstborn, every womb of the children of Israel" - hence, we are talking about the firstborn that meet the definition of "womb" and not those that have passed some time and are outside this "fresh" definition.
Thanks in advance.

I have no opinion on such possibilities. If there was a miracle, there is no point in all the calculations. What I wrote is that in nature it is clearly improbable.

It is possible that the numbers are typological. This is also the opinion of Dr. Yehoshua Berman in his article “Who is afraid of the Exodus?”

According to the scripture, there was a great and immense fertility, to the point that it constituted a threat to Pharaoh and Egypt, quantitatively of course, not qualitatively, so it can be said that the people of Israel were numerous in relation to Egypt even then.
Even if it is not claimed that there was a direct miracle, can it be claimed that there was a dedication of every woman to have at least six children in her life, and the Creator only arranged that every woman indeed tried to have children? Doesn't the plain text of the scripture prevent this and is even appropriate?

And another question for the rabbi: The rabbi answers that perhaps the number is topological, and elsewhere he refers to the question about exact numbers and not round "thousands" and admits that the question is correct and difficult and contradicts the topological issue. In the rest of the answer, I did not see that the rabbi refers to the matter further. I would be happy if the rabbi could explain his position to me again, if it is not a hassle.
If the matter remains a question without an answer, then what does this mean in relation to the verses of the Torah and the tradition that the entire Torah was written prophetically by Moses our Lord? How does the Rabbi handle this matter in relation to the Torah?
Thanks again.

From what I think of the verses that teach and multiplied and multiplied and became very strong, it teaches us that they were all fertile, no matter how many children they brought into the world, but that they probably lived longer and did not die quickly. The miracle was that even though the Israelites were slaves, the women continued to bear children even though they knew that their sons would be slaves - how is that a miracle? Because they were blessed. As it is written, "And your seed shall be as the dust of the earth. As the stars of the sky. And it is written, "You shall know that your seed shall be a stranger in a land not theirs, and they shall serve them and afflict them 400 years." But after that, they left Egypt with great possessions and were entitled to receive the promised land for the seed of Abraham.

In fact, the Egyptians' fear was not from the multiplication of the people of Israel per se. But from their association with the enemies of Egypt. As they say: And he also was added to our enemies.
And the Midrash often say that the Egyptians knew about the faithful exodus of the Israelites from Egypt and therefore tried to kill the savior of the Israelites, but the savior actually grew up in Pharaoh's house. And this is a clear miracle.

With me, I don't understand where this discussion is going. You can say whatever makes sense to you. What are you asking me?
I said what I had to say about typology. I don't understand what the question is: either there was a miracle or there is another explanation (as mentioned, the typological one seems unlikely to me).

If I understood correctly, the Rabbi believes:
It is difficult to explain that there was a natural multiplication and it is also difficult to say that the number is topological - so does the Rabbi believe this is a question that has no answer (and that the question will be answered)?
I ask this because if there is no answer to this issue to which many verses in the Torah are dedicated (among them the question of the small number of firstborns and the tribe of Levi), then how are we supposed to relate to the reliability of the Torah?
On the one hand, there is no doubt that there was a revelation (for other reasons that the Rabbi cites), but on the other hand, the Torah that was given through revelation is quite “unshakable”.
Thank you very much.

With me regarding the number of firstborns – There is an article on this by Rabbi Elchanan Samet in one of his books and quench your thirst.

Regarding typological numbers for the non-circular parts – See the book ‘Commentary on the Book of Exodus’ by Cassuto and also in Avraham on Noah in the Genesis chapters. To the best of my memory, I once saw a suggestion in Kitshin, but I don't remember it at the moment.

The Rabbi somewhere calculates that 1/73 of the population of the people were firstborns. And regardless, the firstborns of the tribe of Levi (if I'm not mistaken) were 1/73 of the tribe. The "typological editor" worked hard

Thank you for the answer, I have indeed already read the articles you mentioned.
But nevertheless, I asked according to the opinion of Rabbi Michael, who is not satisfied with a natural or topological explanation, when there is still no answer to the question: - How should we relate to the reliability of the Torah when there is no explanation for these difficult verses?

Laitai,
I don't understand why you get excited about a question that you don't know the answer to, and think as if everything will rise and fall on this side question.
Someone who accepts the Torah doesn't do so because they have an answer to the question of the firstborn, and to every other specific question.
Are there any questions you don't know how to answer? R’ Akiva Eiger has dozens of questions about the Gemara and the Rishonim that he has placed in the need for study.

As for my personal interest, if it bothered me I would look for material and then I could send you the articles you referred to. It probably doesn't really bother me.