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In the begining of sefer bamidbar, the males between 20 and 60 are counted and it says that there are over 600,000 of them. Theoretically each, or most, of these people should have had a first-born child and half of these children should be males. But two prakim later, the first-born males one month old and up are counted and instead of there being about 300,000, there are only about 22,000. Why are there so few?

I checked several mefarshim and none of them seemed to have an answer.

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They were killed after the egel for being the priests who lead the worship (speculation) –  Double AA Feb 1 '12 at 23:33
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There could have just been some bechorim who were tzadikkim and didn't participate (still speculation) –  Double AA Feb 2 '12 at 0:53
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@AriA, they surely weren't the same. Numbers 3:40ff state explicitly that the bechorim counted there were to be "exchanged" for the Levi'im. (And indeed, Rashi to 3:39, from Bechoros 5a, states that there were only 300 Levi'im aged one month and older who were bechorim.) –  Alex Feb 3 '12 at 2:26
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@ avi: Ok... What? –  Ari A Feb 21 '12 at 18:26
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The question can be made stronger: The Jewish population was growing in the 210 years they were in Mitzrayim. Thus, of the 600,000 men aged 20 to 60 at the exodus, more than 300,000 should have been aged 20 to 40 and they should have had some 150,000 b'choros aged 0 to 20. Of course, they didn't really have half a b'chor each (many b'choros died, etc.), but 20,000 still seems too little. –  msh210 Feb 21 '12 at 18:26
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2 Answers

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+50

Some portion of the 600k males were not married, and some of the married ones had no children at all.

Of those that were, only 22k families had first-borns which needed to be redeemed by a Levite or 5 shekalim. Not all firstborns need redemption, in fact, a Pidyon heBen ceremony is relatively rare.

  1. As you already noted, the child must be male.
  2. If the child was preceded by a non-viable child, it is exempt.
  3. The child must have born naturally (i.e. males born via C-section are exempt).
  4. Neither the father nor the mother may be a member of the tribe of Levi.
  5. Some percentage of the remainder were no longer alive.
  6. The son must have been born first for certain - if there were twins and it isn't certain which arrived first, there is no redemption. (Recall that Jewish mothers gave birth on their own, to 6 at a time, in the fields, sometimes abandoning their children. It is likely that many were unsure which was the first born).
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Although this does explain some of the discrepancy, It still seems very unlikely that these would cause so few bechorim. The fact that half of them were gilrs brings their numbers down to 300,000. Assuming every levi woman was married to a non-Levi man brings it down to 278,000. Also, correct me if i'm wrong, but I don't think they had C-sections. If you subtract the amount of bechorim that it says there were from the 278,000, that leaves 256,000 that were preceded by a non-viable child (2) or had died (5). That's 92% of the would-be bechorim. I suppose it's possible, but it doesn't seem right –  Ari A Feb 21 '12 at 18:37
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You forgot to subtract all the unmarrieds and infertiles. Note that C-sections were done in ancient times. Search the Talmud for "יוצא דופן" and Wikipedia (en.wikipedia.org/wiki/Caesarean_section). I also added a 6th exemption, see post. –  Barry Feb 21 '12 at 20:18
    
The Wikipedia article said the first C-section was done in 320 BCE, about a thousand years after the Torah was given. Still, the numbers make much more sense with the 6th exemption and your first point, which I overlooked. –  Ari A Feb 21 '12 at 21:57
    
    
Your point about twins is inaccurate. Whoever is older, the father is obligated to pay. –  Double AA Jul 8 '13 at 12:09
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Some thoughts:

  1. Rashi in Shemot 1:7 tells us that the Jewish Women gave birth to children 6 at a time.

    If Moshe's family is any indication there were 4 generations of Jews born during the Jews stay in Egypt. Either way, only the children of the last generation (for the most part) would have been younger than 60 and therefore counted in the census.

    Even with regards to those counted, it's possible that the oldest sibling was older than 60, and therefore not counted.

  2. 4/5th of the Jews died before they left Egypt (Rashi Shemot 13:18), perhaps a disproportionate percentage were firstborns.

  3. The math works out (or is at least close enough) if each of the Jewish mothers gave birth 4 times (and some gave birth 5 times), each time to 6 children. 22,000 is roughly 1/27th of 600,000. 4 births would be 24 children with only one firstborn. 5 births would be 30 children with one first born.

  4. It would statistically stand to reason that 50% of the firstborn children would be female.

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"It would stand to reason that the majority of the firstborns of each family were older than 116 years old": why? Weren't there multiple generations born in Egypt? But I grant you that the existence of sextuplets makes for fewer b'choros, as you point out in item 3. +1. –  msh210 Feb 2 '12 at 5:20
    
I don't think the sextuplets explains anything. That would just mean that each of the 600,000 has sextuplets, one of which is the bechor. –  Ari A Feb 2 '12 at 15:17
    
@msh210: I was thinking about that. My answers assumed there was only one generation. If Moshe's family is any indication, then there were 3 generations in egypt (4 if you count Moshe's children). Kehot was already born when the Jews entered, Amram, and Moshe left when he was 80. Amram had Moshe when there were 130 years left of exile. I will update my answer. –  Menachem Feb 2 '12 at 20:59
    
@AriA: That would mean that each of the 600,000 were part of a sextuplet. –  Menachem Feb 2 '12 at 21:18
    
@ Menachem: Yes, but they also have sextuplets. Since the amount of bechorim per generation multiplies (theoretically) with each generation, the bechorim in the youngest generation (who were not counted in the first cencus) should make up for all of the bechorim who were 'lost' by haveing sextuplets in the older generations. –  Ari A Feb 19 '12 at 23:35
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