**
Bar-Ilan****
University's
**

**
Parashat****
Naso 5770/ May 22, 2010**

Lectures on
the weekly Torah reading by the faculty of

*
*

**
Naso****
and Numbers**

**Prof.
Ido Kantor**

**Department of Physics**

The beginning of the book of Numbers, especially the weekly
readings of *Be-Midbar* and *Naso*,
is replete with numbers and computations, perhaps more so than any other
reading in the Torah, and therefore the fourth book of the Pentateuch goes by
the English name of Numbers.
[1]
This brings up the question whether there is
anything unique about the numbers appearing in the Torah and the frequency of
their appearance.
[2]
We shall consider the following two
questions:

- What numbers appear in the Torah an exceptional number of times? Here we shall focus on the lengths of people’s lives mentioned in the Torah.
- What primary numbers [3] appear in the Torah, and what is the order of their appearance? Note the great importance of prime numbers in science in general [4] and in encoding in particular, [5] as well as the fact that many questions surrounding prime numbers remain unsolved.

Three figures in the Torah lived the same number of years –
**137**: “These were the years of the
life of Ishmael: one hundred and
thirty-seven years; then he breathed his last and died, and was gathered to his
kin” (Gen 24:17); “and the span of Amram’s life was
137 years” (Ex. 6:20); “and the span of Levi’s life was 137 years” (Ex.
6:17). Note that 137 is a prime number
having several special characteristics
[6] and of
great importance in science.
[7]
Why does the Torah note that three people
lived an equal number of years? Is there
something comparable among them aside from the length of their lives?
Are other such examples to be found in the
Torah? Our amazement grows as we note
that indeed there are two people mentioned after the Flood as living the same
number of years – Peleg and Reu,
who each lived a total of 239 years.
This is also a prime number, but unlike the case with Ishmael,
Amram, and Levi, the **total length of their lives is not
explicitly summed up in the Torah**.
The Torah notes (Gen. 11:18-90):

When Peleg had lived 30 years, he begot Reu. After the birth of Reu, Peleg lived 209 years and begot sons and daughters.

When Reu had lived 32 years, he begot Serug. After the birth of Serug, Reu lived 207 years and begot sons and daughters.

The Torah does not give the usual summation, “the span of Peleg’s life was 239 years (30+209), or “the span of Reu’s life was 239 years” (32+207). The difference becomes all the more poignant when we notice that not far from the account of Peleg and Reu’s years the Torah mentions Shelah’s years, [8] which come to a total of 433 – also a prime number – but again the sum is not explicitly stated in the Torah. It seems as if the Torah were concealing the prime numbers after the flood.

Thus we see that the Torah does not explicitly mention an equal lifespan of anyone save for the three we have mentioned – Ishmael, Amram and Levi – who lived 137 years, nor does the Torah mention a prime number greater than 137 for anyone’s lifespan.

Examining the Torah, we find that prime numbers greater
than 7 appear for the first time in connection with the flood:
“In the six hundredth year of Noah’s life, in
the second month, on the **seventeenth** day of the month” (Gen. 7:11), and
immediately after the flood: “In the **six
hundred and first** year” (Gen. 8:13), 17 and 601 being prime numbers,
[9] as are
the lifespans of Peleg and
Reu (239) and of Shelah (433),
which are mentioned after the flood.
What accounts for this primal appearance of prime numbers during and
immediately after the flood? Could it be
that as evil became rooted and spread in the world in the generation of the flood,
then suddenly prime numbers, which are the basis for modern encoding systems,
make their appearance, although sometimes in **disguise**?

If I am not mistaken, the Torah has only one prime number
greater than 601 – 22,273, appearing in *Parashat Be-Midbar*
and marking the number of first-borns:
“All the first-born males as listed by name, recorded from the age of
one month up, came to **one-for-one**, 22,000 Levites for
22,000 first-born, and another 273 first-born left over:
“Take the Levites in place of all the
first-born among the Israelite people, … and as the redemption price of the 273
Israelite first-born over and above the number of the Levites,…” (Num.
3:45-46). Why does the Torah use this
system of redeeming and not another?
Because this is the only possible way, since 22,273 is a prime number
and has no common denominator with 22,000, which is the number of Levites.

[1] I wish
to thank Prof. Cyril Domb for encouraging me to
continue in the way I examined the text in my previous articles.

[2] Numbers
in the Torah have also been studied in the books by Prof. Meir Bar-Ilan,
*Numerologiya** Bereshitit*,
Rehovot 2004, and *Numerologiya**
Mikrait*, Rehovot 2008.

[3] A prime
number is a number which is divisible only by itself and by 1.

[4] Prime
numbers were studied by the Greeks (Euclid and Eratosthenes) in the third
century B.C.E. Partial evidence exists
of prime numbers having been known and studied by the Babylonians, 1900-1600
B.C.E., and the special nature of primes may even have been known in ancient

[5] Secure
internet purchases and secure communications are based on prime numbers.

[7] The
number 137 is of fundamental importance in physics.
1/137 is a dimensionless number and is known
as the Fine Structure Constant. It
expresses a relationship between three fundamental quantities:
the speed of light, the charge of an electron
and Planck’s constant.

[8] “**When
Shelah had lived 30 years**, he begot
Eber. After the
birth of Eber, Shelah lived
403 years and begot sons and daughters” (Gen. 11:14-15).

[9] Note
that all the prime numbers mentioned thus far – 17,
137,
239, 433,
601 – are **twin primes**, having another
prime number near them at a distance of 2 (such as 17 and 19), and are very
important scientifically. Cf. http://en.wikipedia.org/wiki/Riemann_zeta_function.

[10] The
number 22,273 is prime, the 2494^{th} in series of primes.
It is known as a special prime, the series of
numbers 22271, 22273, 22277, 22279, and
22283 all being prime. This is a prime
series of five, the eighth such in the prime numbers.