Bar-Ilan University's Parashat Hashavua Study Center

Parashat Naso 5770/ May 22, 2010

Lectures on the weekly Torah reading by the faculty of Bar- Ilan University in Ramat Gan, Israel. A project of the Faculty of Jewish Studies, Paul and Helene Shulman Basic Jewish Studies Center, and the Office of the Campus Rabbi. Published on the Internet under the sponsorship of Bar- Ilan University's International Center for Jewish Identity. Prepared for Internet Publication by the Computer Center Staff at Bar-Ilan University. Inquiries and comments to: Dr. Isaac Gottlieb, Department of Bible, gottlii@mail.biu.ac.il

 

 

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:

  1. 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.
  2. 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 22,273” (Num. 3:43). [10]   The method chosen by the Torah for redeeming the first-borns was based on a method of 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 Egypt.   Http://en.wikipedia.org/wiki/Prime­­_numbers.

[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 2494th 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.