The Primacy of the Prime Numbers

And the messengers returned to Jacob, saying: “We came to thy brother Esau, and moreover he cometh to meet thee, and four hundred men with him.” (Genesis 32:7)

On this blog, we primarily focus on structural parallels between Torah and Physics and, more specifically, quantum physics. Today I would like to explore an interesting parallel between this Torah portion and the number theory.

In my previous essay on the Torah Portion Vayishlach, “Jacob Meets Esau and his 400 men,” I wrote “Esau and his 400 men together were 401 strong. 401 is a prime number that is the sum of seven consecutive prime numbers (43+47+53+59+61+67+71).” In that essay, I focused on the significance of the number seven. Let us now focus on the significance of the prime number.

The structural parallel I see between this Torah portion and the numbers theory is the parallel between prime numbers and the Olam HaTohu, the “Universe of Chaos.”

The Universe of Chaos was created first. However, it was destroyed and the new universe, Olam HaTikun, the “Universe of Rectification” was created instead. The shards of vessels (in Hebrew, nitzutzot, or “sparks”) of the Olam HaTohu fell in the Olam HaTikun. Reconstituting and elevating these sparks, as well as harnessing the spiritual light of the Olam HaTohu in the vessels of the Olam HaTikun is our cosmic mission that is called in Hebrew Tikun Olam—the rectification of the world.

The reason the Universe of Chaos was destroyed is the lack of inter-inclusion of the vessels (kelim). As Kabbalah teaches us, the Divine emanations, Sefirot, are Divine light in the vessels. Whereas the light is the same in all Sefirot, it is the vessels that give unique qualities to the Sefirot. By way of example, when the white light passes through color glasses (filters), it acquires the color of the filter. The vessels serve as color filters that give specific “color” (i.e., specific characteristics) to a particular Sefirah. The vessels of Tohu were each for themselves—the vessel of Chesed was pure Chesed with no room for any other Sefirot. In the Olam HaTikun, on the other hand, all Sefirot are inter-include—each Sefirah contains all other Sefirot. Thus, in Olam HaTikun, we have Chesed of Chesed, Gevurah of Chesed, Tiferet of Chesed, etc.—each Sefirah is made up of all Ten Sefirot, i.e, they are composite.

Let us compare this to the prime numbers. By definition, prime numbers (“primes”) are those integers that have no other factors (divisors) beside themselves and 1. In other words, a prime number is any integer greater than 1 that cannot be formed by multiplying two smaller integers. Integers that are not prime, i.e., that could be formed by multiplying smaller integers are called composite numbers. The fundamental theorem of arithmetic states that every natural number greater than 1 is either prime itself or could be formed (i.e., factorized) as a product of other prime numbers. For example, the number 7 is prime because it can be divided only itself or by 1 (in other words, it is only the product of 7 × 1). On the other hand, the number 8 is a composite number, because it could be formed as a product of 2 × 4 or 2 × 2 × 2. The importance of the prime numbers was already appreciated by ancient Greek who understood that all natural numbers are either primes or could be represented as a product of primes. Prime numbers, therefore, represent the “atoms” or the “elementary particles” of the arithmetic.

What is the connection of the primary numbers to the Olam HaTohu? First, let us recall that the Olam HaTohu was created first. The second universe, the Olam HaTikun was created from the shards of the Olam HaTohu. While we cannot say that primary numbers came first—in mathematics, there is no time; everything is static and exists at the same time, as it were—we can say that they are prime (hence their name— “prime numbers”), and the composite numbers are composed of the prime numbers. Indeed, Sefirot of the Olam HaTikum are composite, similar to the composite numbers, but Sefirot of the Olam HaTohu are not, as they are akin to prime numbers.

There is no formula to predict the next prime number. The distribution of prime numbers among all natural numbers is random and chaotic (at least, to the best of our knowledge). The very name of the first universe is Olam Ha Tohu—the Universe of Chaos.

Lastly, let us note that Esau, who together with his 400 men, represented a primary number 401, was a man from the Universe of Chaos. As the sages of Kabbalah revealed to us, the soul of Esau was indeed from the Olam HaTohu.

There are seven primary numbers that make up the number 401. Jacob may have recognized the primacy of prime numbers when he bowed down seven times approaching his brother Esau.