Eulers’s phi function* of 666 equals 216.

*Euler’s totient function (or Euler’s phi function), denoted as φ(n) or ϕ(n), is an arithmetic function that counts the positive integers less than or equal to n that are relatively prime to n.

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# Category: Number theory

## Euler’s Phi Function

## The Mirror

## It’s time

## Sum of primes and triangular numbers

## The Time Code

## Naturalis Veritas

## Equation of Time

NOTHING IS BIGGER THAN IT LOOKS

Eulers’s phi function* of 666 equals 216.

*Euler’s totient function (or Euler’s phi function), denoted as φ(n) or ϕ(n), is an arithmetic function that counts the positive integers less than or equal to n that are relatively prime to n.

The fundamental algorithm (10+n) star (10-n) gives rise to the number 338 for all n belonging to the set of natural numbers in the form 9.

The fundamental algorithm n taichi (10-n) is extremely logical. It gives rise to the number 216 for all n belonging to the set of natural numbers in the form 9.

Each natural number not equal to 216 can be written in the form *p*+*T*_{x} , where *p* is 0 or a prime, and *T*_{x}=*x*(*x*+1)/2 is a triangular number.

Zhi-Wei Sun, 2009

More than 3,000 years ago, the day of Yom Kippur saw the Jerusalem’s great priest enter the Temple of Jerusalem and pronounce the name of God, which was supposed to be written with a sequence of 216 characters. With the Temple’s destruction the real name of God has been lost for ever.

A 216-digits name for God, called Shem ha-Mephorash or Divided Name, can thus be found in the Jewish Kabbalistic sources as well as in the Christian Kabbalah and in the hermetic Kabbalah, coming from the 72 groups of 3 letters, each one of these triplets being the name of an angel or of intelligence. The reference can be found in the book of Exodus 14:19-21.

In 1998 this theme had gone topical again with the movie π by Darren Aronofsky. The movie’s main character was Maximilian Cohen, a young gifted mathematician who, like Galileo, thought that nature is a book written in mathematical language. He was everywhere looking for a numerical sequence and discovered one of 216-digits.

In 2007, it was not through a mere analogy with the movie’s main character that I was convinced that my research about the sequences that best represent Nature was going to converge to a result of a 216-digits sequence. If, in the movie, the unveiled sequence was wrong, I knew that I could be the first person in the world to discover its essence, to reach its actual deciphering. And it so happened.

My sequence is constructed through the principle of the Fibonacci sequence, with some extensions and some variants. Since the beginning of 1200 to today, this sequence was considered the most important in the history of mathematics. It also took an aesthetic dimension through the golden ratio, the golden spiral and the golden rectangle, which are found both in nature and in architecture.

It was for me a source of intelligence and of spiritual power. As for Yom Kippur that was for me a kind of reconciliation with the world. The sequence is cyclical, and has many symmetries. Each combination of numbers determines 30 binary images that I have produced. These images represents the essence of a link millennium, that between man and God: the Time Code.

The true 216-digit sequence is (Naturalis Veritas, the end of the history, Massimo Nardotto, 2007):

1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9

2 2 4 6 1 7 8 6 5 2 7 9 7 7 5 3 8 2 1 3 4 7 2 9

3 3 6 9 6 6 3 9 3 3 6 9 6 6 3 9 3 3 6 9 6 6 3 9

4 4 8 3 2 5 7 3 1 4 5 9 5 5 1 6 7 4 2 6 8 5 4 9

5 5 1 6 7 4 2 6 8 5 4 9 4 4 8 3 2 5 7 3 1 4 5 9

6 6 3 9 3 3 6 9 6 6 3 9 3 3 6 9 6 6 3 9 3 3 6 9

7 7 5 3 8 2 1 3 4 7 2 9 2 2 4 6 1 7 8 6 5 2 7 9

8 8 7 6 4 1 5 6 2 8 1 9 1 1 2 3 5 8 4 3 7 1 8 9

9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

To verify the uniqueness of my equation of time π (x + y) (t – xy) = k, consider x – y = 144, which represents the tree of knowledge in the Garden of Eden in the Kabbalistic tradition. This happens for t = 3156 before Christ, 42 years before the beginning of the 12th cycle Maya. To reach the year 2028, in which x – y = 0 and x = y = 42, it takes 72 cycles, each of which reduces by 2 units the difference between x and y. The number of years between these two moments is 5184, which corresponds to the square of 72 or to the square of 216 divided by 9. Which means that the average of each cycle in this period is 72 years, which is the number of years that the sun employs to move to a degree around the ecliptic, although the cycles have a duration of descending, which corresponds to the difference between x and y.