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Vedic Astrology and Numerology, ROHIT KR RAO

www.rohitkrrao.com/numerology.html‎

The history of numbers is as old as the recorded history of man. Numerology was in use in ancient Greece, Rome, Egypt, China and India and is to be found in ...

What are the Numbers?

The most familiar form of numbers are natural numbers 0, 1, 2, 3, 4 5, 6, 7, 8, 9.

The numbers 1 to 9 can be called as unit numbers and the numbers from 10 onwards (up to 99) can be called as double-digit numbers which denotes the fusion of two numbers however these can still be reduced to unit numbers, eg; 24 (2+4=6) is reduced to 6. Then, there are Master Numbers such as 11, 22, 33, 44 and so on which are never reduced to a unit number as they carry their own intensified vibration and potency.

Every number expresses its qualities in the form of strengths and challenges. Therefore, no number is good or bad, lucky or unlucky and auspicious or inauspicious as each and every number is equally necessary and important, and each gives strength to the next one and takes what it needs from the one before. Numbers have two aspects viz; exoteric or external and esoteric or inner. In a nut shell, every number possesses its own unique quality and power.

Our ancient seers believed that numbers symbolize divinity and however our mathematicians believed that study of numbers can possibly reveal the principles of creation and laws of time & space. Numbers can be seen as fundamental in art, poetry, architecture, music, and so on.

“The World is built upon the power of Numbers” ...Pythagoras – 6th century BC.


What is Numerology?

The word Numerology comes from the Latin word "Numerus," which means number, and the Greek word "Logos," which means word, thought, and expression.

Numerology, based upon the sacred science of numbers, is an advanced offshoot of the melodious rhythm of the mathematical precision that controls all creation. It influences every aspect of our life unconsciously or consciously whether we are aware of this or not.

Numerology is the science and philosophy of numbers (1 to 9) where each numbers has its own strength, potential and challenge. The whole idea behind this is to know the hidden expression contained in these numbers so as to understand their relationship and progression in our numerology chart. This can help us in knowing the difficulties we may have experienced in the past or under present circumstances and then working towards doing some inner work in our life for bringing harmony, peace and joy.
The belief in Numerology is easier to understand when we put it into a context with realizing how the entire world revolves around numbers and mathematical equations.

 

What is the origin and history of Numerology? top

The history of numbers is as old as the recorded history of man. Numerology was in use in ancient Greece, Rome, Egypt, China and India and is to be found in the ancient books of wisdom, such as the Hebrew Kabala. Most commonly used system for Numerology were developed by the Chaldeans, the Hindus, the Mayans, the Hebrews (Kabala), the Chinese (Book of Changes), and the work of Pythagoras, to name a few. The basic intent behind these systems originally was to understand the relationship between man and his god.

Pythagoras, the old master philosopher and mathematician, who lived in the sixth century BC, propounded the theory that nothing in the universe could exist without numbers. He established a Mystery School in Italy when he was 52 years old. He was born in Greece and lived between 582 and 507 BC, much of his life spent in study and travel. His Mystery School taught esoteric knowledge, which included the secret of number and vibration. The knowledge was passed down by word of mouth and a few manuscripts. The academic teaching rested on a foundation of Mathematics, Music and Astronomy. Much of Pythagoras' background in Egyptian philosophy and religion was based upon Number and Kabalistic principle. He postulated that the triangle was particularly important, as it was the first complete shape, and constituted a blueprint. Thus form is preceded by a blueprint, and each stage of this process is measured through numbers, hence nothing exists without numbers.

 

 

Free Numerology School | A Brief History of Pythagorean Numerology

numerology-school.com/brief-history-of-numerology.html‎

The history of Numerology is closely related to the invention of alphabet. Since letters of alphabet were also used to record numbers, each and every word could ...

A Brief History of Pythagorean Numerology

There are as many different numerologies in the world as there are developed cultures, since wise people have grasped the connection between Creation, Numbers and the reality of our world a long time ago. In this section, we are going to focus on only one kind of numerology: the one associated with Pythagoras.

The Life of Pythagoras

It all began more than 2500 years ago on Samos, a small island in the Mediterranean. Born there was a person who can rightfully be called the very first philosopher of humanity. This is because it was Pythagoras who in fact coined the word philosophy.

In those times, the Mediterranean was a major center of world's civilization, and the young Pythagoras traveled around a great deal in order to find all the available sources of ancient wisdom. He spent 22 years in Egypt absorbing the knowledge of its ancient civilization, he studied with the wise people of Babylon, and journeyed to Persia in order to familiarize himself with the Zoroastrian tradition, and he even met the mysterious Hyperboreans. The sphere of his interests was not limited to the sciences (particularly those of of mathematical nature), but also included religious systems. As a result, Pythagoras was initiated into the mysteries of several cultures.

By the time he was 40, Pythagoras had settled in Southern Italy, established his school and presented his teachings to humanity. The scale of that teaching and its impact on human civilization were so great that even now, after several millennia, the name of Pythagoras is known to every shool kid.

Ironically, though, the proof of the theorem present in school books is probably one of his least achievements. After all, the fact that the sum of the squares of two legs gives the square of hypotenuse was already well known in Egypt and Babylon long before Pythagoras came along. Yet his philosophical system was so impressive that the ever-famous Plato could even be thought of as merely one of Pythagoras’s followers.

However, the interests of Pythagoras weren't exclusively abstract or theoretical. He spent plenty of time researching music (And, again, not simply as an intellectual pursuit — those familiar with the theory of music can confirm that it is quite close to mathematics.) and its application to healing, and as a means of restoring the vibrational structure of one's system. Pythagoras believed that music is an art in which Numbers reach directly to the heart, whereas in mathematics, they just occupy the brain.

It is clear that philosophy, as understood by Pythagoras, was very different from how it is understood now. It had more in common with the concepts in Indian yoga. Consider this: Pythagoras completely accepted the idea of a cycle of numerous incarnations of a human soul and believed that the exit from that circle was found not through religious rituals but through philosophy, i.e., contemplation and comprehension of the main principles of Creation. Philosophy, in his understanding, was a path to perfect the soul, a path towards immortality.

Numbers are at the very core of Pythagoras’s teachings, but as you can see, his understanding of numbers was very different from the contemporary one. Now we understand numbers in a concrete, utilitarian way (two apples, three dollars, etc.), or like a sort of exercise for one's brain (the dreaded math with which we were all fed up at school and believed we’d never use in real life).

For Pythagoras, numbers, especially the first ten, are the highest manifestations of the Creative Principle in the creation of our world. They can be called the different aspects of the Creator of the Universe. Interacting and gradually descending from the world of ideas into the world of matter, the numbers create, according to their rules, everyone and everything.

And to show that this idea might not be not just wild speculation, consider that according to contemporary physics, at some deep level, microparticles and the quanta of energy are indistinguishable. In other words, material particles are in fact bundles of energy, or electromagnetic waves. And waves—or vibrations—are directly related to the numbers that define their frequency.

From Theory to Practice

Enough theoretical speculations for now. Let's concentrate on life’s utilitarian, practical application of numbers. We are all used to counting things, using money, applying numbers to our cars, telephones, addresses, and so on. The day, month and year of a person's birth also contains their numbers. Numbers surround us everywhere. And even though this is true, we do not think about them in terms of bearing some special mystical properties, but rather we are simply using them for convenience, taking one or another sequence of numbers as yet another random thing in our chaotic and senseless world.

Still, sooner or later many of us start asking questions the answers to which cannot be found in either schoolbooks or academic treatises. What are we doing in this world? Is there any reason for our existence here? Is the world really as chaotic and void of any sense as it seems to be? Are we really here simply to hang around in this chaos and somehow come to our natural end? Or does our existence have some purpose? Is there perhaps something that we are supposed to learn in our lives? Is there someone or something that can help us to understand what's going on, which path to take so that we can eventually reach our true destination?

Questions like these have been asked since man’s beginning on this Earth. To some people, these kinds of questions come early in youth, while others need to gain some life experience before they start asking these things, and others still who simply can't be bothered with them.

Understanding the connection between the everyday numbers that surround us and the Numbers (with a capital N), which are the acting principles of the universe, is important in our search for the answers to the questions above. This is where numerology comes in.

In the lessons that follow, I will share with you my fascination with the wonders of the universe, as seen with the help of the tools of practical numerology. I don't promise that you will understand everything about your life and the surrounding world, but if you were to get even the smallest glimpse of understanding, this could prove to be very important. After all, even a tiny lantern is much better than complete darkness.

More History

Below you'll find a collection of bits and pieces of information that will help you to better understand the history of Numerology. I plan to add more to this collection from time to time.

Isopsephy and Gematria

The history of Numerology is closely related to the invention of alphabet. Since letters of alphabet were also used to record numbers, each and every word could be given a numeric value. The process of adding together the numeric values of separate letters to obtain a value for the whole word was called by the Greeks Isopsephy. Later, when this method was used to interpret the Torah, it was called Gematria.

Isopsephy was widely used by the Greeks in magic and interpretation of dreams. According to tradition, Pythagoras used isopsephy for divination. The idea is that if two words or two phrases have the same numeric value, then there is some kind of an invisible link between them. For example, Jesus in Greek (Ιησούς) adds up to 888, as well as the phrase "I am life" (η ζωη ειμι). Clearly, Christians felt this made a lot of sense.

As you will see, the approach that is used today to obtain the numeric value of a name or a word is substantially different from the method used in isopsephy.

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

0
-
Z
=
8
1
4
ZERO
64
28
1
1
-
O
=
6
2
3
ONE
34
16
7
2
-
T
=
2
3
3
TWO
58
13
4
3
-
T
=
2
4
5
THREE
56
29
2
4
-
F
=
6
5
4
FOUR
60
24
6
5
-
F
=
6
6
4
FIVE
42
24
6
6
-
S
=
1
7
3
SIX
52
16
7
7
-
S
=
1
8
5
SEVEN
65
20
2
8
-
E
=
5
9
5
EIGHT
49
31
4
9
-
N
=
5
10
4
NINE
42
24
6
45
-
-
-
42
-
40
Add
522
225
45
4+5
-
-
-
4+2
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4+0
Reduce
5+2+2
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4+5
9
-
-
-
6
-
4
Deduce
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
1
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
O
=
6
2
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
3
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
4
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
5
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
6
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
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1
7
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
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1
8
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
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5
9
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
10
4
NINE
42
24
6
-
-
-
-
-
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6
-
-
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45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
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4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
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-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
1
4
ZERO
64
28
1
-
1
-
3
-
5
-
-
8
9
1
-
O
=
6
2
3
ONE
34
16
7
-
-
-
3
-
5
-
7
8
9
2
-
T
=
2
3
3
TWO
58
13
4
-
-
-
3
4
5
-
-
8
9
3
-
T
=
2
4
5
THREE
56
29
2
-
-
2
3
-
5
-
-
8
9
4
-
F
=
6
5
4
FOUR
60
24
6
-
-
-
3
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5
6
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8
9
5
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F
=
6
6
4
FIVE
42
24
6
-
-
-
3
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5
6
-
8
9
6
-
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=
1
7
3
SIX
52
16
7
-
-
-
3
-
5
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7
8
9
7
-
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=
1
8
5
SEVEN
65
20
2
-
-
2
3
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5
-
-
8
9
8
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5
9
5
EIGHT
49
31
4
-
-
-
3
4
5
-
-
8
9
9
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N
=
5
10
4
NINE
42
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6
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-
-
3
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5
6
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8
9
45
-
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42
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Add
522
225
45
-
1
4
3
8
5
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8
9
4+5
-
-
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4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
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5
9
5
8
9

 

 

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7
-
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0
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8
1
4
ZERO
64
28
1
-
1
-
-
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-
1
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6
2
3
ONE
34
16
7
-
-
-
-
-
7
2
-
T
=
2
3
3
TWO
58
13
4
-
-
-
4
-
-
3
-
T
=
2
4
5
THREE
56
29
2
-
-
2
-
-
-
4
-
F
=
6
5
4
FOUR
60
24
6
-
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6
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5
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=
6
6
4
FIVE
42
24
6
-
-
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6
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6
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=
1
7
3
SIX
52
16
7
-
-
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7
7
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5
SEVEN
65
20
2
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2
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8
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EIGHT
49
31
4
-
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4
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9
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42
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Add
522
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1
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4+0
Reduce
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2+2+5
4+5
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-
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-
1+8
1+4
9
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6
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4
Deduce
9
9
9
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1
4
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9
5

 

 

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1
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9
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-
-
-
-
-
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-
0
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8
1
4
ZERO
64
28
1
-
1
-
3
-
5
-
-
8
9
3
-
T
=
2
4
5
THREE
56
29
2
-
-
2
3
-
5
-
-
8
9
7
-
S
=
1
8
5
SEVEN
65
20
2
-
-
2
3
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5
-
-
8
9
2
-
T
=
2
3
3
TWO
58
13
4
-
-
-
3
4
5
-
-
8
9
8
-
E
=
5
9
5
EIGHT
49
31
4
-
-
-
3
4
5
-
-
8
9
4
-
F
=
6
5
4
FOUR
60
24
6
-
-
-
3
-
5
6
-
8
9
5
-
F
=
6
6
4
FIVE
42
24
6
-
-
-
3
-
5
6
-
8
9
9
-
N
=
5
10
4
NINE
42
24
6
-
-
-
3
-
5
6
-
8
9
1
-
O
=
6
2
3
ONE
34
16
7
-
-
-
3
-
5
-
7
8
9
6
-
S
=
1
7
3
SIX
52
16
7
-
-
-
3
-
5
-
7
8
9
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
4
6
7
-
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-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
1
4
ZERO
64
28
1
-
1
-
-
-
-
3
-
T
=
2
4
5
THREE
56
29
2
-
-
2
-
-
-
7
-
S
=
1
8
5
SEVEN
65
20
2
-
-
2
-
-
-
2
-
T
=
2
3
3
TWO
58
13
4
-
-
-
4
-
-
8
-
E
=
5
9
5
EIGHT
49
31
4
-
-
-
4
-
-
4
-
F
=
6
5
4
FOUR
60
24
6
-
-
-
-
6
-
5
-
F
=
6
6
4
FIVE
42
24
6
-
-
-
-
6
-
9
-
N
=
5
10
4
NINE
42
24
6
-
-
-
-
6
-
1
-
O
=
6
2
3
ONE
34
16
7
-
-
-
-
-
7
6
-
S
=
1
7
3
SIX
52
16
7
-
-
-
-
-
7
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
8
18
14
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
1+8
1+4
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
8
9
5

 

 

1
-
O
=
6
1
3
ONE
34
16
7
2
-
T
=
2
2
3
TWO
58
13
4
3
-
T
=
2
3
5
THREE
56
29
2
4
-
F
=
6
4
4
FOUR
60
24
6
5
-
F
=
6
5
4
FIVE
42
24
6
6
-
S
=
1
6
3
SIX
52
16
7
7
-
S
=
1
7
5
SEVEN
65
20
2
8
-
E
=
5
8
5
EIGHT
49
31
4
9
-
N
=
5
9
4
NINE
42
24
6
45
-
-
-
34
-
36
Add
458
197
44
4+5
-
-
-
3+4
4
3+6
Reduce
4+5+8
1+9+7
4+4
9
-
-
-
7
4
9
Deduce
17
17
8
-
-
-
-
-
-
-
Produce
1+7
1+7
-
9
-
-
-
7
-
9
Essence
8
8
8

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
O
=
6
1
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
2
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
3
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
4
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
5
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
6
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
7
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
8
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
9
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
34
-
36
Add
458
197
44
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
7
4
9
Deduce
17
17
8
-
1
4
3
8
5
18
14
8
9
-
-
-
-
-
-
-
Produce
1+7
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
7
-
9
Essence
8
8
8
-
1
4
3
8
5
9
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
O
=
6
1
3
ONE
34
16
7
-
1
-
3
-
5
-
7
8
9
2
-
T
=
2
2
3
TWO
58
13
4
-
1
-
3
4
5
-
-
8
9
3
-
T
=
2
3
5
THREE
56
29
2
-
1
2
3
-
5
-
-
8
9
4
-
F
=
6
4
4
FOUR
60
24
6
-
1
-
3
-
5
6
-
8
9
5
-
F
=
6
5
4
FIVE
42
24
6
-
1
-
3
-
5
6
-
8
9
6
-
S
=
1
6
3
SIX
52
16
7
-
1
-
3
-
5
-
7
8
9
7
-
S
=
1
7
5
SEVEN
65
20
2
-
1
2
3
-
5
-
-
8
9
8
-
E
=
5
8
5
EIGHT
49
31
4
-
1
-
3
4
5
-
-
8
9
9
-
N
=
5
9
4
NINE
42
24
6
-
1
-
3
-
5
6
-
8
9
45
-
-
-
34
-
36
Add
458
197
44
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
7
4
9
Deduce
17
17
8
-
1
4
3
8
5
18
14
8
9
-
-
-
-
-
-
-
Produce
1+7
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
7
-
9
Essence
8
8
8
-
1
4
3
8
5
9
5
8
9

 

 

0
-
4
ZERO
8
5
9
6
-
=
28
2+8
=
10
1+0
1
1
-
3
ONE
6
5
5
-
-
=
16
1+6
=
7
-
7
2
-
3
TWO
2
5
6
-
-
=
13
1+3
=
4
-
4
3
-
5
THREE
2
8
9
5
5
=
29
2+9
=
11
1+1
2
4
-
4
FOUR
6
6
3
9
-
=
24
2+4
=
6
-
6
5
-
4
FIVE
6
9
4
5
-
=
24
2+4
=
6
-
6
6
-
3
SIX
1
9
6
-
-
=
16
1+6
=
7
-
7
7
-
5
SEVEN
1
5
4
5
5
=
20
2+0
=
2
-
2
8
-
5
EIGHT
5
9
7
8
2
=
31
3+1
=
4
-
4
9
-
4
NINE
5
9
5
5
-
=
24
2+4
=
6
-
6
45
-
40
Add
42
70
58
43
12
-
225
-
-
63
-
45
4+5
-
4+0
-
4+2
7+0
5+8
4+3
1+2
-
2+2+5
-
-
6+3
-
4+5
9
-
4
Reduce
6
7
13
7
3
-
9
-
-
9
-
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
9
-
4
Deduce
6
7
4
7
3
-
9
-
-
9
-
9

 

 

NUMBER = 534259 = 1 = 534259 NUMBER

NUMBER = 234559 NUMBER

NUMBER = 534259 = 1 = 534259 NUMBER

 

 

NUMBERS = 5342591 = 2 = 5342591 NUMBERS

SBUMNER = 1234559 = SBUMNER

NUMBERS = 5342591 = 2 = 5342591 NUMBERS

 

-
-
-
-
Q
NUMBERS
-
Q
Q
-
1
2
3
4
5
6
7
8
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
6
7
8
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
6
7
8
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
6
7
8
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
6
7
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
6
7
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
6
7
8
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
6
7
8
-
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
6
7
8
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
-
-
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
6
7
8
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
9
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
-
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
3
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
9

 

 

I = 9 9 = I
ME = 9 9 = ME
BRAIN + BODY = 9 9 = BODY + BRAIN
LIGHT + DARK = 9 9 = DARK + LIGHT
ENERGY + MASS = 9 9 = MASS +ENERGY
MIND + MATTER = 9 9 = MATTER + MIND
MAGNETIC + FIELD = 9 9 = FIELD + MAGNETIC
POSITIVE + NEGATIVE = 9 9 = NEGATIVE + POSITIVE
973 OM AZAZAZAZAZAZAZAZAZZAZAZAZAZAZAZAZAZAOM 973

 

 

0
-
Z
=
8
-
4
ZERO
64
28
1
1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
42
-
40
Add
522
225
45
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
9
-
-
-
6
-
4
Deduce
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
-
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
34
-
36
Add
458
197
44
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
9
-
-
-
7
4
9
Deduce
17
17
8
-
-
-
-
-
-
-
Produce
1+7
1+7
-
9
-
-
-
7
-
9
Essence
8
8
8

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
34
-
36
Add
458
197
44
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
7
4
9
Deduce
17
17
8
-
1
4
3
8
5
18
14
8
9
-
-
-
-
-
-
-
Produce
1+7
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
7
-
9
Essence
8
8
8
-
1
4
3
8
5
9
5
8
9

 

 

0
-
4
ZERO
8
5
9
6
-
=
28
2+8
=
10
1+0
1
1
-
3
ONE
6
5
5
-
-
=
16
1+6
=
7
-
7
2
-
3
TWO
2
5
6
-
-
=
13
1+3
=
4
-
4
3
-
5
THREE
2
8
9
5
5
=
29
2+9
=
11
1+1
2
4
-
4
FOUR
6
6
3
9
-
=
24
2+4
=
6
-
6
5
-
4
FIVE
6
9
4
5
-
=
24
2+4
=
6
-
6
6
-
3
SIX
1
9
6
-
-
=
16
1+6
=
7
-
7
7
-
5
SEVEN
1
5
4
5
5
=
20
2+0
=
2
-
2
8
-
5
EIGHT
5
9
7
8
2
=
31
3+1
=
4
-
4
9
-
4
NINE
5
9
5
5
-
=
24
2+4
=
6
-
6
45
-
40
Add
42
70
58
43
12
-
225
-
-
63
-
45
4+5
-
4+0
-
4+2
7+0
5+8
4+3
1+2
-
2+2+5
-
-
6+3
-
4+5
9
-
4
Reduce
6
7
13
7
3
-
9
-
-
9
-
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
9
-
4
Deduce
6
7
4
7
3
-
9
-
-
9
-
9

 

 

4

ZERO

64
-

28
-

1
3

ONE
34
-
16
-
7
3

TWO
58
-
13
-
4
5

THREE
56
-
29
-
2
4

FOUR
60
-
24
-
6
4

FIVE
42
-
24
-
6
3

SIX
52
-
16
-
7
5

SEVEN
65
-
20
-
2
5

EIGHT
49
-
31
-
4
4

NINE
42
-
24
-
6
3

TEN
39
-
12
-
3
6

ELEVEN
63
-
27
-
9
6

TWELVE
87
-
24
-
6
8

THIRTEEN
99
-
45
-
9
8

FOURTEEN
104
-
41
-
5
7

FIFTEEN
65
-
38
-
2
7

SIXTEEN
96
-
33
-
6
9

SEVENTEEN
109
-
37
-
1
8

EIGHTEEN
73
-
46
-
1
8

NINETEEN
86
-
41
-
5
6

TWENTY
107
-
26
-
8
9

TWENTYONE
141
-
42
-
6
9

TWENTYTWO
165
-
39
-
3
11

TWENTYTHREE
163
-
55
-
1
10

TWENTYFOUR
167
-
50
-
5
10

TWENTYFIVE
149
-
50
-
5
9

TWENTYSIX
159
-
42
-
6
11

TWENTYSEVEN
172
-
46
-
1
11

TWENTYEIGHT
156
-
57
-
3
10

TWENTYNINE
149
-
50
-
5
6

THIRTY
100
-
37
-
1
9

THIRTYONE
134
-
53
-
8
9

THIRTYTWO
158
-
50
-
5
11

THIRTYTHREE
156
-
66
-
3
10

THIRTYFOUR
160
-
61
-
7
10

THIRTYFIVE
142
-
61
-
7
9

THIRTYSIX
152
-
53
-
8
11

THIRTYSEVEN
165
-
57
-
3
11

THIRTYEIGHT
149
-
68
-
5
10

THIRTYNINE
142
-
61
-
7
5

FORTY
84
-
30
-
3
8

FORTYONE
118
-
46
-
1
8

FORTYTWO
142
-
43
-
7
10

FORTYTHREE
140
-
59
-
5
9

FORTYFOUR
144
-
54
-
9
9

FORTYFIVE
126
-
54
-
9
8

FORTYSIX
136
-
46
-
1
10

FORTYSEVEN
149
-
50
-
5
10

FORTYEIGHT
133
-
61
-
7
9

FORTYNINE
126
-
54
-
9
5

FIFTY
66
-
30
-
3
8

FIFTYONE
100
-
46
-
1
8

FIFTYTWO
124
-
43
-
7
10

FIFTYTHREE
122
-
59
-
5
9

FIFTYFOUR
126
-
54
-
9
9

FIFTYFIVE
108
-
54
-
9
8

FIFTYSIX
118
-
46
-
1
10

FIFTYSEVEN
131
-
50
-
5
10

FIFTYEIGHT
115
-
61
-
7
9

FIFTYNINE
108
-
54
-
9
5

SIXTY
97
-
25
-
7
8

SIXTYONE
131
-
41
-
5
8

SIXTYTWO
155
-
38
-
2
10

SIXTYTHREE
153
-
54
-
9
9

SIXTYFOUR
157
-
49
-
4
9

SIXTYFIVE
139
-
49
-
4
8

SIXTYSIX
149
-
41
-
5
10

SIXTYSEVEN
162
-
45
-
9
10

SIXTYEIGHT
146
-
56
-
2
9

SIXTYNINE
139
-
49
-
4
7

SEVENTY
110
-
29
-
2
10

SEVENTYONE
144
-
45
-
9
10

SEVENTYTWO
168
-
42
-
6
12

SEVENTYTHREE
166
-
58
-
4
11

SEVENTYFOUR
170
-
53
-
8
11

SEVENTYFIVE
152
-
53
-
8
10

SEVENTYSIX
162
-
45
-
9
12

SEVENTYSEVEN
175
-
49
-
4
12

SEVENTYEIGHT
159
-
60
-
6
11

SEVENTYNINE
152
-
53
-
8
6

EIGHTY
74
-
38
-
2
9

EIGHTYONE
108
-
54
-
9
9

EIGHTYTWO
132
-
51
-
6
11

EIGHTYTHREE
130
-
67
-
4
10

EIGHTYFOUR
134
-
62
-
8
10

EIGHTYFIVE
116
-
62
-
8
9

EIGHTYSIX
126
-
54
-
9
11

EIGHTYSEVEN
139
-
58
-
4
11

EIGHTYEIGHT
123
-
69
-
6
10

EIGHTYNINE
116
-
62
-
8
6

NINETY
87
-
33
-
6
9

NINETYONE
121
-
49
-
4
9

NINETYTWO
145
-
46
-
1
11

NINETYTHREE
143
-
62
-
8
10

NINETYFOUR
147
-
57
-
3
10

NINETYFIVE
129
-
57
-
3
9

NINETYSIX
139
-
49
-
4
11

NINETYSEVEN
152
-
53
-
8
11

NINETYEIGHT
136
-
64
-
1
10

NINETYNINE
129
-
57
-
3

 

 

 

LOOK AT THE FIVES LOOK AT THE FIVES LOOK AT THE FIVES THE FIVES THE FIVES

LOOK AT TH5 FIV5S LOOK AT THE FIV5S LOOK AT TH5 FIV5S TH5 FIV5S TH5 FIV5S

 

123456789

ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

O55 T5O THR55 FOUR FIV5 SIX S5V55 5IGHT 5I55

 

 

10 11 12 13 14 15 16 17 18

TEN ELEVEN TWELVE THIRTEEN FOURTEEN FIFTEEN SIXTEEN SEVENTEEN EIGHTEEN

T55 5L5V55 T55LV5 THIRT555 FOURT555 FIFT555 SIXT555 S5V55T555 5IGHT555

 

 

19 20 21 22V 23 24 25 26 27

NINETEEN TWENTY TWENTYONE TWENTYTWO TWENTYTHREE TWENTYFOUR TWENTYFIVE TWENTYSIX TWENTYSEVEN

5I55T555 T555TY T555TYO55 T555TYT5O T555TYTHR55 T555TYFOUR T555TYFIVE T555TYSIX T555TYS5V55

 

 

28 29 30 31 32 33 34 35 36

TWENTYEIGHT TWENTYNINE THIRTY THIRTYONE THIRTYTWO THIRTYTHREE THIRTYFOUR THIRTYFIVE THIRTYSIX

T555TY5IGHT T555TY5I55 THIRTY THIRTYONE THIRTYTWO THIRTYTHREE THIRTYFOUR THIRTYFIV5 THIRTYSIX

 

 

37 38 39 40 41 42 43 44 45

THIRTYSEVEN THIRTYEIGHT THIRTYNINE FORTY FORTYONE FORTYTWO FORTYTHREE FORTY FOUR FOURTY FIVE

THIRTYS5V55 THIRTY5IGHT THIRTY5I55 FORTY FORTYO55 FORTYT5O FORTYTHR55 FORTY FOUR FORTY FIV5

 

 

46 47 48 49 50 51 52 53 54

FORTYSIX FORTYSEVEN FORTYEIGHT FORTYNINE FIFTY FIFTYONE FIFTYTWO FIFTYTHREE FIFTYFOUR

FORTYSIX FORTYS5VE5 FORTY5IGHT FORTY5I55 FIFTY FIFTYO55 FIFTYT5O FIFTYTHR55 FIFTYFOUR

 

 

55 56 57 58 59 60 61 62 63

FIFTYFIVE FIFTYSIX FIFTYSEVEN FIFTYEIGHT FIFTYNINE SIXTY SIXTYONE SIXTYTWO SIXTYTHREE

FIFTYFIV5 FIFTYSIX FIFTYS5V55 FIFTY5IGHT FIFTY5I55 SIXTY SIXTYO55 SIXTYT5O SIXTYTHR55

 

 

64 65 66 67 68 69 70 71 72

SIXTYFOUR SIXTYFIVE SIXTYSIX SIXTYSEVEN SIXTYEIGHT SIXTYNINE SEVENTY SEVENTYONE SEVENTYTWO

SIXTYFOUR SIXTYFIV5SIXTYSIX SIXTYS5V55 SIXTY5IGHT SIXTY5I55 S5V55TY S5V55TYO55 S5V55TYT5O

 

 

73 74 75 76 77 78 79 80 81

SEVENTYTHREE SEVENTYFOUR SEVENTYFIVE SEVENTYSIX SEVENTYSEVEN SEVENTYEIGHT SEVENTYNINE EIGHTY

EIGHTYONE

5IGHTYO55

S5V55TYTHR55 S5V55TYFOUR S5V55TYFIV5 S5V55TYSIX S5V55TYS5V55 S5V55TY5IGHT S5V55TY5I55 5IGHTY

 

 

82 83 84 85 86 87 88 89 90

EIGHTYTWO EIGHTYTHREE EIGHTYFOUR EIGHTYFIVE EIGHTY SIX EIGHTY SEVEN EIGHTYNINE NINETY

5IGHTYT5O 5IGHTYTHR55 5IGHTYFOUR 5IGHTYFIV5 5IGHTY SIX 5IGHTY S5V55 5IGHTY5I55 5I55TY

 

 

90 91 92 93 94 95 96 97 98 99

NINETY NINETYONE NINETYTHREE NINETYFOUR NINETYFIVE NINETYSIX NINETYSEVEN NINETYEIGHT NINETYNINE

5I55TY 5I55TYO55 5I55TYTHR55 5I55TYFOUR 5I55TYFIV5 5I55TYSIX 5I55TYS5V55 5I55TY5IGHT 5I55TY5I55

 

 

ZERO - NINE x 2
ONE THREE
FOUR FIVE NINE
SIX SEVEN
THREE SEVEN
TWO EIGHT
ONE SIX
THREE, SIX, FIVE
THREE SIX, THREE, SIX
SIXTYTHREE
SIXTYTHREE, SIXTY, THREE, SIXTYTHREE
SIXTY THREE, SIXT, YT, H, R, EE, SIXTYTHREE
THIRTY SIX, THIRTY, SIX
THIRTY SIX, SIXTY THREE
SIXTY NINE, NINETY SIX
TWENTY SEVEN, SEVENTY TWO
INCLUSIVE NUMBERS, NINE TO NINETY NINE, ZERO
NINE, EIGHTEEN, TWENTY SEVEN, THIRTY SIX, FORTY FIVE, FIFTY FOUR,
SIXTY THREE, SEVENTY TWO, EIGHTY ONE, NINETY NINE
ZERO, NINE, EIGHTEEN, TWENTY SEVEN, THIRTY SIX, FORTY FIVE, FIFTY
FOUR, SIXTY THREE, SEVENTY TWO, EIGHTY ONE, NINETY NINE
FORTY FIVE, FIFTY FOUR, SIXTY THREE, EIGHTY ONE
EIGHTEEN, THIRTY SIX
ZERO, EIGHTEEN, THIRTY SIX, FIFTY FOUR, SEVENTY TWO, NINE,
TWENTY SEVEN, FORTY FIVE, SIXTY THREE, EIGHTY ONE
EIGHTEEN, THIRTY SIX, FIFTY FOUR, SEVENTY TWO
NINE, TWENTY SEVEN, FORTY FIVE, SIXTY THREE, EIGHTY ONE
NINE, NINETY NINE
NINE NINETY NINE
ELEVEN, TWENTY TWO, THIRTY THREE, FORTY FOUR, FIFTY FIVE, SIXTY SIX,
SEVENTY SEVEN, EIGHTY EIGHT, NINETY NINE
ONE THREE FIVE SEVEN NINE, TWO FOUR SIX EIGHT NINE
NINETY SIX, SIXTY NINE
NINETY NINE, EIGHTY EIGHT
FORTY FOUR, FIFTY FIVE
EIGHTY ONE, FIFTY FOUR
ZERO, EIGHTEEN, TWENTY SEVEN, SEVENTY TWO
NINE ELEVEN
FOURTEEN, FOURTEEN
FOUR ONE
FIFTY FOUR
FORTY FIVE
ELEVEN TWELVE
T
 
THE CALENDAR, THE, CALENDAR
NINE ELEVEN
KNOW DIVINE LOVE, KNOW GODS LOVE, KNOW NAMES OF GOD

 

 

 

 

4

ZERO

64

28

1
3

ONE
34
16
7
3

TWO
58
13
4
5

THREE
56
29
2
4

FOUR
60
24
6
4

FIVE
42
24
6
3

SIX
52
16
7
5

SEVEN
65
20
2
5

EIGHT
49
31
4
4

NINE
42
24
6
40
-
522
225
45
4+0
-
5+2+2
2+2+5
4+5
4
-
9
9
9

 

 

0
Z
=
8
4

ZERO

64

28

1
1
O
=
6
3

ONE
34
16
7
2
T
=
2
3

TWO
58
13
4
3
T
=
2
5

THREE
56
29
2
4
F
=
6
4

FOUR
60
24
6
5
F
=
6
4

FIVE
42
24
6
6
S
=
1
3

SIX
52
16
7
7
S
=
1
5

SEVEN
65
20
2
8
E
=
5
5

EIGHT
49
31
4
9
N
=
5
4

NINE
42
24
6
45
42
40
-
522
225
45
4+5
4+2
4+0
-
5+2+2
2+2+5
4+5
9
6
4
-
9
9
9

 

 

1
-
O
=
6
-
3

ONE
34
16
7
3
-
T
=
2
-
5

THREE
56
29
2
4
-
-
-
8
-
8
-
90
45
9
-
-
-
-
-
-
-
9+0
4+5
-
4
-
-
-
-
8
-
9
9
9

 

 

4
-
F
=
6
-
4

FOUR
60
24
6
5
-
F
=
6
-
4

FIVE
42
24
6
9
-
N
=
5
-
4

NINE
42
24
6
18
-
-
-
17
-
12
-
144
72
18
1+8
-
-
-
1+7
-
1+2
-
1+4+4
7+2
1+8
9
-
-
-
8
-
3
-
9
9
9

 

 

6
-
S
=
1
-
3

SIX
52
16
7
7
-
S
=
1
-
5

SEVEN
65
20
2
13
-
-
-
2
-
8
-
117
36
9
1+3
-
-
-
-
-
-
-
1+1+7
2+2+5
-
4
-
-
-
2
-
8
-
9
9
9

 

 

3
-
T
=
2
-
5

THREE
56
29
2
7
-
E
=
1
-
5

SEVEN
65
20
2
10
-
-
3
-
10
-
121
49
4
1+0
-
-
-
-
1+0
-
1+2+1
4+9
-
1
-
-
3
-
1
-
4
13
4
-
-
-
-
-
-
-
1+3
-
1
-
3
-
1
-
4
4
4

 

 

2
-
T
=
2
-
3

TWO
58
13
4
8
-
E
=
5
-
5

EIGHT
49
31
4
10
-
-
7
-
8
-
107
44
8
1+0
-
-
-
-
-
-
1+0+7
2+2+5
4+5
1
-
-
7
-
8
-
8
8
8

 

 

1
-
O
=
6
-
3

ONE
34
16
7
6
-
S
=
1
-
3

SIX
52
16
7
7
-
-
-
7
-
6
-
86
32
14
-
-
-
-
-
-
-
-
8+6
3+2
1+4
7
-
-
-
7
-
6
-
14
5
5
-
-
-
-
-
-
-
-
1+4
-
-
7
7
6
-
5
5
5

 

 

5
THREE
56
29
2
3
SIX
52
25
7
4
FIVE
42
24
6

 

 

-
-
-
THREE SIX
-
-
-
3
-
5
THREE
56
29
2
6
-
3
SIX
52
25
7
9
-
8
THREE SIX
108
54
9
-
-
-
-
1+0+8
5+4
-
9
-
8
THREE SIX
9
9
9

 

 

-13
S
I
X
T
Y
T
H
R
E
E
-
-
-
-
-
  
-
1
9
6
-
-
-
8
-
-
-
+
=
24
2+4
=
6
-
10
9
24
-
-
-
8
-
-
-
+
=
60
6+0
=
6
10
S
I
X
T
Y
T
H
R
E
E
-
-
-
-
-
-
-
19
9
24
20
25
20
8
18
5
5
+
=
153
1+5+3
=
9
-
1
9
6
2
7
2
8
9
5
5
+
=
54
5+4
=
9
10
S
I
X
T
Y
T
H
R
E
E
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
+
=
1
-
-
1
-
-
-
-
2
-
2
-
-
-
-
+
=
4
-
-
4
-
-
--
-
-
-
-
-
-
5
5
+
=
10
1+0
=
1
-
-
-
6
-
-
-
-
-
-
-
+
=
6
-
-
6
-
-
-
-
-
7
-
-
-
-
-
+
=
7
-
-
7
-
-
-
-
-
-
-
8
-
-
-
+
=
8
-
-
8
-
-
-
-
-
-
-
-
9
-
-
+
=
9
-
-
9
10
S
I
X
T
Y
T
H
R
E
E
-
-
-
-
-
-

 

 

-
SIXTY THREE
-
-
-
5
SIXTY
97
34
7
5
THREE
56
29
2
10
SIXTY THREE
153
63
9
1+0
-
1+5+3
6+3
-
1
SIXTY THREE
9
9
9

 

 

-
SIXTY THREE
-
-
-
4
S+I+X+T
72
27
9
2
Y+T
45
9
9
1
H
8
8
8
1
R
18
9
9
2
E+E
10
1
1
10
SIXTY THREE
153
54
36
1+0
-
1+5+3
5+4
3+6
1
SIXTY THREE
9
9
9

 

 

-
THIRTY SIX
-
-
-
6
THIRTY
100
37
1
3
SIX
52
25
7
9
THIRTY SIX
152
62
8
-
-
1+5+2
6+2
-
9
THIRTY SIX
8
8
8

 

 

9
THIRTY SIX
152
62
8
10
SIXTY THREE
153
54
9
19
-
305
116
17
1+9
-
3+0+5
1+1+6
1+7
10
-
8
8
8

 

 

69
-
9
SIXTY NINE
139
58
4
96
-
9
NINETY SIX
139
58
4
165
-
18
-
278
116
8
1+6+5
-
1+8
-
2+7+8
1+1+6
-
12
-
9
-
17
8
8
1+2
-
-
1+7
-
-
3
-
9
-
8
8
8

 

 

11
TWENTY SEVEN
172
55
1
10
SEVENTY TWO
172
55
1
21
-
344
110
2
2+1
-
3+4+4
1+1+0
-
3
-
11
2
2
-
-
1+1
-
-
3
-
2
2
2

 

 

INCLUSIVE NUMBERS
- - -
NINE TO NINETY NINE
1253
515
2
ZERO
64
28
1
-
1317
543
3
-
1+3+1+7
5+4+3
-
-
12
12
3
-
1+2
1+2
-
-
3
3
3

 

 

9
-
4
NINE
42
24
6
18
-
8
EIGHTEEN
73
46
1
27
-
11
TWENTY SEVEN
172
55
1
36
-
9
THIRTY SIX
152
62
8
45
-
9
FORTY FIVE
126
54
9
54
-
9
FIFTY FOUR
126
54
9
63
-
10
SIXTY THREE
153
54
9
72
-
10
SEVENTY TWO
172
55
1
81
-
9
EIGHTY ONE
108
54
9
99
-
10
NINETY NINE
129
57
3
504
-
89
-
1253
515
56
5+0+4
-
8+9
-
1+2+5+3
5+1+5
5+6
9
-
17
-
11
11
11
-
-
1+7
-
1+1
1+1
1+1
9
-
8
-
2
2
2

 

 

0
-
4
ZERO
64
28
1
9
-
4
NINE
42
24
6
18
-
8
EIGHTEEN
73
46
1
27
-
11
TWENTY SEVEN
172
55
1
36
-
9
THIRTY SIX
152
62
8
45
-
9
FORTY FIVE
126
54
9
54
-
9
FIFTY FOUR
126
54
9
63
-
10
SIXTY THREE
153
54
9
72
-
10
SEVENTY TWO
172
55
1
81
-
9
EIGHTY ONE
108
54
9
405
-
83
-
1188
486
54
4+0+5
8+3
-
1+1+8+8
4+8+6
5+4
9
  
11
18
18
9
-
1
1+1
-
1+8
1+8
-
-
-
2
-
9
9
9
99
-
10
NINETY NINE
129
57
3

 

 

9
FORTY FIVE
126
54
9
9
FIFTY FOUR
126
54
9
18
-
252
108
18
1+8
-
2+5+2
1+0+8
1+8
9
-
9
9
9

 

 

45
-
9
FORTY FIVE
126
54
9
54
-
9
FIFTY FOUR
126
54
9
63
-
10
SIXTY THREE
153
54
9
81
-
9
EIGHTY ONE
108
54
9
243
-
37
-
513
216
36
2+4+3
3+7
-
5+1+3
2+1+6
3+6
9
-
10
-
9
9
9

 

 

18
-
8
EIGHTEEN
73
46
1
36
-
9
THIRTY SIX
152
62
8
54
-
17
Add to reduce
225
108
9
5+4
1+7
Reduce to deduce
2+2+5
1+0+8
-
9
-
8
Essence of number
9
9
9

 

 

18
-
8
EIGHTEEN
73
46
1
36
-
9
THIRTY SIX
152
62
8
54
-
9
FIFTY FOUR
126
54
9
72
-
10
SEVENTY TWO
172
55
1
180
-
36
-
523
217
19
1+8+0
3+6
-
5+2+3
2+1+7
1+9
9
  
9
  
10
10
10
-
1
-
-
1+0
1+0
1+0
9
-
9
-
1
1
1

 

 

9
-
4
NINE
42
24
6
27
-
11
TWENTY SEVEN
172
55
1
45
-
9
FORTY FIVE
126
54
9
63
-
10
SIXTY THREE
153
54
9
81
-
9
EIGHTY ONE
108
54
9
225
-
43
-
601
241
34
2+2+5
4+3
-
6+0+1
2+4+1
3+4
9
  
7
-
7
7
7

 

 

4
NINE
42
24
6
10
NINETY NINE
129
57
3
14
Add to reduce
171
81
9
1+4
Reduce to dedeuce
1+7+1
8+1
-
5
Essence of number
9
9
9

 

 

14
NINE NINETY NINE
171
81
9

 

 

4
 NINE
42
24
6
6
 ELEVEN
72
36
9

 

 

11
-
6
ELEVEN
63
27
9
22
-
9
TWENTY TWO
165
39
3
33
-
11
THIRTY THREE
156
66
3
44
-
9
FORTY FOUR
144
54
9
55
-
9
FIFTY FIVE
108
54
9
66
-
8
SIXTY SIX
149
59
5
77
-
12
SEVENTY SEVEN
175
67
4
88
-
11
EIGHTY EIGHT
123
69
6
99
-
10
NINETY NINE
129
57
3
580
-
85
-
1212
492
51
5+8+0
-
8+5-
-
1+2+1+2
4+9+2
5+1
13
-
13
-
6
15
6
1+4
-
1+4
-
-
1+5
-
5
-
5
-
6
6
6

 

 

O
=
6
3
ONE
34
16
7
T
=
2
5
THREE
56
29
2
F
=
6
4
FIVE
42
24
6
S
=
1
5
SEVEN
65
20
2
N
=
5
4
NINE
42
24
6
-
-
20
21
-
239
113
23
-
-
2+0
2+1
-`
2+3+9
1+1+3
2+3
-
-
2
3
-
14
5
5
-
-
-
-
-`
1+4
-
-
-
-
2
3
-
5
5
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
3
TWO
58
13
4
F
=
6
4
FOUR
60
24
6
S
=
1
3
SIX
52
16
7
E
=
1
5
EIGHT
49
31
4
-
-
10
15
-
219
84
21
-
-
1+0
1+5
-`
2+1+9
8+4
2+1
-
-
1
6
-
12
12
3
-
-
-
-
-`
1+2
1+2
-
-
-
1
6
-
3
3
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Z
=
8
4
ZERO
64
28
1

 

 

9
NINETY SIX
139
58
4
9
SIXTY NINE
139
58
4

 

 

99
-
10
NINETY NINE
129
57
3
88
11
11
EIGHTY EIGHT
123
69
6
187
-
21
-
252
126
9
1+8+7
-
2+1
-
2+5+2
1+2+6
-
16
-
3
-
9
9
9
1+6
-
-
-
-
-
-
7
--
3
-
9
9
9

 

 

44
-
9
FORTY FOUR
144
54
9
55
11
9
FIFTY FIVE
108
54
9
99
-
18
-
252
108
18
9+9
-
1+8
-
2+5+2
1+0+8
1+8
18
-
9
-
9
9
9
1+8
-
-
-
-
-
-
9
-
9
-
9
9
9

 

 

81
-
9
EIGHTY ONE
108
54
9
54
11
9
FIFTY FOUR
126
54
9
135
-
18
-
234
108
18
1+3+5
1+8
-
2+3+4
1+0+8
1+8
9
-
9
-
9
9
9

 

 

0
-
4
ZERO
64
28
1
18
-
8
EIGHTEEN
73
46
1
27
-
11
TWENTY SEVEN
172
55
1
72
-
10
SEVENTY TWO
172
55
1
117
-
33
-
481
184
4
1+1+7
-
3+3
-
4+8+1
1+8+4
-
9
-
6
  
13
13
4
-
-
-
-
1+3
1+3
-
99
-
6
-
4
4
4

 

 

8
FOURTEEN
-
-
-
-
F
6
6
6
-
O+U+R
54
18
9
9
T+E+E+N
44
17
8
8
FOURTEEN
104
41
23
-
-
1+0+4
4+1
2+3
8
FOURTEEN
5
5
5

 

 

8
FOURTEEN
-
-
-
-
F+O+U+R
60
24
6
9
T+E+E+N
44
17
8
8
FOURTEEN
104
41
14
-
-
1+0+4
4+1
1+4
8
FOURTEEN
5
5
5

 

 

F
=
6
4
FOUR
60
24
6
O
=
6
3
ONE
34
16
7
-
-
12
7
-
94
40
13
-
-
1+2
 -
-
9+4
4+0
1+3
-
-
3
7
-
13
4
4
-
-
-
8
THIRTEEN
99
45
9

 

 

9
FIFTY FOUR
-
-
-
-
FIFTY
66
30
3
9
FOUR
60
24
6
9
FIFTY FOUR
126
54
9
-
-
1+2+6
5+4
-
9
FIFTY FOUR
9
9
9

 

 

9
FORTY FIVE
-
-
-
-
FORTY
84
30
3
4
FIVE
42
24
6
9
FORTY FIVE
126
54
9
-
-
1+2+6
5+4
-
9
FORTY FIVE
9
9
9

 

-
TEN
-
-
-
1
T
20
2
2
1
E
5
5
5
1
N
14
5
5
3
TEN
39
12
12
-
-
3+9
1+2
1+2
3
TEN
12
3
3
-
-
3+9
-
-
3
TEN
12
3
3

 

 

-
3
T
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
-
-
-
14
+
=
14
1+4
=
5
-
5
=
5
-
3
T
E
N
-
-
-
-
-
--
-
-
-
-
-
-
2
5
-
+
=
7
-
=
7
-
7
=
7
-
-`
20
5
-
+
=
25
2+5
=
7
-
7
=
7
-
3
T
E
N
-
-
-
-
-
--
-
-
-
-
-
-
20
5
14
+
=
39
3+9
=
12
1+2
3
=
3
-
-
2
5
5
+
=
12
1+2
=
3
-
3
=
3
-
3
T
E
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
2
3
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
-
-
38
3
T
E
N
-
-
7
-
-
3
-
12
-
3
3+8
-
-
-
-
-
-
-
-
-
-
-
1+2
-
-
11
3
T
E
N
-
-
7
-
-
3
-
3
-
3
1+1
-
2
5
5
-
-
-
-
-
-
-
-
-
-
2
3
T
E
N
-
-
7
-
-
3
-
3
-
3

 

 

-
15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
+
=
10
1+3
=
5
=
1
=
1
-
-
-
-
14
-
-
-
-
-
-
14
-
-
-
-
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
2
5
-
-
5
3
5
4
5
-
-
2
5
5
3
4
5
+
=
53
5+3
=
8
-
8
=
8
-
-`
20
5
-
-
5
12
5
22
5
-
-
20
23
5
12
22
5
+
=
161
1+6+1
=
8
-
8
=
8
-
15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
20
5
14
-
5
12
5
22
5
14
-
20
23
5
12
22
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
-
2
5
5
-
5
3
5
4
5
5
-
2
5
5
3
4
5
+
=
63
6+3
=
9
-
9
=
9
-
15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
-
6
-
--
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
5
5
-
5
-
5
-
5
5
-
-
5
5
-
-
5
-
-
5
occurs
x
9
=
45
4+5
9
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
31
15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
14
-
-
15
-
63
-
27
3+1
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+4
-
-
1+5
-
6+3
-
2+7
4
6
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
5
-
-
6
-
9
-
9
-
-
2
5
5
-
5
3
5
4
5
5
-
2
5
5
3
4
5
-
-
-
-
-
-
-
-
-
-
4
6
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
5
-
-
6
-
9
-
9

 

 

15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
+
=
10
1+3
=
5
=
1
=
1
-
-
-
14
-
-
-
-
-
-
14
-
-
-
-
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
2
5
-
-
5
3
5
4
5
-
-
2
5
5
3
4
5
+
=
53
5+3
=
8
-
8
=
8
-`
20
5
-
-
5
12
5
22
5
-
-
20
23
5
12
22
5
+
=
161
1+6+1
=
8
-
8
=
8
15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
20
5
14
-
5
12
5
22
5
14
-
20
23
5
12
22
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
2
5
5
-
5
3
5
4
5
5
-
2
5
5
3
4
5
+
=
63
6+3
=
9
-
9
=
9
15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
-
6
--
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
-
8
-
-
5
5
-
5
-
5
-
5
5
-
-
5
5
-
-
5
-
-
5
occurs
x
9
=
45
4+5
9
15
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
14
-
-
15
-
63
-
27
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+4
-
-
1+5
-
6+3
-
2+7
6
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
5
-
-
6
-
9
-
9
-
2
5
5
-
5
3
5
4
5
5
-
2
5
5
3
4
5
-
-
-
-
-
-
-
-
-
-
6
T
E
N
-
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
5
-
-
6
-
9
-
9

 

 

-
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
-
-
-
-
-
14
-
-
-
-
-
-
-
+
=
14
1+4
=
5
-
5
=
5
-
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
5
3
5
4
5
-
-
2
5
5
3
4
5
+
=
46
4+6
=
10
1+0
1
=
1
-
-`
5
12
5
22
5
-
-
20
23
5
12
22
5
+
=
136
1+3+6
=
10
1+0
1
=
1
-
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
5
12
5
22
5
14
-
20
23
5
12
22
5
+
=
150
1+5+0
=
6
-
6
=
6
-
-
5
3
5
4
5
5
-
2
5
5
3
4
5
+
=
51
5+1
=
6
-
6
=
6
-
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
-
6
-
--
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
-
8
-
-
5
-
5
-
5
5
-
-
5
5
-
-
5
-
-
5
occurs
x
7
=
35
3+5
8
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
31
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
14
-
-
12
-
51
-
24
3+1
1+2
5
-
5
-
5
5
-
-
5
5
-
-
5
-
-
1+4
-
-
1+2
-
5+1
-
2+4
4
3
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
5
-
-
3
-
6
-
6
-
-
5
3
5
4
5
5
-
2
5
5
3
4
5
-
-
-
-
-
-
-
-
-
-
4
3
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
5
-
-
3
-
6
-
6

 

 

-
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
-
-
-
-
-
14
-
-
-
-
-
-
-
+
=
14
1+4
=
5
-
5
=
5
-
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
5
3
5
4
5
-
-
2
5
5
3
4
5
+
=
46
4+6
=
10
1+0
1
=
1
-
-`
5
12
5
22
5
-
-
20
23
5
12
22
5
+
=
136
1+3+6
=
10
1+0
1
=
1
-
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
--
-
-
-
-
-
-
5
12
5
22
5
14
-
20
23
5
12
22
5
+
=
150
1+5+0
=
6
-
6
=
6
-
-
5
3
5
4
5
5
-
2
5
5
3
4
5
+
=
51
5+1
=
6
-
6
=
6
-
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
-
6
-
--
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
-
8
-
-
5
-
5
-
5
5
-
-
5
5
-
-
5
-
-
5
occurs
x
7
=
35
3+5
8
31
12
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
14
-
-
12
-
51
-
24
3+1
1+2
5
-
5
-
5
5
-
-
5
5
-
-
5
-
-
1+4
-
-
1+2
-
5+1
-
2+4
4
3
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
5
-
-
3
-
6
-
6
-
-
5
3
5
4
5
5
-
2
5
5
3
4
5
-
-
-
-
-
-
-
-
-
-
4
3
E
L
E
V
E
N
-
T
W
E
L
V
E
-
-
5
-
-
3
-
6
-
6

 

 

-
THE CALENDAR
-
-
-
3
THE
33
15
6
8
CALENDAR
58
31
4
11
-
91
46
10
1+1
-
9+1
4+6
1+0
2
-
10
10
1
-
-
1+0
1+0
-
2
-
1
1
1

 

 

DAILY MAIL

EERIE REPITITION OF THE 'MYSTICAL' NUMBER 7

Eleanor Mayne

Date of report missing, appeared between 9th and 15th of July

Page 19

Few people can have failed to spot the symmetry in the date of the London bombings: 7/7.

And some are already claiming that a closer study of the numbers around the attacks reveals a bizarrely frequent occurrence of the single digit 'seven' considered a mystical number by numerologists,

After any major incident, and particularly those with tragic consequences, many people have a need to search for some kind of order in their surroundings.

Websites are already pointing out that the London attacks appear to show a similar pattern to one that emerged following the 9/11 attack on America - only it is the number seven rather than 11 that keeps cropping up.

Reducing the date of the London attacks - 7/7/2005 - gives the the three repeated digits 7, 7 and 2 + 5 = 7. Adding together all the figures of the date 7 + 7 + 2 + 5 gives 21, a multiple of seven. The serial number of the bus struck at Tavistock Square was '17758', which adds up to 28, again a multiple of seven. The total time from the first attack at 8.51 am to the final one at 9.47am was 56 minutes another multiple of seven. The attacks began at 8.51am, the digits of which add up to 14, or two times seven. And Al Qaeda has seven letters.

Numerologists, who attribute magical properties to numbers believe that 'seven' has a special significance as a mystical number.

Ironically, it has long been considered lucky in most major cultures and religions - there are seven graces, wonders of the world, ages of man, days of creation, days of the week, phases of the moon, biblical plagues, continents and circles of the universe.

In Islam, seven is the 'perfect number'. There are seven layers of heaven and the sacred Ka'aba stone at Mecca is circumambulated seven times by Muslim pilgrims, representing the seven attributes of God.

Page 19

"Within weeks of the devastating attacks on New York and the Pentagon in 2001, e-mails were circulated pointing out the astonishing repetition of the number '11' in the events."

 

4
 NINE
42
24
6
6
 ELEVEN
72
36
9

 

"The date expressed in US terms was 9/11. There were 111 days until the end of the year and Flight 11 was the first flight to hit the Twin Towers. September 11 is the 254th day of the year, and 2 + 5 + 4 are Eleven.

New York City has 11 letters, as does Afghanistan and The Pentagon. New York was the 11th state added to the union. The number of another doomed aeroplane that day - Flight 777 - is a multiple of 11."

 

Page 19

"Within weeks of the devastating attacks on New York and the Pentagon in 2001, e-mails were circulated pointing out the astonishing repetition of the number '11' in the events.

4
 NINE
42
24
6
6
 ELEVEN
72
36
9

 

The date expressed in US terms was 9/11. There were 111 days until the end of the year and Flight 11 was the first flight to hit the Twin Towers. September 11 is the 254th day of the year, and 2 + 5 + 4 are Eleven

 

 

S
=
1
-
4
SIGN
49
22
4
S
=
1
-
5
SIGNS
68
23
5
S
=
1
-
6
SIGNAL
62
26
8
S
=
1
-
7
SIGNALS
81
27
9
S
=
1
-
6
SIGNALLED
164
38
2
S
=
1
-
7
SIGNALLING
104
50
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SYMBOL
86
23
5
S
=
1
-
7
SYMBOLS
105
24
6
S
=
1
-
9
SYMBOLISE
119
38
2
S
=
1
-
9
SYMBOLOGY
133
43
7
S
=
1
-
10
SYMBOLISED
123
42
6
S
=
1
-
11
SYMBOLISING
144
54
9
S
=
1
-
12
SYMBOLOGICAL
133
52
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
N
=
5
-
6
NUMBER
73
28
1
N
=
5
-
7
NUMBERS
92
29
2
N
=
5
-
7
NUMERAL
84
30
3
N
=
5
-
8
NUMERALS
103
31
4
N
=
5
-
9
NUMERICAL
96
42
6
N
=
5
-
8
NUMBERED
82
37
1
N
=
5
-
9
NUMBERING
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
D
=
4
-
5
DIGIT
49
31
4
D
=
4
-
6
DIGITS
68
32
5
D
=
4
-
7
DIGITAL
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
L
=
3
-
6
LETTER
80
26
8
L
=
3
-
7
LETTERS
99
27
9
L
=
3
-
8
LETTERED
89
35
9
L
=
3
-
9
LETTERING
110
56
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
C
=
3
-
5
COUNT
73
19
1
C
=
3
-
6
COUNTS
92
20
2
C
=
3
-
7
COUNTED
82
28
1
C
=
3
-
8
COUNTING
103
40
4
C
=
3
-
9
COUNTLESS
128
29
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CYPHER
75
39
3
C
=
3
-
7
CYPHERS
94
40
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
7
ENCRYPT
101
28
1
E
=
5
-
8
ENCRYPTS
120
39
3
E
=
5
-
9
ENCRYPTED
110
47
2
E
=
5
-
10
ENCRYPTION
139
58
4
E
=
5
-
10
ENCRYPTING
131
59
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
-
4
GODS
45
18
9
C
=
3
-
5
CYCLE
48
21
3
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CIRCLE
68
32
5
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CIRCLE
68
32
5
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
C
=
3
-
5
CYCLE
48
21
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
C
=
3
-
8
CREATORS
99
36
9
D
=
4
-
6
DIVINE
63
36
9
E
=
5
-
7
ETERNAL
75
30
3
L
=
3
-
6
LIVING
73
37
1
M
=
4
-
4
MIND
40
22
4

 

 

-
13
T
H
E
-
D
I
G
I
T
A
L
-
A
G
E
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
9
-
9
-
-
-
-
-
-
-
+
=
26
2+6
=
8
8
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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z = 351 = Z Y X W V U T S R Q P O N M L K J I H G F E D C B A

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z = 126 = Z Y X W V U T S R Q P O N M L K J I H G F E D C B A

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z = 9 = Z Y X W V U T S R Q P O N M L K J I H G F E D C B A

 

 

ABCDEFGH I JKLMNOPQ R STUVWXYZ = 351 = ZYXWVUTS R QPONMLKJ I HGFEDCBA

ABCDEFGH I JKLMNOPQ R STUVWXYZ = 126 = ZYXWVUTS R QPONMLKJ I HGFEDCBA

ABCDEFGH I JKLMNOPQ R STUVWXYZ = 9 = ZYXWVUTS R QPONMLKJ I HGFEDCBA

 

 

www.merriam-webster.com/dictionary/algorithm

a procedure for solving a mathematical problem (as of finding the greatest common divisor) in a finite number of steps that frequently involves repetition of an ...

algorithm [ˈælgəˌrɪðəm]
n
1. (Mathematics) a logical arithmetical or computational procedure that if correctly applied ensures the solution of a problem Compare heuristic
2. (Mathematics) Logic Maths a recursive procedure whereby an infinite sequence of terms can be generated Also called algorism
[changed from algorism, through influence of Greek arithmos number]
algorithmic adj
aal·go·rithm (lg-rm)
n.
A step-by-step problem-solving procedure, especially an established, recursive computational procedure for solving a problem in a finite number of steps.
algorithmically adv

algorithm (lg-rthm)
A finite set of unambiguous instructions performed in a prescribed sequence to achieve a goal, especially a mathematical rule or procedure used to compute a desired result. Algorithms are the basis for most computer programming.

Noun 1. algorithm - a precise rule (or set of rules) specifying how to solve some problem
algorithmic program, algorithmic rule
formula, rule - (mathematics) a standard procedure for solving a class of mathematical problems; "he determined the upper bound with Descartes' rule of signs"; "he gave us a general formula for attacking polynomials"
sorting algorithm - an algorithm for sorting a list
stemming algorithm, stemmer - an algorithm for removing inflectional and derivational endings in order to reduce word forms to a common stem algorithm
any methodology for solving a certain kind of problem.
See also: Mathematics

 

 

Algorithm
From Wikipedia, the free encyclopedia

Flow chart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" (or true) (more accurately the number b in location B is greater than or equal to the number a in location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b). Similarly, IF A > B, THEN A ← A − B. The process terminates when (the contents of) B is 0, yielding the g.c.d. in A. (Algorithm derived from Scott 2009:13; symbols and drawing style from Tausworthe 1977).
In mathematics and computer science, an algorithm (i/ˈælɡərɪðəm/) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning.

More precisely, an algorithm is an effective method expressed as a finite list[1] of well-defined instructions[2] for calculating a function.[3] Starting from an initial state and initial input (perhaps empty),[4] the instructions describe a computation that, when executed, will proceed through a finite [5] number of well-defined successive states, eventually producing "output"[6] and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.[7]

Though al-Khwārizmī's algorism referred to the rules of performing arithmetic using Hindu-Arabic numerals and the systematic solution of linear and quadratic equations, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability"[8] or "effective method";[9] those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.[10]

Informal definition
For a detailed presentation of the various points of view around the definition of "algorithm" see Algorithm characterizations. For examples of simple addition algorithms specified in the detailed manner described in Algorithm characterizations, see Algorithm examples.
While there is no generally accepted formal definition of "algorithm," an informal definition could be "a set of rules that precisely defines a sequence of operations."[11] For some people, a program is only an algorithm if it stops eventually; for others, a program is only an algorithm if it stops before a given number of calculation steps.[12]

A prototypical example of an algorithm is Euclid's algorithm to determine the maximum common divisor of two integers; an example (there are others) is described by the flow chart above and as an example in a later section.

Boolos & Jeffrey (1974, 1999) offer an informal meaning of the word in the following quotation:

No human being can write fast enough, or long enough, or small enough† ( †"smaller and smaller without limit ...you'd be trying to write on molecules, on atoms, on electrons") to list all members of an enumerably infinite set by writing out their names, one after another, in some notation. But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.[13]

The term "enumerably infinite" means "countable using integers perhaps extending to infinity." Thus, Boolos and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be chosen from 0 to infinity. Thus an algorithm can be an algebraic equation such as y = m + n—two arbitrary "input variables" m and n that produce an output y. But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example):
Precise instructions (in language understood by "the computer")[14] for a fast, efficient, "good"[15] process that specifies the "moves" of "the computer" (machine or human, equipped with the necessary internally contained information and capabilities)[16] to find, decode, and then process arbitrary input integers/symbols m and n, symbols + and = ... and "effectively"[17] produce, in a "reasonable" time,[18] output-integer y at a specified place and in a specified format.
The concept of algorithm is also used to define the notion of decidability. That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules. In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension. From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term.

[edit] Formalization

Algorithms are essential to the way computers process data. Many computer programs contain algorithms that detail the specific instructions a computer should perform (in a specific order) to carry out a specified task, such as calculating employees' paychecks or printing students' report cards. Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system. Authors who assert this thesis include Minsky (1967), Savage (1987) and Gurevich (2000):

Minsky: "But we will also maintain, with Turing . . . that any procedure which could "naturally" be called effective, can in fact be realized by a (simple) machine. Although this may seem extreme, the arguments . . . in its favor are hard to refute".[19]

Gurevich: "...Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ... according to Savage [1987], an algorithm is a computational process defined by a Turing machine".[20]

Typically, when an algorithm is associated with processing information, data is read from an input source, written to an output device, and/or stored for further processing. Stored data is regarded as part of the internal state of the entity performing the algorithm. In practice, the state is stored in one or more data structures.

For some such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable).

Because an algorithm is a precise list of precise steps, the order of computation will always be critical to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom", an idea that is described more formally by flow of control.

So far, this discussion of the formalization of an algorithm has assumed the premises of imperative programming. This is the most common conception, and it attempts to describe a task in discrete, "mechanical" means. Unique to this conception of formalized algorithms is the assignment operation, setting the value of a variable. It derives from the intuition of "memory" as a scratchpad. There is an example below of such an assignment.

For some alternate conceptions of what constitutes an algorithm see functional programming and logic programming.

[edit] Expressing algorithms

Algorithms can be expressed in many kinds of notation, including natural languages, pseudocode, flowcharts, programming languages or control tables (processed by interpreters). Natural language expressions of algorithms tend to be verbose and ambiguous, and are rarely used for complex or technical algorithms. Pseudocode, flowcharts and control tables are structured ways to express algorithms that avoid many of the ambiguities common in natural language statements. Programming languages are primarily intended for expressing algorithms in a form that can be executed by a computer, but are often used as a way to define or document algorithms.

There is a wide variety of representations possible and one can express a given Turing machine program as a sequence of machine tables (see more at finite state machine, state transition table and control table), as flowcharts (see more at state diagram), or as a form of rudimentary machine code or assembly code called "sets of quadruples" (see more at Turing machine).

Representations of algorithms can be classed into three accepted levels of Turing machine description:[21]
1 High-level description:
"...prose to describe an algorithm, ignoring the implementation details. At this level we do not need to mention how the machine manages its tape or head." 2 Implementation description:
"...prose used to define the way the Turing machine uses its head and the way that it stores data on its tape. At this level we do not give details of states or transition function." 3 Formal description:
Most detailed, "lowest level", gives the Turing machine's "state table". For an example of the simple algorithm "Add m+n" described in all three levels see Algorithm examples.
[edit] Implementation

Most algorithms are intended to be implemented as computer programs. However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect looking for food), in an electrical circuit, or in a mechanical device.

[edit] Computer algorithms

Flowchart examples of the canonical Böhm-Jacopini structures: the SEQUENCE (rectangles descending the page), the WHILE-DO and the IF-THEN-ELSE. The three structures are made of the primitive conditional GOTO (IF test=true THEN GOTO step xxx) (a diamond), the unconditional GOTO (rectangle), various assignment operators (rectangle), and HALT (rectangle). Nesting of these structures inside assignment-blocks result in complex diagrams (cf Tausworthe 1977:100,114).
In computer systems, an algorithm is basically an instance of logic written in software by software developers to be effective for the intended "target" computer(s), in order for the target machines to produce output from given input (perhaps null).

"Elegant" (compact) programs, "good" (fast) programs : The notion of "simplicity and elegance" appears informally in Knuth and precisely in Chaitin:
Knuth: ". . .we want good algorithms in some loosely defined aesthetic sense. One criterion . . . is the length of time taken to perform the algorithm . . .. Other criteria are adaptability of the algorithm to computers, its simplicity and elegance, etc"[22] Chaitin: " . . . a program is 'elegant,' by which I mean that it's the smallest possible program for producing the output that it does"[23]
Chaitin prefaces his definition with: "I'll show you can't prove that a program is 'elegant'"—such a proof would solve the Halting problem (ibid).

Algorithm versus function computable by an algorithm: For a given function multiple algorithms may exist. This will be true, even without expanding the available instruction set available to the programmer. Rogers observes that "It is . . . important to distinguish between the notion of algorithm, i.e. procedure and the notion of function computable by algorithm, i.e. mapping yielded by procedure. The same function may have several different algorithms".[24]

Unfortunately there may be a tradeoff between goodness (speed) and elegance (compactness)—an elegant program may take more steps to complete a computation than one less elegant. An example of using Euclid's algorithm will be shown below.

Computers (and computors), models of computation: A computer (or human "computor"[25]) is a restricted type of machine, a "discrete deterministic mechanical device"[26] that blindly follows its instructions.[27] Melzak's and Lambek's primitive models[28] reduced this notion to four elements: (i) discrete, distinguishable locations, (ii) discrete, indistinguishable counters[29] (iii) an agent, and (iv) a list of instructions that are effective relative to the capability of the agent.[30]

Minsky describes a more congenial variation of Lambek's "abacus" model in his "Very Simple Bases for Computability".[31] Minsky's machine proceeds sequentially through its five (or six depending on how one counts) instructions unless either a conditional IF–THEN GOTO or an unconditional GOTO changes program flow out of sequence. Besides HALT, Minsky's machine includes three assignment (replacement, substitution)[32] operations: ZERO (e.g. the contents of location replaced by 0: L ← 0), SUCCESSOR (e.g. L ← L+1), and DECREMENT (e.g. L ← L − 1).[33] Rarely will a programmer have to write "code" with such a limited instruction set. But Minsky shows (as do Melzak and Lambek) that his machine is Turing complete with only four general types of instructions: conditional GOTO, unconditional GOTO, assignment/replacement/substitution, and HALT.[34]

Simulation of an algorithm: computer (computor) language: Knuth advises the reader that "the best way to learn an algorithm is to try it . . . immediately take pen and paper and work through an example".[35] But what about a simulation or execution of the real thing? The programmer must translate the algorithm into a language that the simulator/computer/computor can effectively execute. Stone gives an example of this: when computing the roots of a quadratic equation the computor must know how to take a square root. If they don't then for the algorithm to be effective it must provide a set of rules for extracting a square root.[36]

This means that the programmer must know a "language" that is effective relative to the target computing agent (computer/computor).

But what model should be used for the simulation? Van Emde Boas observes "even if we base complexity theory on abstract instead of concrete machines, arbitrariness of the choice of a model remains. It is at this point that the notion of simulation enters".[37] When speed is being measured, the instruction set matters. For example, the subprogram in Euclid's algorithm to compute the remainder would execute much faster if the programmer had a "modulus" (division) instruction available rather than just subtraction (or worse: just Minsky's "decrement").

Structured programming, canonical structures: Per the Church-Turing thesis any algorithm can be computed by a model known to be Turing complete, and per Minsky's demonstrations Turing completeness requires only four instruction types—conditional GOTO, unconditional GOTO, assignment, HALT. Kemeny and Kurtz observe that while "undisciplined" use of unconditional GOTOs and conditional IF-THEN GOTOs can result in "spaghetti code" a programmer can write structured programs using these instructions; on the other hand "it is also possible, and not too hard, to write badly structured programs in a structured language".[38] Tausworthe augments the three Böhm-Jacopini canonical structures:[39] SEQUENCE, IF-THEN-ELSE, and WHILE-DO, with two more: DO-WHILE and CASE.[40] An additional benefit of a structured program will be one that lends itself to proofs of correctness using mathematical induction.[41]

Canonical flowchart symbols[42]: The graphical aide called a flowchart offers a way to describe and document an algorithm (and a computer program of one). Like program flow of a Minsky machine, a flowchart always starts at the top of a page and proceeds down. Its primary symbols are only 4: the directed arrow showing program flow, the rectangle (SEQUENCE, GOTO), the diamond (IF-THEN-ELSE), and the dot (OR-tie). The Böhm-Jacopini canonical structures are made of these primitive shapes. Sub-structures can "nest" in rectangles but only if a single exit occurs from the superstructure. The symbols and their use to build the canonical structures are shown in the diagram.

 

 

EVOLVE LOVE EVOLVE

LOVES SOLVE LOVES

EVOLVE LOVE EVOLVE

 

 

Algorithm - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/Algorithm

In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and ...

 

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I
T
H
M
S
-
-
9
-
-
1
-
5

 

 

A
=
1
-
10
ALGORITHMS
122
59
5
A
=
1
-
9
ALGORITHM
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALGORITHM
-
-
-
A
=
1
-
1
A
1
1
1
L
=
3
-
1
L
12
3
3
G
=
7
-
1
G
7
7
7
O
=
6
-
1
O
15
6
6
R
=
9
-
1
R
18
9
9
I
=
9
-
1
I
9
9
9
T
=
2
-
1
T
20
2
2
H
=
8
-
1
H
8
8
8
M
=
4
-
1
M
13
4
4
-
-
49
-
9
ALGORITHM
103
49
49
-
-
4+9
-
-
-
1+0+3
4+9
4+9
-
-
13
-
9
ALGORITHM
103
13
13
-
-
1+3
-
-
-
-
1+3
1+3
-
-
4
-
9
ALGORITHM
103
4
4

 

 

A
=
1
-
10
ALGORITHMS
122
59
5
A
=
1
-
9
ALGORITHM
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALGORITHM
-
-
-
A
=
1
-
1
A
1
1
1
T
=
2
-
1
T
20
2
2
L
=
3
-
1
L
12
3
3
M
=
4
-
1
M
13
4
4
5
-
5
-
-
5
-
-
5
O
=
6
-
1
O
15
6
6
G
=
7
-
1
G
7
7
7
H
=
8
-
1
H
8
8
8
R
=
9
-
1
R
18
9
9
I
=
9
-
1
I
9
9
9
-
-
49
-
9
ALGORITHM
103
49
49
-
-
4+9
-
-
-
1+0+3
4+9
4+9
-
-
13
-
9
ALGORITHM
103
13
13
-
-
1+3
-
-
-
-
1+3
1+3
-
-
4
-
9
ALGORITHM
103
4
4

 

 

A
=
1
-
10
ALGORITHMS
122
59
5
A
=
1
-
9
ALGORITHM
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALGORITHM
-
-
-
A
=
1
-
1
A
1
1
1
L
=
3
-
1
L
12
3
3
G
=
7
-
1
G
7
7
7
O
=
6
-
1
O
15
6
6
R
=
9
-
1
R
18
9
9
I
=
9
-
1
I
9
9
9
T
=
2
-
1
T
20
2
2
H
=
8
-
1
H
8
8
8
M
=
4
-
1
M
13
4
4
-
-
49
-
9
ALGORITHM
103
49
49
-
-
4+9
-
-
-
1+0+3
4+9
4+9
-
-
13
-
9
ALGORITHM
103
13
13
-
-
1+3
-
-
-
-
1+3
1+3
-
-
4
-
9
ALGORITHM
103
4
4

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
-
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
5
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
7
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
6
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
5
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
5
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
5
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
5
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
5
-
-
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
5
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
5
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
5
-
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
5
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
5
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
6
7
8
9

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Preface to the New Edition

Page 5
Twelve years ago a little boy entered my imagination as he hopped across the centuries and played with numbers. I began to see how the simple architecture of our decimal system could be constructed in secret ways — not a building project this time but an abstract one. On the surface of our arithmetic countless combinations of numbers take part in tedious and exacting calculations but underneath it all there is pattern, governed by a repeating code of integers. The Sigma Code reduces numbers to a single digit and the illusion of the many is seen to be but the reflection of a few. This is not a book on maths: this is a book for anyone who can carry out simple sums in their heads, and who won't be short-changed knowingly.
When Number 9 first came out I received mail from many who played with numbers. They chased patterns; some had special numbers and even mystical systems. I was tempted to write about numerology but resisted. I wanted to write about the intricacy of what the.. numbers actually do and leave the reader to wonder about the larger irrational that seems to hover around such constructions.
If I were writing this book today the numbers would have featured in a wider context of structuring nature's patterns, and also playing the role of animator in algorithms that create unique architectural forms and shapes. I would also include my previous research into other base systems. But this book was a first step which came from a child-like urge, like playing with building blocks, to build out of our numbers — just the simple 1, 2, 3, up to number 9.

 

RESEARCH R E SEARCH ER RESEARCH

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

NUMBER = 534259 = 1 = 534259 NUMBER

NUMBER = 234559 NUMBER

NUMBER = 534259 = 1 = 534259 NUMBER

 

 

NUMBERS = 5342591 = 2 = 5342591 NUMBERS

SBUMNER = 1234559 = SBUMNER

NUMBERS = 5342591 = 2 = 5342591 NUMBERS

 

-
-
-
-
Q
NUMBERS
-
Q
Q
-
1
2
3
4
5
6
7
8
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
6
7
8
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
6
7
8
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
6
7
8
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
6
7
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
6
7
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
6
7
8
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
6
7
8
-
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
6
7
8
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
-
-
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
6
7
8
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
9
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
-
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
9

 

 

-
-
-
-
Q
NUMBERS
-
Q
Q
-
1
2
3
4
5
6
7
8
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
6
7
8
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
6
7
8
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
6
7
8
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
6
7
8
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
6
7
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
6
7
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
6
7
8
9
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
6
7
8
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
-
-
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
6
7
8
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
9
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
9

 

 

THE

BALANCING

ONE TWO THREE FOUR

FIVE

NINE EIGHT SEVEN SIX

4 FIVE 42 24 6

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

15 ONE TWO THREE FOUR 208 82 1
4 FIVE 42 24 6
17 NINE EIGHT SEVEN SIX 208 91 1

1234 5 6789

 

 

prime number - Whatis Techtarget
https://whatis.techtarget.com/definition/prime-number
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

 


Prime number - Wikipedia
https://en.wikipedia.org/wiki/Prime_number

The first 25 prime numbers (all the prime numbers less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 (sequence A000040 in the OEIS).
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 6 is composite because it is the product of two numbers (2 × 3) that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.

There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen number being prime is inversely proportional to its number of digits, that is, to its logarithm.
Several historical questions regarding prime numbers are still unsolved. These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals.

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. There are several proofs of the theorem.

 

Prime numbers
www-groups.dcs.st-and.ac.uk/history/HistTopics/Prime_numbers.html
Euclid also showed that if the number 2n - 1 is prime then the number 2n-1(2n - 1) is a perfect number. The mathematician Euler (much later in 1747) was able to ...
Prime numbers

Number theory index History Topics Index

Version for printing

Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians.
The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
A perfect number is one whose proper divisors sum to the number itself. e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors 1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28.
A pair of amicable numbers is a pair like 220 and 284 such that the proper divisors of one number sum to the other and vice versa.
You can see more about these numbers in the History topics article Perfect numbers.

By the time Euclid's Elements appeared in about 300 BC, several important results about primes had been proved. In Book IX of the Elements, Euclid proves that there are infinitely many prime numbers. This is one of the first proofs known which uses the method of contradiction to establish a result. Euclid also gives a proof of the Fundamental Theorem of Arithmetic: Every integer can be written as a product of primes in an essentially unique way.

Euclid also showed that if the number 2n - 1 is prime then the number 2n-1(2n - 1) is a perfect number. The mathematician Euler (much later in 1747) was able to show that all even perfect numbers are of this form. It is not known to this day whether there are any odd perfect numbers.

In about 200 BC the Greek Eratosthenes devised an algorithm for calculating primes called the Sieve of Eratosthenes.

There is then a long gap in the history of prime numbers during what is usually called the Dark Ages.

 

PRIME NUMBERS

 

P
=
2
-
5
PRIME
61
34
7
N
=
2
-
7
NUMBERS
92
38
2
-
-
17
-
12
Add to Reduce
153
72
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
8
-
3
Essence of Number
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
34
-
11
-
61
34
34
-
-
-
-
-
-
-
-
-
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
29
-
10
-
92
38
29
-
1
2
3
8
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
6
7
8
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
6
7
8
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
6
7
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
6
-
8
9
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
6
-
8
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
6
-
8
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
6
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
6
-
8
-
-
-
-
-
-
-
-
-
-
-
1
2
3
8
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
6
7
8
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
6
7
8
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
6
-
8
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
6
-
8
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
6
-
8
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
6
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
6
7
8
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
6
-
8
9
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
8
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
6
7
8
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
6
7
8
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
6
7
8
9

 

6 +8 = 14 1+4 = 5

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
7
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
9
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
1
2
3
8
15
7
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
7
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
7
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
7
9

 

 

I = 9 9 = I
ME = 9 9 = ME
BRAIN + BODY = 9 9 = BODY + BRAIN
LIGHT + DARK = 9 9 = DARK + LIGHT
ENERGY + MASS = 9 9 = MASS +ENERGY
MIND + MATTER = 9 9 = MATTER + MIND
MAGNETIC + FIELD = 9 9 = FIELD + MAGNETIC
POSITIVE + NEGATIVE = 9 9 = NEGATIVE + POSITIVE
973 OM AZAZAZAZAZAZAZAZAZZAZAZAZAZAZAZAZAZAOM 973

 

KNOW DIVINE LOVE LOVE DIVINE KNOW

 

14
 KNOW DIVINE LOVE
180
72
9
12
 KNOW GODS LOVE
162
54
9
14
 KNOW NAMES OF GOD
162
63
9

 

THAT THAT THAT

AM

I

 
 
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