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Mathematical beauty of 666
NOTICEThis review of the elegant mathematical properties of the 666 is primarily inspired by the electronic publications of Gerard Colombat, S. Desrosiers, Eli Eshoh, Mike Keith and Naohiro. We present also certain new properties which were discovered as well as references to biblical numerology. The results exposed here can be better appreciated by means of the Microsoft Calculator available under this link (display of 32 digits) or in your computer under the path Start/Programs/Accessories/Calculator. We suggest also our links to a powerful on line calculator, MegaCalculator and its Instructions.
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666 and basic integersGeneralities on numbers 6 and 666By nature, 6 is the very first "perfect number", quite special: it is at the same time equal to the sum and the product of its own dividers (see also this Perfect numbers page). Moreover, its dividers comprise a remarkable property associated with the specific number of their respective dividers. Indeed number 6 has 4 dividers (1, 2, 3 and 6). Its three clean dividers have in their turn respectively 1, 2 and 2 dividers: 1 is its single divider, 2 has 2 and 1 for dividers and 3 has 3 and 1. Such as it comes to light from the relation below, these numbers are bound by square (2) and cubic (3) powers, which evokes triple 6 (= 2 x 3).
| 1 + 2 + 3 | = | 6 | = | 1 x 2 x 3 |
| (1 + 2 + 2 + 4)2 | = | 13 + 23 + 23 + 43 |
| 4 + 6 + 8 | = | 6 + 6 + 6 |
| 666 | = | (3 x 37 x 3) + (3 x 37 x 3) |
| 666 | = | 2 x 32 x 37 |
| 666 | = | 18 x 37 |
| 666 | = | (6 + 6 + 6) x 37 |
The "Trinity of the Beast" is consigned in the following relation:
| 6 x 37 x 3003003 | = | 666 666 666 |
Here is another remarkable identity due to Mike Keith in Dottable Fractions (July 1998), where triple 6 appears in all the numerators and the denominators of the two fractions:
| 666 ÷ 6x6x6 | = | 64676 ÷ 6x46x76 | = | 3.08 333 333 333 ... |
Number 666 has 11956824258286445517629485 partitions, letting appear triple 6. Patrick De Geest reports that this number can be written in the form of product comprising also triple 6:
| p(666) | = | 11956824258286445517629485 |
| p(666) | = | 5 x 11 x 709 x 306624548231476997503 |
The attentive observation of the number of partitions of the 666 made it possible to Enoch Haga to note the absence in this result of two basic digits (0 and 3) and to establish the following relation [which curiously does not take account of the occurrences after the 666, 29485 being completely excluded]:
| 11 + 95 + 68 + 24 + 25 + 82 + 86 + 44 + 55 + 176 | = | 666 |
More simply, triple 6 is obtained by the sum of 3 terms comprising 3 times 6. The relation which results from this could receive a double and contradictory interpretation: first of all, one can see there the expression of a perfect universe (as figure 6), created in 6 days, starting from the infinite vacuum (000), by a basically trinitary God; but one can perceive also there the satanic snake which, under the hypocritical appearance of divine trinity (triple 6) will success to corrupt the human being and will try to destroy (000) the perfection.
| 6 + 60 + 600 | = | 666 |
Even our own genetic or nuclear structure would comprise 666 reducible numerical combinations!... In nuclear physics, the scientists Hans Jensen (1907-1973) and Maria Gœppert-Mayer (1906-1972), indeed established a "magic" numerical sequence of 7 numbers (all even numbers), them even associated with the number of protons or neutrons in the core of many elements and which confer a better nuclear stability to them. The discoveries of these two authors were published in 1955 in a common book, "Elementary Theory of Nuclear Shell Structure", N.Y.: John Wiley & Sons, 269 pages. Eight years afterwards, they shared the Nobel Prize of physics for 1963. These "magic numbers" are:
2 - 8 - 20 - 28 - 50 - 82 - 126
Their symmetrical or mirror numbers are thus:
2 - 8 - 02 - 82 - 05 - 28 - 621
However, Gerard Colombat (in The magic of numbers) noted that the sum of 6 of these mirror-numbers is very right equal to 666:
| 2 + 8 + 02 + 05 + 28 + 621 | = | 666 |
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666 and number 36According to the checkup of S. Desrosiers, the word beast is mentioned 36 times in the Apocalypse whereas the name of Satan is used 36 times in the New Testament. Moreover, number 36 is employed only 2 times in the Bible [Joshua, 7/5 and 2nd Chronicles 16/1].
The number of the Beast from the Apocalypse, 666, is a triangular number of which the root or secret value is 36. Such a number is of form Tn = ½ [n(n+1)], n being a natural entirety.
666 = T36 = T6x6 = 36(36 + 1)/2 = 18 x 37 (18 = 36÷2)
In addition, the sum of the first 36 numbers is equal to 666.
| 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18
+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36 |
= | 666 |
For Pythagore, 36 is the number of Large Tetraktis (or Large Quaternary), obtained by the sum of the first four odd numbers [1 + 3 + 5 + 7 = 16] and of the first four even numbers [2 + 4 + 6 + 8 = 20], is 36 = 16 + 20. It is problablement this internal duality of the number 36 which confers to him the capacity of generating at the same time the beast and the anti-beast, and this, of multiple ways. In addition, the sum of the figures of number 36 gives 9, that is to say the basic MAXIMUM figure... another sign of the power of the 36.
| 36=3!x6 (Triple 6...) 36=13+23+33 (Trinity...) 36=22x(1!+2!+3!)
"Mirror" of 36 = 1/36 = 0.27 777 777 777 ... ⇒ 777 (1+6+7+9+6+1+6)4 = 364 = 1 679 616 |
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| 36 ⇒ 3+6=9 1/9= 0.111 111 111 ... ⇒111x6=666 111x7=777 111x9=999 | ||
| 2/7 = 0.2 857 142 857 142 ... | ⇒ 857 + 142 = 999
857 ⇒ 8+5+7 = 20 142 ⇒ 1+4+2 = 7 |
⇒ 20/7=2. 857 142 857 142 ...
⇒ 857 + 142 = 999 |
| 2/77=0.0 259 740 259 740 ... |
⇒ 259 + 740 = 999
740/259 = 2.857 142 857 142 ... 259 ⇒ 2 + 5 + 9 = 16 740 ⇒ 7 + 4 + 0 = 11 |
⇒ 857+142=999 ⇒ 16/11=1. 454 545 454 545 ... ⇒ 454+545=999 |
| 2/777=0.00 257 400 257 400 ... |
⇒ 257+400 = 657
257 ⇒ 2 + 5 + 7 = 14 400 ⇒ 4 + 0 + 0 = 4 |
⇒ 7/65=0.107 692 307 692 307 ...
⇒ 692 + 307=999 ⇒ 65/7=9.2 857 142 857 142 ... ⇒ 857 + 142=999 ⇒ 4/14=0.2 857 142 857 142 ... ⇒ 857 + 142=999 |
| 27/7=3.857 142 857 142 ... | ⇒ 857 + 142=999 | ⇒ 999 |
| 27/77=0.350 649 350 649 ... |
⇒ 350 + 649=999
⇒ 649/350=1.8 542 857 142 857 142 ... |
⇒ 857 + 142=999 |
| 27/777 =0.0347 490 347 490 ... |
⇒ 347 + 490 = 837
347 ⇒ 3 + 4 +7 = 14 490 ⇒ 4 + 9 + 0 = 13 |
⇒ 83/7=11. 857 142 857 142 ...
⇒ 857 + 142=999 ⇒14/13=1.0 769 230 769 230 ... ⇒ 769 + 230=999 ⇒13/14=0.92 857 142 857 142 ... ⇒ 857 + 142=999 |
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1.3
666 and number 39The partition of the square of 39 conduct to the 666. Number 39, employed 4 times in the Bible, is related to the punishment. According to Judaïc Mishna, there are 39 types of prohibited works during the Sabbath and any individual who transgressed the laws was to receive 39 blows of whips.
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| 15 + 21 = 36 = Numerical root or secret value of 666 666 = 36(36 + 1)/2 |
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| 1/15 = 0.0 666 666 666 ... | ⇒ 666 |
| 1/21 = 0.0 476 190 476 190 ... | ⇒ 476 + 190 = 666 |
| 15/21 = 0.714 285 714 285 ... | ⇒ 714 + 285 = 999 |
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"
Five [5] times at the hands of the Jews I received forty lashes minus one." (2nd Epistle in Corinthians, 11 / 24), says Holy Paul about 39 blows of whip which he received five times from the Jews. |
11 ⇒ 1+1=2 24 ⇒ 2+4=6
39 ⇒ 3+9=12 12 ⇒ 1+2=3 1÷39=0.0 256 410 256 410 ... 5÷39=0.128 205 128 205 ... 5÷12 = 0.41 666 666 666 ... 5÷3= 1.666 666 666 ... 11÷24=0.458 333 333 333 ... 2÷6=0.333 333 333 ... |
⇒ 256+410=666 ⇒ 128 + 205=333 ⇒ 333x2=666 ⇒ 666 ⇒ 666 ⇒ 333x2=666 ⇒ 333x2=666 |
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666 and number 72The 666 is also related to number 72:
| 666 | = | (22 x 62 x 999) ÷ 63 |
| 666 | = | (2 x 72 x 999) ÷ (3 x 72) |
| 666 | = | (144000 - 144) ÷ 216 |
In addition, 72 intervenes like product in the numbers observed in the preceding table:
| 72 = 36 x 2 = 62 x 2 | 144 = 72 x 2 = 62 x 22 |
| 216 = 72 x 3 = 63 | 144 000 = 72 x 2000 |
| 1/72 = 0.013 888 888 888 ... | ⇒ 888 and 13 |
| 1/13 = 0.0769 230 769 230 ... | ⇒ 769 + 230 = 999 |
However this number 72, very invaluable and thus rare in the Bible, contains protection against the beast (888 or Jesus, the 13 or Last Supper and 999 or the anti-beast). The number 72 is quoted only 4 times in the Bible, in particular in NUMBERS, 31/38.
| "Thirty-six [36] thousand,
oxen of which seventy-two [72 = 2 x 36] fell as tax to the LORD;" (Numbers, 31 / 38). |
36 ⇒ 3+6=9 72 ⇒ 7+2=9
31 ⇒ 3+1=4 38 ⇒ 3+8=11 4 ÷ 11 = 0.363 636 363 636 ... 36 ÷ 72 ≈ 9 ÷9 = 1 1/36 = 0.02 777 777 777 ... 1/72 ≈ 1/9 = 0.111 111 111 ... |
⇒ 363 + 636 = 999 ⇒ "tribute for the Eternal [1]" ⇒ 777 ⇒ 111 x 6 = 666 ⇒ 111 x 7 = 777 ⇒ 111 x 8 = 888 ⇒ 111 x 9 = 999 |
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666 and number 108| 666 = 72 ÷ 0.108 108 108 ... |
| 72 ÷ 666 = 0. 108 108 108 ... = 120 ÷ 1110 |
| 0.6 x 1110 = 666 = (72 ÷ 120) x 1110 |
| 120 ÷ 72 = 10/6 = 5/3 = 1.666 666 666 ... ⇒ 666 |
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666 and number 120| 120 | = | 5! = 5x4x3x2x1 |
| 120 | ⇒ | 1 + 2 + 0 = 3 |
Number 120 is a triangular number of which the root or secret value is 15. Let us recall that such a number is form Tn = ½ [n(n+1)], n being a natural entirety.
120 = T15 = 15(15 + 1)/2 = 15 x 8
Combination of number 120 and its secret value 15 conducts to the number of the beast, triple 6:
| 120 | ⇒ | 1+2+0=3 | ⇒ | 3 "times" 6 666 |
| 15 | ⇒ | 1+5=6 |
| 666 = 80 ÷ 0.120 120 120 ... |
| 80 ÷ 666 = 0. 120 120 120 ... = 133.333 333 333 ... ÷ 1110 |
| 0.6 x 1110 = 666 = (80 ÷ 133.333 333 333 ...) x 1110 |
| 133.333 333 333 ... ÷ 80 = 10/6 = 5/3 = 1.666 666 666 ... ⇒ 666 |
| NOTE: 133.3 ÷ 1110 = 0.120 09 0090 0900 900 900 900 ...
⇒ 09 + 0090 + 0900 = 999 80÷0.120120120120 = 666.000000000666000000000666 |
Like 672, number 120 is a "tri-perfect" number; it is equal to three times the sum of its 16 clean dividers (see also Perfect numbers):
| Sum of the 16 dividers of number 120 | ||
| 1+2+3+4+5+6+8+10+12+15+20+24+30+40+60+120 | = | 360 = 3 x 120 |
It is important to note that 360 is the symbol of the circle. Describing the other properties and the symbolism of number 120, S. Desrosiers recalls that it
«représente la puissance et la gloire du Christ-Roi. C'est la limite d'âge fixée par Dieu pour l'homme. (Gn 6,3). Le Christ Jésus aurait eu 120 disciples, incluant les apôtres. Le Pape Paul VI fixa à 120 la limite de "cardinaux-électeurs" de moins de 80 ans. L'Arche de Gilgamesh, le Noé mésopotamien, mesurait 120 coudés des trois côtés, formant un cube. Ces dimensions auraient été fixées par Anu, Père des dieux. Il est écrit dans le Talmud que Noé disposa de cent vingt ans pour construire son arche. La vie du globule rouge du sang est de 120 jours ...»In addition, the number of the beast is exactly equal to the sum of the whole of circular shifts of 120.
[Our translation]
«represents the power and the glory of the Christ-King. It is the limit age fixed by God for the man. (Gn 6,3). Jesus Christ would have had 120 disciples, including the apostles. The Pope Paul VI fixed at 120 the limit of "cardinal-voters" of less than 80 years. The Arch of Gilgamesh, the mesopotamian Noah, measured 120 cubits on the three sides, forming a cube. These dimensions would have been fixed by Anu, Father of the gods. It is written in Talmud that Noah had one hundred twenty years to build his arch. The life of the red globule of blood is 120 days ...»
| Circular shifts of 120: 012, 021, 102, 120, 201 and 210 |
⇒ | 666=(012+021+102+120+201+210) |
The circular shifts of 120 are generators of the anti-beast.
| Trinitary-circular shifts of 120: 012, 021, 102, 120, 201 et 210 Generators of the anti-beast 999 |
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| 1÷12=0.08 333 333 333 ... | ⇒ 3x333=999 |
| 1÷21=0.047619 047619 047619 ... | ⇒ 3x(476+190)÷2=999
⇒ 3x(47+619)÷2=999 ⇒ 476+190=666 47+619=666 |
| 1÷102=0.0 0980392156862745 0980392156862745 ...
980+392+156+862+745 = 3135 98+03+92+15+68+62+74+50=462 31÷35=0.8 85714285 7142 857142 857142 ... 35÷31=1.129032258064516 129032258064516 129032258064516 ... 4÷62=0.0645161290322580 64516129032258 064516129032258 ... 2÷46=1/23=0. 0434782608695652173913 0434782608695652173913 ... 434+782+608+695+652+173+913=4257 57÷42=1.357 14285714 2857 142857 142857 ... 425÷7=60.714285714 2857 142857 142857 ... 42÷57=0.736842105263157894 736842105263157894 ... Note: 1÷19=0.052631578947368421 052631578947368421 ... |
⇒ 142+857=999 571+428=999 ⇒ 285+714=999 ⇒ 129+032+258+064+516=999 ⇒ (645+161+290+322+580)÷2=999 ⇒ 142+857=999 571+428=999 ⇒ 285+714=999 ⇒ (736+842+105+263+157+894)÷3=999 |
| 1÷120=0.008 333 333 333 ... | ⇒ 3x333=999 |
| 1÷201=0.00 4975 1243 7810 9452 7363 1840 7960 199
49÷75=0.65 333 333 333 ... 12÷43=0.279069767441860465116279069767441860465116 ... 279+069+767+441+860+465+116 = 2997 10÷78=0.128205 128205 128205 ... 94÷52=1.80 7692307 69230 769230 769230 ... 63÷73=0.863013698 6301369 86301369 86301369 ... 73÷63=1.158730 158730 158730 ... |
⇒ 3x333=999 ⇒ 2997÷3=999 ⇒ 3x(128+205)=999 ⇒ 769+230=999 ⇒ 692+307=999 ⇒ 76+923=999 ⇒ 863+136=999 ⇒ 630+369=999 ⇒ 301+698=999 ⇒ 15+873=888 158+730=888 |
| 1÷210=0.0 0476190 47619 047619 047619 ... |
⇒ 3x(476+190)÷2=999
⇒ 3x(47+619)÷2=999 ⇒ 476+190=666 47+619=666 |
or under the computer path Start/Programs/Accessories/Calculator.
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666 and number 123| 666 = 82 ÷ 0.123 123 123 ... |
| 82 ÷ 666 = 0. 123 123 123 ... = 136.666 666 666 ... ÷ 1110 |
| 0.6 x 1110 = 666 = (82 ÷ 136.666 666 666 ...) x 1110 |
| 136.666 666 666 ... ÷ 82 = 10/6 = 5/3 = 1.666 666 666 ... ⇒ 666 |
| NOTE: 136.7 ÷ 1110 = 0.123 153 153 153 ... |
The number of the beast is expressed according to the whole of the circular shifts of 123.
| Circular shifts of 123: 123, 312, 231, 132, 213 et 321 |
⇒ | 666 = (123+132+213+231+312+321)÷2=(1332)÷2 |
According to Raymond Abellio (in its book The Bible, quantified document), the number of the beast would be the "key-number of the life", because being the sum of two series of which an ordinate [123 + 231 + 312 = 666] and the other disordered [132 + 321 + 213 = 666]. It would be the manifestation of the Trinity on three plans: material, animist and spiritual. However, number 123 and its circular shifts are truly generators of anti-beast.
| Trinitary-circular shifts of 123:
123, 312, 231, 132, 213 et 321 Generators of anti-beast 999 |
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| 1/123=0.00 813 00 813 00 813 ... | ⇒ 813 + 00 = 813 8÷13=0.6 153 846 153 846 ... |
⇒ 153 + 846 = 999 |
| 1/312=0.00 320 512 820 512 | ⇒ 320 + 512 + 820 = 1652 16÷52= 0.307 692 307 692 ... |
⇒ 307 + 692 = 999 |
| 1/231=0.00 432 900 432 900 ... | ⇒ 432 + 900 = 1332=2 x 666 32÷13=2.46 153 846 153 846 ... |
⇒ 153 + 846 = 999 |
| 1/132=0.00 757 575 757 575 ... | ⇒ 757 + 575 = 1332=2 x 666 32÷13 =2.46 153 846 153 846 ... ⇒ 2÷13=0.153 846 153 846... |
⇒ 153 + 846 = 999
⇒ 153 + 846 = 999 |
| 1/213=0.00 469 483 568 075 | ⇒ 469 + 483 = 952 9÷52=0.17 307 692 307 692 ... 52÷9=5.777 777 777 ... ⇒ 2÷13=0.153 846 153 846... ⇒ 3÷21=0.142 857 142 847 ... |
⇒ 307 + 692 = 999 ⇒ 777 ⇒ 153 + 846 = 999 ⇒ 142 + 857 = 999 |
| 1/321=0.00 311 526 479 750 | ⇒ 311 + 526 = 837 83÷7=11. 857 142 857 142 ... ⇒ 3÷21=0.142 857 142 847 ... 311 ⇒ 3+1+1 = 5 526 ⇒ 5+2+6 = 13 5÷13=0.3 846 153 846 153 ... |
⇒ 857 + 142 = 999 ⇒ 142 + 857 = 999 ⇒ 846 + 153 = 999 |
Number 123 would be measurements of the arms of the Glorious Cross recommended by Jesus. Relative with the properties of number 123, S. Desrosiers written:
«Dans l'un de ses messages, Jésus recommande qu'une Croix Glorieuse soit élevée à la limite du territoire de Dozulé, sur la Haute-Butte. Les bras de la Croix doivent se dresser de l'orient à l'occident, chacun mesurant 123 mètres, et sa hauteur, 6 x 123 mètres. Or, 123 x 6 = 738 mètres. En observant une carte de la ville de Jérusalem mentionnant les courbes de niveau, on s'aperçoit que 738 mètres correspondent exactement à l'altitude du Calvaire, où a été crucifié le Christ à Jérusalem, en Israël. De plus, 7+3+8 = 18, ce qui fait 3 x 6 = 6+6+6, symbole du péché d'iniquité. La Croix Glorieuse, qui est aussi Jésus ressuscité, se couvre ainsi du péché d'iniquité, symbolisé par les mensurations 666, afin de racheter le péché du monde.»
[Our translation]
«In one of his messages, Jesus recommends that a Glorious Cross should be built in extreme limits of the territory of Dozule, on High-Ridges. The arms of the Cross must draw up from East to Occident, each one measuring 123 meters, and its height, 6 x 123 meters. However, 123 x 6 = 738 meters. By observing a card of the city of Jerusalem mentioning the level lines, one realizes that 738 meters correspond exactly to the altitude of the Martyrdom, where Christ was crucifixed in Jerusalem, Israel. Moreover, 7+3+8 = 18, which makes 3 x 6 = 6+6+6, symbol of the sin of iniquity. The Glorious Cross, which is also Jesus risen from dead, thus covers sin of iniquity, symbolized by measurements 666, in order to repurchase the sin of the world.»
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666 and number 126| 666 = 84 ÷ 0.126 126 126 ... |
| 84 ÷ 666 = 0. 126 126 126 ... = 140 ÷ 1110 |
| 0.6 x 1110 = 666 = (84 ÷ 140) x 1110 |
| 140 ÷ 84 = 10/6 = 5/3 = 1.666 666 666 ... ⇒ 666 |
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666 and number 135| 666 = 90 ÷ 0.135 135 135 ... |
| 90 ÷ 666 = 0. 135 135 135 ... = 150 ÷ 1110 |
| 0.6 x 1110 = 666 = (90 ÷ 150) x 1110 |
| 150 ÷ 90 = 10/6 = 5/3 = 1.666 666 666 ... ⇒ 666 |
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666 and number 153Number 153 is the symbol of God and of the Church (according to Cyrille of Alexandria), it is also the symbol of the mission of Christ in the New Testament. S. Desrosiers (Numbers: Symbolism and Properties) recalls in its excellent document that the ministry of Christ lasted 918 days from its baptism to the festival of Passover. However 918 = 153 x 6. Desrosiers also underlines that «the word "beasts" appears 153 times in the biblical version of King James. The word "command" returns 153 times in the Old Testament». It is also the number of fish indicated in biblical miraculous fishing:
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"So Simon Peter went over and dragged the net ashore full of one hundred fifty-three [153] large fish. Even though there were so many, the net was not torn." (John 21/11). |
21 ⇒ 2+1=3 11 ⇒ 1+1=2 21 ÷ 11 = 1.90 90 90 90 90 ... 2 ÷ 3 = 0.666 666 666 ... 11÷21 = 0.523 809 523 809 ... |
⇒ 90 + 909 = 999 ⇒ 666 ⇒ 523 + 809 = 1332 1332÷2=666 1332÷3=444 1332÷4=333 ⇒666, 888,999 |
The 153th verse of the Genesis relates to Noah's Ark: "This is how you shall build it: the length of the ark shall be three hundred cubits, its width fifty cubits, and its height thirty cubits." (Genesis 6/15). God having taken the decision to destroy the human race, as consigned to the 151th verse of the Genesis: "He said to Noah: "I have decided to put an end to all mortals on earth; the earth is full of lawlessness because of them. So I will destroy them and all life on earth." (Genesis 6/13). Number 153 is used only 2 times in the Bible.
| 666 = 102 ÷ 0.153 153 153 ... |
| 102 ÷ 666 = 0. 153 153 153 ... = 170 ÷ 1110 |
| 0.6 x 1110 = 666 = (102 ÷ 170) x 1110 |
| 170 ÷ 102 = 10/6 = 5/3 = 1.666 666 666 ... ⇒ 666 |
| NOTE: 136.7 ÷ 1110 = 0.123 153 153 153 ... |
Triple 6 is expressed according to the whole of the circular shifts of number 153.
| Circular shifts of 153: 153, 351, 135, 513, 315 et 531 |
⇒ | 666 = (135+153+315+351+513+531)÷3=1998÷3 |
In addition, number 153, characteristic of the miracles of Jesus, as its circular shifts are truly generators of anti-beast.
| Trinitary-circular shifts of 153:
153, 351, 135, 513, 315 et 531 Generators of anti-beast 999 |
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| 1/153=0.00 653 594 771 241 ... | ⇒ 653 + 594 = 1247 124÷7=17.7 142 857 142 857 ... 653 ⇒ 6+5+3=14 594 ⇒ 5+9+4=18 18÷14=1.2 857 142 857 142 ... 14÷18=0.777 777 777 777 ... |
⇒ 142 + 857 = 999 ⇒ 857 + 142 = 999 ⇒ 777 |
| 1/351=0.00 284 900 284 900 ... | ⇒ 284 + 900 = 1184 84÷11= 7.636 363 636 363 ... ⇒ 1÷35= 0.02 857 142 857 142 ... 284 ⇒ 2+8+4=14 900 ⇒ 9+0+0=9 9÷14=0.642 857 142 857 142 ... |
⇒ 636 + 363 = 999 ⇒ 857 + 142 = 999 ⇒ 857 + 142 = 999 |
| 1/135=0.00 740 740 740 ... | ⇒ 740 + 740 = 1480 80÷14=5.7 142 857 142 857 ... ⇒ 1÷35= 0.02 857 142 857 142 ... ⇒ 5÷13=0.3 846 153 846 153 ... 740 ⇒ 7 + 4 + 0 = 11 1÷11=0.0 909 090 909 090 ... |
⇒ 142 + 857 = 999 ⇒ 857 + 142 = 999 ⇒ 846 + 153 = 999 ⇒ 909 + 090 = 999 |
| 1/513=0.00 194 931 773 879 ... | ⇒ 194 + 931 = 1266 12÷66 = 0.181 818 181 818 ... ⇒ 5÷13 = 0.3 846 153 846 153 ... 194 ⇒ 1+9+4=14 931 ⇒ 9+3+1=13 14÷13=1.0 769 230 769 230 ... 13÷14=0.92 857 142 857 142 ... |
⇒ 181 + 818 = 999 ⇒ 846 + 153 = 999 ⇒ 769 + 230 = 999 ⇒ 857 + 142 = 999 |
| 1/315=0.00 317 460 317 460 ... | ⇒ 317 + 460 = 777 7÷77=0.909 090 909 090 ... 1÷777=0.00 128 700 128 700 ... ⇒ 128 + 700 = 828 8÷28=0.2 857 142 857 142 ... 317 ⇒ 3+1+7=11 460 ⇒ 4+6+0=10 10÷11=0.909 090 909 090 ... 128 ⇒ 1+2+8=11 700 ⇒ 7+0+0=7 11÷7=1.57 142 857 142 857 ... 7÷11=0.636 363 636 363 ... |
⇒ 909 + 090 = 999 ⇒ 857 + 142 = 999 ⇒ 909 + 090 = 999 ⇒ 142 + 857 = 999 ⇒ 636 + 363 = 999 |
| 1/531=0.00 188 323 917 137 | ⇒ 188 + 323 = 511 5÷11=0. 454 545 454 545 ... |
⇒ 454 + 545 = 999 |
On the mathematical level, number 153 comprises remarkable properties. It is equal to the sum of the cubes of its three components. Consequently, number 153 is thus qualified as a number of Armstrong (still called "a more perfect number" or PDI, "Perfect Digital Invariant"), i.e. a number with n figures which is exactly the sum of nth powers of its n components. Only three other numbers with 3 digits, 370, 371 and 407, have this property. However, the following sequence, produced by Sloane Neil J A. [A005188], 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, ... is made up only of numbers of Armstrong. Actually, a number of Armstrong is only one particular case of the general category of