In the previous 9 articles we looked at the number 6 and its related numbers 66, 60 and 600. It is the number of Man. We showed that 6 has a bearing on 666. But 60, 66 and 600 do not generally contribute much more to 666. We show they support the general premise that 6 relates to Man. This article covers the mathematical aspects of 6 and 666 as an introduction to the study of the famous number mentioned by John in the Apostolic Writings in the next article.

Let us see the mathematical interrelationship between 6 and 666. Mathematically 6 is a unique number. Many numbers have certain patterns or relationships, but 6 appears to have more than most. Some of its characteristics that would have been known during the Second Temple period include:

• It is the only number where the sum and product of the same 3 different numbers are equal. That is 1+2+3=6 and 1x2x3=6. (The other is 2+2=4and 2x2=4, where the number repeated).

• 36 is 62 or a square of 6 units on each side.

• If we take a square of 6x6 and divide it into 36 squares and arrange the numbers 1 to 36 within the squares their sum is 666. But it is possible to arrange the numbers in such a way that each horizontal, vertical and diagonals sum to 111.

• An equilateral triangle made up of 3 units on each of its 3 sides requires 6 units to build – 1+2+3.

• 36 is an equilateral triangle of 8 units on each side, i.e. 1+2+3+4+5+6+7+8=36.

• The equilateral triangle of 36 units each side is the sum of 1 +2 +3 +4 +5 +6 +.... +31 +32 +33 +34 +35 +36 =666.

• An equilateral triangle with 5 units per side has the value 1+2+3+4+5=15 and with 6 units per side is has the value 1+2+3+4+5+6=21, sum to 36 (15+21). If we take 152+212, we get 225+441 =666.

• Another way to look at this 36 unit sided equilateral triangle is that it is made up of 15, 5 sided and 21 6 sided equilateral triangles. In total 36 equilateral triangles (15+21). Note the 5 possible equilateral triangle combinations in a 36 unit sided triangle are;

o 1 seventeen sided and 3 eighteen sided equilateral triangles, totalling 4 (22) equilateral triangles

o 6 eight sided and 10 nine sided equilateral triangles totalling 16 (42) equilateral triangles,

o 15 five sided and 21 six sided equilateral triangles totalling 36 (62) equilateral triangles

o 36 three sided and 45 four sided equilateral triangles totalling 81 (92) equilateral triangles, and

o 66 two sided and 78 three sided equilateral triangles totalling 144 (122) equilateral triangles,

o The above shows a unique sequence of natural numbers in a simple cumulative form =0 +1= 1 +2=3 +3=6 +4=10 +5=15 +6=21 +7=28 +8=36 +9=45 +10=55 +11=66 +12=78. Note, only 55 does not appear in the above.

o Also the total number of triangles in each above case is a square (X2) of a smaller number.

• The number of prime numbers up to 36 is 11. But 112 is 121 which is the number of prime numbers up to 666.

• 66 is smallest number which the sum of 2 prime numbers can be summed in 6 ways, 61+5 = 66, 59+7=66, 53+13=66, 47+19=66, 43+23=66 and 37+29=66.

• The sum of the ancient Roman numbers DCLXVI=666 (D=500, C=100, L=50, X=10, V=5, I=1). M=1,000 was added later.

Therefore when John wrote the Book of Revelation he would have understood the above last point on the Roman numbering system that gave 666. The Greeks and Hebrews number all the letters in their respective alphabets. However the Romans only numbered the Latin letters DCLXVI. Therefore we can only assign numbers to complete words, names and phases in Hebrew and Greek. We cannot apply numbers to the Latin or other alphabets which do not have a numbering system embedded in it. One reason is that if we are going to interpret 666 in Revelation chapter 13, we need to put ourselves in the position of the people at that time, over 1,900 years ago. The statement by John in the Book of Revelation was understood then, just as it is now. I will show that this number was interpretable then, from the facts available at that time.

Our advantage today (and perhaps a disadvantage) is that we have a lot more information available in order to make an informed conclusion on the number 666. An example is that more recently we have discovered other scientific and mathematical relationships of 666 which include:

• The most common carbon isotope (Carbon 12), the base of all known life consists of 6 protons, 6 neutrons and 6 electrons. It is the 6th element on the Periodic scale. That is, Chemically or physically we are mainly built on the number 6.

• A prime reciprocal magic square based on 1/149 in base 10 has a total of 666 (one for the mathematicians to interpret).

• The binary number of 666 is 1010011010. One half is in reverse digit order to the other (one for computer freaks).

• The cumulative of the first 6 numbers =21. The cumulative of 66=2,211. The cumulative of 666=222,111. The cumulative of 6,666=22,221,111. Six is the only number that I know of that has this simple symmetrical relationship. Without calculating, the cumulative of 66,666 is therefore 2,222,211,111. The next most simple relationship involves the number 3. Cumulative of 3 =6, of 33=561, of 333=55611, of 3,333=5556111, etc.

• The transliteration of www (World Wide Web) into Hebrew is waw 3 times ווו . This Hebrew letter has the value of 6. Therefore www has a numerical value of 666.

The above leads us to the study of 666. We have concluded the study of 6 and the other values connected with 6. What is left is the controversial number 666. In the next article (YbD036) we will begin looking at 666 in the Apostolic writings and the Tanakh.

יוסף בן דרגן Yosef ben Dragan

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