# Fun with 666

Outside of Jewish circles, interest in gematria tends to focus on a single number — 666, gematria’s unholy grail. One can only tinker around with gematria for so long before succumbing to the temptation to play “pin the tail on the antichrist” — it’s just too much fun. Here I’ll be using my own pet system, S:E:G: (Simple English Gematria, in which A=1 and Z=26), to explore this most deliciously evil of numbers.

The idea of the number of the beast comes from Revelation 13:18 in the Bible: “Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.” S:E:G: points us to that very verse.

• Revelation of Jesus to John, thirteenth chapter, eighteenth verse = 666
• Bible, Revelation of St. John the Divine, chapter thirteen, verse eighteen = 666
• Wisdom: Let him that hath understanding count the number of the beast. = 666

Aside from its biblical significance, 666 has some interesting mathematical properties. It is the 36th triangular number — that is, the sum of all the integers from 1 to 36.

• the thirty-sixth triangular number, declared the number of the beast = 666
• a numeral thrice repeated, the triangular expansion of thirty-six = 666

Unlike, say, Greek isopsephy or Hebrew gematria, which are based on powers of ten and can represent thee- and four-digit numbers with just a few letters, S:E:G: can requires a fairly long string to yield a number as large as 666. So when it comes to pegging an actual person as “the beast,” an unadorned name is not enough; some kind of title or description must be added. Here are a few examples:

• the ridiculous Scientologist actor Thomas Cruise Mapother IV = 666
• George Walker Bush, the Texan President of the United States of America = 666
• Jann Wenner, who publishes Rolling Stone and other such magazines = 666
• Hu Jintao, Paramount Leader of the Communist [expletive] occupying China = 666
• Joseph Smith, Jr., of the Church of Jesus Christ of Latter-day Saints = 666
• folk music icon Robert Allen Zimmerman, commonly known as Bob Dylan = 666
• Professor Clinton Richard Dawkins, famous ethologist and atheist = 666
• William James (also abbreviated Wm Jas) Tychonievich, the second of that name = 666

If you think the people listed above are not really antichrists but have been unfairly accused, don’t blame me; blame the English language. Maybe the alphabet itself is evil!

• a bee cee dee e ef gee haitch i jay kay el em en o pee cue ar ess tee u vee double-u ex wy zee = 666.

Or perhaps the real blame lies with the book that gave us the whole idea of 666 and the antichrist: the New Testament.

• the Gospels, the Acts of the Apostles, the Epistles, and the Apocalypse = 666

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### One response to “Fun with 666”

1. The Translucent Amoebae

Other Curious Properties of 666
( Lifted ( OCRed ) from a Book that i found in the library,
and whose name & author i neglected to make note of! )
The number 666, popularly known through its biblical association,
is often referred to as the “number of the beast” and signifies bad luck omens. Yet again, we are only concerned about this number’s mathematical properties, many of which are quite amazing. To begin with, the number 666 is obviously a palindrome 2-that is, it is a number that reads the same in both directions. Yet if we were to write this number in Roman numerals- 666 = DCLXVI -we find that all the numerals less than 1,000 are used and in descending order!
The number 666 just happens to be the sum of the first thirty-six numbers:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + …
… + 30 + 31 + 32 + 33 + 34 + 35 + 36 = 666

Triangular Numbers
. 1
.. 2 = 3
… 3 = 6
…. 4 = 10

Not only is the sum 666, but since the sum of initial consecutive natural numbers always yields a triangular number 666 is a triangular number. Surely, we know that 36 is a square number (that is, 6^2). Therefore, for 666, we can say that a square number of initial natural numbers has given us a triangular number.

To further demonstrate the uniqueness of the number 666, consider the first seven prime numbers: 2, 3, 5, 7, 11, 13, 17.
If we take the square of each of them and then find their sum, yes, we arrive at 666.

2^2 +3^2 +5^2 + 7^2 + 11^2 + 13^2 + 17^2 = 4+9+25+49+ 121+169+289 = 666

Another amazing fact about this strange number, 666, is that the sum of its digits (6 + 6 + 6) is equal to the sum of the digits of its prime factors. That is, since we have in prime factored form 666 = 2·3·3·37, the sum of the digits, 2 + 3 + 3 + 3 + 7 = 18, is equal to 6 + 6 + 6 = 18

It is also curious that the sum of two consecutive palindromic prime numbers, 313 + 353, is equal to 666.

The number 666 is equal to the sum of the digits of its 47th power, and is also equal to the sum of the digits of its 51st power. That is,

666^47= 504996968442079675317314879840556477294151629526540818811763266 8936540446616033068653028889892718859670297563286219594665904733945856

666^51= 993540757591385940334263511341295980723858637469431008997120691 313460713282967582530234558214918480960748972838900637634215694097683599029436416

You can check this by finding that the sum of the digits of each of the above large numbers is equal to 666.

– – –
The number 666 is equal to the sum of the cubes of the digits of its square, plus the digits of its cube. This means that if we find the square and the cube of 666:

666^2 = 443,556
666^3 = 295,408,296

and then take the sum of the cubes of the digits of the square of 666:
4^3 + 4^3 + 3^3 + 5^3 + 5^3 + 6^3 + = 621
and add it to the sum of the digits of cube of 666:
2+9+5+4+0+8+2+9+6=45
we then get 621 + 45 = 666.

– – –
Another peculiarity of 666 is that if we consider the prime factors of each of the two consecutive numbers 20,772,199 and 20,772,200, each of the sums of their prime factors
is 666. That is:

20,772,199 = 7·41·157·461 —> 7 +41 + 157 +461 = 666

20,772,200 = 2· 2· 2·5·5·283 ·367 —> 2+2+ 2+5+5+283+367 = 666

A strange occurrence of the number 666 is when we try to insert + signs, into the sequence of numbers 1,2,3,4,5,6,7,8,9.

Here are two ways to do it:

1 + 2 + 3 + 4 + 567 + 89 = 666
or 123 + 456 + 78 + 9 = 666

If we consider the reverse sequence 9,8, 7, 6, 5, 4, 3, 2, 1, we can do it as follows:

9 + 87 + 6 + 543 + 21 = 666

The value of π is known to about 1.24 trillion places, where the decimal digits follow no discernab1e pattern.? Yet, strangely enough, when you take the sum of the first 144 decimal places (We refer here to the numerals after the decimal point. ) you find it to be 666.

π = 3.141592653589793238462643383279502884197169399375105820974944592 307816406286208998628034825342117067982148086513282306647093844609550582231725359

The sum of the digits is: 1 + 4 + 1 + 5 + 9 + 2 + 6 + 5 + 3 + 5 + 8 + 9 + 7 + 9 + 3 + 2 + 3+8+4+6+2+6+4+3+3+8+3+2+7+9+5+0+2+8+8+4+1+9+7+ 1+6+9+3+9+9+3+7+5+1+0+5+8+2+0+9+7+4+9+4+4+5+9+2 +3+0+7+8+1+6+4+0+6+2+8+6+2+0+8+9+9+8+6+2+8+0+3 +4+8+2+5+3+4+2+1+1+7+0+6+7+9+8+2+1+4+8+0+8+6+5 +1+3+2+8+2+3+0+6+6+4+7+0+9+3+8+4+4+6+0+9+5+5+0 + 5 + 8 + 2 + 2 + 3 + 1 + 7 + 2 + 5 + 3 + 5 + 9 = 666.

This remarkable-and sometimes “unlucky”-number seems to almost have a boundless array of number “coincidences” embedded within, such as that the sum of the numbers on a roulette wheel is 666.

Here are a few delectable number relationships that lead to 666:

666=1^6-2^6+3^6

666 = (6 + 6 + 6) + (6^3 + 6^3 + 6^3)

666 = (6^4 – 6^4 +6^4) – (6^3 +6^3 +6^3)+(6+6+6)
666 =5^3 +6^3 +7^3 -(6+6+6)

666 = 2^1 * 3^2 + 2^3 * 3^4

We can even generate 666 by representing each of its three digits in terms of 1, 2, and 3:

6=1+2+3
6=1·2·3

6 = The Square Root of 1^3 + 2^3 + 3^3

Therefore, 666 = (100)(1 + 2 + 3) + (10)(1· 2· 3) + ( SqRoot of 1^3 + 2^3 + 3^3 )

The number 666 is also related to the Fibonacci numbers in a variety of ways. Consider me following, where Fn is the nth Fibonacci number:

Fl – F9 + Fll + Fl5 = 1 + 1 + 27 + 125 + 512 = 666

and when you inspect the subscripts, you get:

1 – 9 + 11 + 15 = 6 + 6 + 6

Similarly, for the cubes of the Fibonacci numbers:

1 + 1 + 27 + 125 + 512 = 666
and now the subscripts give us:

1+2+4+5+6 = 6+6+6

Our fascination with the number 666 is just to exhibit the beauty that lies in much of mathematics. Exploring the recreational side of mathematics is an enjoyable by-product of the important role it plays in all of scientific exploration and discovery.

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