### Strange Properties of 666

"The Number of the Beast"

Sudhy P S - XII B

The last book of the Bible, Revelation, brings up the number 666 as being the number of the beast connected with the end of this age and the coming of the Messiah. You will find the direct reference in Chapter 13, verse 18 of Revelation. Besides that cataclysmic reference, the number 666 has quite a few very interesting properties.

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

666 = 6^3 + 6^3 + 6^3 + 6 + 6 + 6

(Mike Keith mentions that there are only five other positive integers that exhibit this property...find 'em!)

(Mike Keith mentions that there are only five other positive integers that exhibit this property...find 'em!)

666 = 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2

666 = 1 + 2 + 3 + 4 + 567 + 89 = 123 + 456 + 78 + 9 = 9 + 87 + 6 + 543 + 21

Moreover, 666 is equal to the sum of the cubes of the digits in its square (666^2 = 443556, and the sum of the cubes of these digits is 4^3 + 4^3 + 3^3 + 5^3 + 5^3 + 6^3 = 621) plus the sum of the digits in its cube (666^3 = 295408296, and 2+9+5+4+0+8+2+9+6 = 45, and 621+45 = 666).

Incredibly, 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 = 5049969684420796753173148798405564772941516295265

4081881176326689365404466160330686530288898927188

59670297563286219594665904733945856

4081881176326689365404466160330686530288898927188

59670297563286219594665904733945856

666^51 = 9935407575913859403342635113412959807238586374694

3100899712069131346071328296758253023455821491848

0960748972838900637634215694097683599029436416

and the sum of the digits on the right hand side is, in both cases, 666. In fact, 666 is

3100899712069131346071328296758253023455821491848

0960748972838900637634215694097683599029436416

and the sum of the digits on the right hand side is, in both cases, 666. In fact, 666 is

*the only integer greater than one with this property*. (Also, note that from the two powers, 47 and 51, we get (4+7)(5+1) = 66.)
Mr. Keith also points out that if we assign numerical values for the letters of the alphabet starting with A = 36, B = 37, and so on, we find that the letters in the word

SUPERSTITIOUS = 666 !!!

From contributor James Watt comes the following: "Here are some other neat things about 666 I seem to have discovered (since I never found any reference anywhere else). 6+6+6 =18 and 18 x 37 = 666.

Similarly, 4+4+4 = 12. 12 x 37 = 444. etc. In Roman numerals (and the Greek equivalents), which John would have used to write them, it is DCLXVI, the exact sequential descending order of Roman Numerals.

Now 1/81 = .012345679012345679012345679.... Notice the 8 is missing. 1+2+3+4+5+6+7+9 = 37.

The other 'number of the beast' is called the vulgate number. It is 616. If 'vulgar' Roman numerals are used in ascending order, vulgate Roman numerals 616 is IVXCD. The'L' is missing."

Similarly, 4+4+4 = 12. 12 x 37 = 444. etc. In Roman numerals (and the Greek equivalents), which John would have used to write them, it is DCLXVI, the exact sequential descending order of Roman Numerals.

Now 1/81 = .012345679012345679012345679.... Notice the 8 is missing. 1+2+3+4+5+6+7+9 = 37.

The other 'number of the beast' is called the vulgate number. It is 616. If 'vulgar' Roman numerals are used in ascending order, vulgate Roman numerals 616 is IVXCD. The'L' is missing."

From contributor Matt Westwood comes this interesting fact: "666 is also the total of all the numbers in a 6x6 magic square. That is, it's the 36th triangle number, being <math>sum_{k=1}^{36} k</math>." He also goes on to mention "In one of the many branches of Hermitic magic that I once studied, the magic squares of the various sizes were talismans for the various planetary influences: 3x3: Saturn, 4x4: Jupiter, 5x5: Mars, 6x6: Sun, 7x7: Venus, 8x8: Mercury, 9x9: Moon. A more recent book on the subject tried to convince that 11x11 was Neptune, or something, but this is far from profound: there exists a simple algorithm for creating *any* odd-order magic square with consecutive natural numbers starting from 1. Although I did find it profound at the time that I won a raffle ticket with the number 369 (the number of the 9x9 square) on the very day I moved into a new house. Add or subtract n from every digit of any magic square, and it remains magic of course."

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