>>Some items of interest realting to bar codes, SSANs, microchips, and the like
... from the # 666 standpoint ... A<>E<>R <<
>From http://www.greaterthings.com/Word-Number/666/
666-Mark of the Beast Studies Index
>>Partial listing; entire listing at site<<
> Documents
>
> vote for this page
>
> Essay: 666-Related Studies & Ramifications: Why aren't we talking about it?
>
> Precursors to the Mark -- 666 in every UPC bar code
>
> Related Scriptures in the Book of Revelation
>
> Key Sister Prophecies in Daniel 7, Revelation13, III Nephi 16,20,21 and Doctrine
> and Covenants 103
>
> Synonyms for BEAST
>
> Some Points to Ponder
>
> Some Pertinent Questions
>
> So . . .
>
> click
>
> News Flash Service
> Human microchip implants in use and mass production planned; photos of UN
> vehicles on US soil; Federal Detention Centers for dissident citizen roundup;
> Federal Police badges; more.
>
> Alphabetics Prophecy: My Social Security Number in the Alphabetics Bible Code
>
> Alphabetics Prophecy: My Voter ID# 13864 Foretells and Exposes the
> Conspiratorial Maritime Lobby Deception
>
> Section 666 of Title 42 (the Social Security Act) (42 USC Sec. 666)
>
> now requires every state, as a condition of Federal Revenue Sharing, to obtain
> "the number of your name" before you can receive any state services (e.g., a
> license to work, a license to drive, a license to marry).
>
> Alphabetics Prophecy: 666: Coincidentally Related Scriptural Word and Page
> Number
>From http://users.aol.com/s6sj7gt/mike666.htm
}}>Begin
The Number of the Beast
Mike Keith
The number 666 is cool. Made famous by the Book of Revelation (Chapter 13,
verse 18, to be exact), it has also been studied extensively by mathematicians
because of its many interesting properties. Here is a compendium of
mathematical facts about the number 666. The early ones include some of the
old, well-known "chestnuts", but many of the later ones are new and have not
been published elsewhere.
The number 666 is a simple sum and difference of the first three 6th powers:
666 = 16 - 26 + 36.
It is also equal to the sum of its digits plus the cubes of its digits:
666 = 6 + 6 + 6 + 6³ + 6³ + 6³.
There are only five other positive integers with this property. Exercise: find
them, and prove they are the only ones!
666 is related to (6² + n²) in the following interesting ways:
666 = (6 + 6 + 6) · (6² + 1²)
666 = 6! · (6² + 1²) / (6² + 2²)
The sum of the squares of the first 7 primes is 666:
666 = 2² + 3² + 5² + 7² + 11² + 13² + 17²
16661 is the first beastly palindromic prime, of the form 1[0...0]666[0...0]1.
The next one after 16661 is
1000000000000066600000000000001
which can be written concisely using the notation 1 013 666 013 1, where the
subscript tells how many consecutive zeros there are. Harvey Dubner determined
that the first 7 numbers of this type have subscripts 0, 13, 42, 506, 608,
2472, and 2623 [see J. Rec. Math, 26(4)].
A very special kind of prime number [first mentioned to me by G. L. Honaker,
Jr.] is a prime, p (that is, let's say, the kth prime number) in which the sum
of the decimal digits of p is equal to the sum of the digits of k. The beastly
palindromic prime number 16661 is such a number, since it is the 1928'th prime,
and
1 + 6 + 6 + 6 + 1 = 1 + 9 + 2 + 8.
The triplet (216, 630, 666) is a Pythagorean triplet, as pointed out to me by
Monte Zerger. This fact can be rewritten in the following amazing form:
(6·6·6)² + (666 - 6·6)² = 666²
The sequence of palindromic primes begins 2, 3, 5, 7, 11, 101, 131, 151, 181,
191, 313, 353, etc. Taking the last two of these, we discover that 666 is the
sum of two consecutive palindromic primes:
666 = 313 + 353.
[from G. L. Honaker, Jr.] There are exactly 6 6's in 6666. After seeing this,
I immediately noticed that there are 6 6's in that statement as well!
[by P. De Geest, slight refinement by M. Keith] 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,
66647 =
5049969684420796753173148798405564772941516295265
4081881176326689365404466160330686530288898927188
59670297563286219594665904733945856
66651 =
9935407575913859403342635113412959807238586374694
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.)
The number 666 is one of only two positive integers equal to the sum of the
cubes of the digits in its square, plus the digits in its cube. On the one
hand, we have
6662 = 443556
6663 = 295408296
while at the same time,
(43 + 43 + 33 + 53 + 53 + 63) + (2+9+5+4+0+8+2+9+6) = 666.
The other number with this property is 2583.
We can state properties like this concisely be defining Sk(n) to be the sum of
the kth powers of the digits of n. Then we can summarize the last two items (as
well as the second one on this page) as:
666
= S1(666) + S3(666)
= S1(66647) = S1(66651)
= S3(6662) + S1(6663)
[P. De Geest and G. L. Honaker, Jr.] Now that we have the Sk(n) notation,
define SP(n) as the sum of the first n palindromic primes. Then:
S3( SP(666) ) = 3 · 666
where the same digits (3, 666) appear on both sides of the equation!
[by Carlos Rivera] The number 20772199 is the smallest integer with the
property that the sum of the prime factors of n and the sum of the prime
factors of n+1 are both equal to 666:
20772199 = 7 x 41 x 157 x 461, and 7+41+157+461 = 666
20772200 = 2x2x2x5x5x283x367, and 2+2+2+5+5+283+367 = 666.
Of course, integers n and n+1 having the same sum of prime factors are the
famous Ruth-Aaron pairs. So we can say that (20772119,20772200) is the smallest
beastly Ruth-Aaron pair.
[by G. L. Honaker, Jr.] The sum of the first 666 primes contains 666:
2 + 3 + 5 + 7 + 11 · · · + 4969 + 4973 = 1533157 = 23 · 66659
[Wang, J. Rec. Math, 26(3)] The number 666 is related to the golden ratio! (If
a rectangle has the property that cutting off a square from it leaves a
rectangle whose proportions are the same as the original, then that rectangle's
proportions are in the golden ratio. Also, the golden ratio is the limit, as n
becomes large, of the ratio between adjacent numbers in the Fibonacci
sequence.) Denoting the Golden Ratio by t, we have the following identity,
where the angles are in degrees:
sin(666) = cos(6·6·6) = -t/2
which can be combined into the lovely expression:
t = - (sin(666) + cos(6·6·6) )
There are exactly two ways to insert '+' signs into the sequence 123456789 to
make the sum 666, and exactly one way for the sequence 987654321:
666 = 1 + 2 + 3 + 4 + 567 + 89 = 123 + 456 + 78 + 9
666 = 9 + 87 + 6 + 543 + 21
A Smith number is an integer in which the sum of its digits is equal to the
sum of the digits of its prime factors. 666 is a Smith number, since
666 = 2·3·3·37
while at the same time
6 + 6 + 6 = 2 + 3 + 3 + 3 + 7.
Consider integers n with the following special property: if n is written in
binary, then the one's complement is taken (which changes all 1's to 0's and
all 0's to 1's), then the result is written in reverse, the result is the
starting integer n. The first few such numbers are
2 10 12 38 42 52 56 142 150 170 178 204 212 232 240 542 558 598 614...
For example, 38 is 100110, which complemented is 011001, which reversed is
100110. Now, you don't really need to be told what the next one after 614 is,
do you?
The following fact is quite well known, but still interesting: If you write
the first 6 Roman numerals, in order from largest to smallest, you get 666:
DCLXVI = 666.
The previous one suggests a form of word play that was popular several
centuries ago: the chronogram. A chronogram attaches a numerical value to an
English phrase or sentence by summing up the values of any Roman numerals it
contains. (Back then, U,V and I,J were often considered the same letter for the
purpose of the chronogram, however I prefer to distinguish them.) What's the
best English chronogram for 666? My offering is a statement about, perhaps,
what you should do when you encounter the number 666:
Expect The Devil.
Note that four of the six numerals are contained in the last word.
[from Martin Gardner's "Dr. Matrix" columns] The Dewey Decimal System
classification number for "Numerology" is 133.335. If you reverse this and add,
you get
133.335 + 533.331 = 666.666
A standard function in number theory is phi(n), which is the number of
integers smaller than n and relatively prime to n. Remarkably,
phi(666) = 6·6·6.
The nth triangular number is given by the formula T(n) = (n)(n+1)/2. 666 is
the 36th triangular number - in other words,
T(6·6) = 666.
In 1975 Ballew and Weger proved (see J. Rec. Math, Vol. 8, No. 2):
666 is the largest triangular number that's also a repdigit
(A repdigit is a number consisting of a single repeated non-zero digit, like 11
or 22 or 555555.)
A polygonal number is a positive integer of the form
P(k,n) = n((k - 2)n + 4 - k)/2
where k is the 'order' of the polygonal number (k=3 gives the triangular
numbers, k=4 the squares, k=5 the pentagonal numbers, etc.), and n is its
index. A repdigit polygonal number is a polygonal number that also happens to
be a repdigit. Finally, define the wickedness of a polygonal number as n/k.
Now, the amazing fact:
666 is conjectured to be the most wicked repdigit polygonal number.
Since 666 = P(3,36), n/k = 12. I recently showed by computer calculation that
there are no counterexamples to this conjecture less than 1050. See my paper
here for more details. It seems quite certain that this is true but so far no
one has proved it.
Whilst on the subject of polygonal numbers, we can find among them some rather
beastly configurations. One of the more striking is the following:
If one arranges a group of people in a filled 3010529326318802-sided polygon
with 666 people on each side, there will be a total of 666666666666666666666
persons in all.
Or, more simply, P(3010529326318802, 666) = 666666666666666666666. See the
paper link in the previous item for more like this.
Define pi(n,d) as the d consecutive digits of pi starting at the nth digit
after the decimal point. Then we can make the following pretty statement:
pi(666, 3) = 7·7·7.
as well as the following one, which contains nothing but 6's and 3's (and two
666's):
pi(666 · 3.663663663..., 3) = 666.
One day, as I was staring at the number 666, I saw two (evil?) eyes peering
between the digits, like so: 6o6o6. This seemed to imply that the number 60606
might worthy of further contemplation. Indeed, note the following facts:
60606 = 7 x 13 x 666.
60606 has exactly 6 prime factors.
60606+1 is a prime number. Not only that, but it's a prime (p) for which the
period length of the decimal expansion of its reciprocal (1/p) attains the
maximum possible value of p-1. In other words:
1/(60606 + 1) has period length 60606.
60606 is, just like 666, the sum of two consecutive palindromic primes (both of
which contain the evil eyes!):
60606 = 30203 + 30403.
[Thanks to G. L. Honaker, Jr., in collaboration with Jud McCranie and Patrick
De Geest, for these.]
[found by Jud McCranie] It is a theorem that every positive integer occurs as
the period length of the reciprocal of some prime. So, the obvious question
arises: what's the smallest prime with period length 666? The answer was found
in June 1998:
p = 902659997773 is the smallest prime whose reciprocal has period length 666.
The first 666 digits after the decimal point of 1/p (which then repeat) are:
000000000001107836840523732794015856393629176199911567364459
553453849096605279881838076680979988886781773038423114524370
500571392445408560228574284480352437836776725525116619485115
892576776519141738094220028289530945207260114524370499463555
604884827434558428086723261636865158160657066031266795971496
637303661413240039402749172168836999999999998892163159476267
205984143606370823800088432635540446546150903394720118161923
319020011113218226961576885475629499428607554591439771425715
519647562163223274474883380514884107423223480858261905779971
710469054792739885475629500536444395115172565441571913276738
363134841839342933968733204028503362696338586759960597250827
831163
Note: if you turn the prime p upside down, there's a 666 inside, slightly to
the left of the middle, and if you turn the single period of 1/p upside down,
there's a 66666666666 inside, slightly to the left of the middle!
[sent in by P. De Geest] The smallest prime number with a gap of 666 (that is,
such that the prime following it is larger than it by exactly 666) is
18691113008663
Note the three sixes!
Define a dottable fraction as one in which dots (representing multiplication)
can be interspersed in both the numerator and denominator to produce an
expression that's equal to the original fraction. The noteworthy dottable
fraction
666 = 6·6·6
64676 6·46·76
has a numerator of 666 and has 666 embedded in the denominator!
The alphametic below has a unique solution (i.e., there is only one way to
replace letters with digits so that the addition sum is correct):
SIX
SIX
SIX
+BEAST
SATAN
[by Monte Zerger] Note that 1998 (a recent year) = 666 + 666 + 666. Not only
that, but if we set A=3, B=6, C=9, etc., we find, amazingly, that
NINETEEN NINETY EIGHT = 666
Finally, we close with an observation that makes a commentary on the folly of
attaching a specific meaning to the number 666. If the letter A is defined to
be equal to 36 (=6·6), B=37, C=38, and so on, then:
The sum of the letters in the word SUPERSTITIOUS is 666.
End<{{
A<>E<>R
~~~~~~~~~~~~~~~
Integrity has no need of rules. -Albert Camus (1913-1960)
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
The only real voyage of discovery consists not in seeking
new landscapes but in having new eyes. -Marcel Proust
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
"Believe nothing, no matter where you read it, or who said
it, no matter if I have said it, unless it agrees with your
own reason and your common sense." --Buddha
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
It is preoccupation with possessions, more than anything else, that
prevents us from living freely and nobly. -Bertrand Russell
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
"Everyone has the right...to seek, receive and impart
information and ideas through any media and regardless
of frontiers." Universal Declaration of Human Rights
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
"Always do sober what you said you'd do drunk. That will
teach you to keep your mouth shut." Ernest Hemingway
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
Forwarded as information only; no endorsement to be presumed
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
In accordance with Title 17 U.S.C. section 107, this material
is distributed without charge or profit to those who have
expressed a prior interest in receiving this type of information
for non-profit research and educational purposes only.
<A HREF="http://www.ctrl.org/">www.ctrl.org</A>
DECLARATION & DISCLAIMER
==========
CTRL is a discussion & informational exchange list. Proselytizing propagandic
screeds are unwelcomed. Substance—not soap-boxing—please! These are
sordid matters and 'conspiracy theory'—with its many half-truths,
misdirections
and outright frauds—is used politically by different groups with major and
minor
effects spread throughout the spectrum of time and thought. That being said,
CTRL
gives no endorsement to the validity of posts, and always suggests to readers;
be wary of what you read. CTRL gives no credence to Holocaust denial and
nazi's need not apply.
Let us please be civil and as always, Caveat Lector.
========================================================================
Archives Available at:
http://home.ease.lsoft.com/archives/CTRL.html
<A HREF="http://home.ease.lsoft.com/archives/ctrl.html">Archives of
[EMAIL PROTECTED]</A>
http:[EMAIL PROTECTED]/
<A HREF="http:[EMAIL PROTECTED]/">ctrl</A>
========================================================================
To subscribe to Conspiracy Theory Research List[CTRL] send email:
SUBSCRIBE CTRL [to:] [EMAIL PROTECTED]
To UNsubscribe to Conspiracy Theory Research List[CTRL] send email:
SIGNOFF CTRL [to:] [EMAIL PROTECTED]
Om
