Saturday, September 17, 2005

archaeologically deceitful life!!!

well i have no fuckin clue as to y i chose this title for my poem that i'll be jottin down right after this note to u all.... i guess the first title of the poem came bout in my head cos i was studyin bout the subject at the time i was thinkin of a title to my poem...funny ha!!!!
i wanted to write smthin for my blog, and it has taken me a lot time..and i cudn't bear the depth of my thirst anymore,so i thought of quenchin it,forcefully...

i was waitin for my sketches to be displayed b4 i start off with an another poem...but smthin went wrong and my sketches got jammed...luckily i still have them on the floppy...
so...i cudn't wait any longer..."enough is enough"...i realised that until it really scragged the shit out of me....thus,i have opted to write down another poem of mine...right here and right now!!!
i know i have kept u all waitin,but u know wat.... my ramblings were gettin more upset than u all,for they all wanted to be exploited by u all...hahahaha
hope u enjoy this poem....the rebirth of 666,after a long hiatus...though its a really small poem...


where can i go,
i'm so tired of this deceit...

which has left me with nothin,
except for this hallowness...

which has been left,
for me to find out!!!!!


Blogger LadyWhiteSpirit said...

just blog hopping.this too shall past hang on :)

7:10 AM  
Blogger TripleSix said...

@ladywhitespirit... it so?

7:58 AM  
Blogger Random said... can go to the next whisky bar! well thats what you told me, so now i tell you.

9:19 AM  
Blogger MS said...

it is every where,
in that car passing u seeing the eyes of happiness in its headlights,
in those ppl promising of taking ur hand and pulling u out of the mud,
in those moments of youth thinking u could change anything,
in the moments themselves promising of the present,
in these words which intend to talk about deceit.

1:51 PM  
Blogger TripleSix said...

i like that comment.....has it been written by u...if it has,i like it...

but who's goin to pay the bill for my drinks..?!!!!?

12:41 AM  
Blogger Mirage said...

Short...but nice! So howre the essays coming along?

1:13 AM  
Blogger TripleSix said...

there r still on
i'm almost done with them....

8:24 AM  
Blogger Random said...

i'll pay!

8:56 AM  
Blogger MS said...


11:54 AM  
Blogger Arz000n said...

where can i go,
Drop by in Delhi....
Me anyway getting pissed off here....


Khoob jamega rang jab mil baithenge teen yaar....insane poem writer, bizarre blogger and :)


Waiting for ur sketches...take ur time...I know u r busy out there..


9:35 PM  
Blogger khelnayak said...

Yeah...nice one. Does it reflect your present state of mind?

And yeah...its you and you alone who can find it out. :)

And update me abt that young writer hunt contest. Best luck. :)

10:34 PM  
Blogger milo said...

welcome bk dear..short n crisp...dats wat we r learning these days!!

1:53 AM  
Blogger TripleSix said...

i know

well,i think't tell wat my mind is upto...keeps fluctuatin and that gets me indecisive regardin serious matter as well..

i will once i get the response frm those talent hunters..btw,thnk u!!

ru sure...cos i'm a an ardent lover of wine...
aaahhhh...i can see those holes in ur!!

chal phir...kabh mil rahe hai hum?


5:59 AM  
Blogger Jithu said...

cool! there u are.. :-) btw when will we get a chance to see ur collages mam? btw ur entire frustration is evident in that poem.. :-)

3:31 PM  
Blogger Random said...

hmm..true..i shld back off. u know how broke i am. cant afford pockets, let alone holes in them.

6:43 PM  
Blogger Arz000n said...

Im here tentative till this friday...after that if ma Singapore trip mein koi kida nahi karega toh main chala for atleast 6 months in S'pore :)


Mereko Mirage ke b'day party mein invite bhi nahi kiya :(

Bad...bad...bad :(

8:58 PM  
Blogger TripleSix said...

as if she predicted u were here....
but u know wat? we kept talkin bout all our blogger frnds at the party,and u were one of those whom we talked in that sense,u were there with us at the party...howzzat!!!
ahhhh....the only thing is u missed out on wodka and cake...yummy!!!
ru in delhi?batayaa kyun nahi..budhu..plan hota toh mirage and i cud have met u..


yup...i'm here
and soon my sketches will be too..
just hang on,pal!!!

9:27 PM  
Blogger Arz000n said...

the only thing is u missed out on wodka and cake...
I dont drink...but cakeeee :((
I missed pet pein and then dil pein :(

1:51 AM  
Blogger Keshi said...

**i'm so tired of this deceit...

me too..

Life is an illusion...a mirage that laughs at ur stupidity when u get closer to it...

good one!

11:45 PM  
Blogger Arz000n said...

K000kie in stalking mode :)

12:46 AM  
Blogger TripleSix said...

thnks for the appreciation and thnks for droppin by...

tu kya kahne ki koshish kar raha hai,bby!!! :)

11:11 AM  
Blogger Arz000n said...

Almost every evening I spend in CAKE PALACE, after office, for those yummy yummy stuff kept in there :)

Main toh cake khane ki koshish raha hoon....woh bhi miss ho gaya

Thanks to poor planning


11:04 PM  
Blogger D'yer Mak'er said...

Haven't I told you this before had I spent a few moments with myself behind this number 666, I'd have broken this code. Down below must be the facts which made mirage give you this name 666.

In the King James Version, Revelation 13:18 reads:
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 three score and six.

In the Good News Bible, the same verse runs:
This calls for wisdom. Whoever is intelligent can figure out the meaning of the number of the beast, because the number stands for the name of someone. Its number is 666.

The number 666 is also seen in the Old Testament book of II Chronicles; verse 9:13 reads (KJV) and in its parallel (1Ki 10:14):
Now the weight of gold that came to Solomon in one year was six hundred threescore and six talents of gold....
The number is also in the genealogy (Ezr 2:13, see also Neh 7:18):
The children of Adonikam, six hundred sixty and six.

But something you may not know about this number!

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


The sum of the first 144 (= (6+6)·(6+6)) digits of pi is 666.


16661 is the first beastly palindromic prime, of the form 1[0...0]666[0...0]1. The next one after 16661 is


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 nice form:

(6·6·6)² + (666 - 6·6)² = 666²


There are only two known Pythagorean triangles whose area is a repdigit number:

(3, 4, 5) with area 6
(693, 1924, 2045) with area 666666

It is not known whether there are any others, though a computer search has verified that there are none with area less than 1040. [see J. Rec. Math, 26(4), Problem 2097 by Monte Zerger]


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.


A well-known remarkably good approximation to pi is 355/113 = 3.1415929... If one part of this fraction is reversed and added to the other part, we get

553 + 113 = 666.


[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


[from G. L. Honaker, Jr.] There are exactly 6 6's in 6666. There are also exactly 6 6's in the previous sentence!


[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

66651 = 9935407575913859403342635113412959807238586374694

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 items #13, #14, and #2 on this page by simply writing:

666 = S2(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 (20772199, 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.


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, and is equal to the sum of the numbers from 1 to n.

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.)


The doubly-triangular numbers are those numbers of the form T(T(n)), where T(n) are the triangular numbers defined in the previous item. The sequence of doubly-triangular numbers begins

1, 6, 21, 55, 120, 321, 406, 666, 1035

so we see that 666 is the eighth doubly-triangular number (i.e., T(T(8)) = 666).

The nth doubly-triangular number is, among other things, the number of ways to paint the vertices of a square using a set of n colors, where the colors are distinct but rotations and reflections of a given colored square are considered the same. So there are 666 distinct ways of painting the vertices of a square with a set of eight colors.


[from Monte Zerger] 6 (= T(3)), 66 (= T(11)), and 666 (= T(36)) are all triangular numbers in base 10. These three numbers are also triangular in two other bases: 49 and 2040:

(6)49 = 6 = T(3)
(66)49 = 300 = T(24)
(666)49 = 14706 = T(171)

(6)2040 = 6 = T(3)
(66)2040 = 12246 = T(1564)
(666)2040 = 24981846 = T(7068)


[from Monte Zerger] 6666 = 87266061345623616, which contains 6 6's. In addition, the digits of 6666 can be split into two sets in two different ways, both of which sum up to the same value, 36 (= 6 x 6).

The first eight and last nine digits both sum to 36:

8 + 7 + 2 + 6 + 6 + 0 + 6 + 1 = 6 x 6 = 3 + 4 + 5 + 6 + 2 + 3 + 6 + 1 + 6

while the 6's and non-6's also add up to 36:

6 + 6 + 6 + 6 + 6 + 6 = 6 x 6 = 8 + 7 + 2 + 0 + 1 + 3 + 4 + 5 + 2 + 3 + 1

Finally, note that 6666 is almost pandigital - the only digit it's missing is an upside-down 6 (i.e., 9).


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, an amazing fact:

666 is conjectured to be the most wicked repdigit polygonal number.

Since 666 = P(3,36), its wickedness value is 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 solid 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 decimal 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 (since the digits at that position are "343", or 7 cubed)

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.


Inserting zeros between the sixes in 666 gives the number 60606, which has a few interesting properties of its own:

60606 = 7 x 13 x 666 = 91 x 666 = T(13) x T(36) - i.e., 60606 is the product of two triangular numbers.

60606 = 7 x 37 x (13 x 18), which is interesting in that Rev 13:18 is the place where 666 is mentioned.

60606 = P(7,156) - i.e., 60606 is a 7-gonal number. (Note that this can be written entirely using the evocative numbers 6, 7, and 13, by saying 60606 = P(7, (6+6)·13)). In addition we can make a statement using only 7's:

60606 is the 7th palindromic 7-gonal number.

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., Jud McCranie, Monte Zerger, 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:


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!


[from Simon Whitechapel] A mathematically important number sequence is:

7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, ...

which is the sequence of primes p whose reciprocal in base 10 has maximum period p-1. The last one, 1/149 with period 148, has the following digits after the decimal point (which then repeat):


As luck would have it, the sum of these is 666. If these 148 numbers (the first 148 digits of 1/149) are written as the top row of a 148x148 square grid, and then the digits of 2/149 as the second row, then 3/149 and so on, the result is a 148x148 pseudo-magic square, in which every row and column sums to 666.


[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


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 a denominator of the form 6x6y6.


Here's another one (actually, two) based on a fraction [by Manley Perkel and Mike Keith]. The fraction 1666/6664 (which has a 666 in both numerator and denominator) has two interesting properties:

(1) The numerical value of the fraction (0.25) is the same as the numerical value of the fraction you get by "canceling" (i.e., erasing or removing) the 666 from both the numerator and denominator.

(2) The value of the fraction is the same as the value you get by splitting the fraction in half and multiplying the two parts together; that is,

1666 = 16 . 66
6664 66 64
A fraction like this is known as a fractured fraction.


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):



[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


Frank Fiederer points out that the age of the United States in 1998 is also related to 666, since

1998 - 1776 = 666/3.

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.

p.s. actually the "rebirth of 666" phrase made me go for this, n' I couldn't stop myself!!

12:34 AM  
Blogger TripleSix said...

so sad...
u know wat...i'm havin all the b's right now...
b for brownie,b for beer and b for beethoven...

@stangers inc...
reivival of the strangeness after a!!!
u actually did all that research work just to break the code of three similar and simple digits...
good!!! :)
looks like u've been missin me alot...
its gr8 to have u back,but wud be btr if its for a perpetual reason..
take care of urself!!!!mr dyer maker :)

6:44 AM  
Blogger Mirage said...

Nika, u gotta feel flattered girl!! Someone actually went thru so much trouble to let u know a HELL LOT about ur nick!

Um Dyer, I only gave her that name coz she reminds me of the devil child from the movie Omen. A piece of advice tho...chill out dude!! :)

10:50 AM  
Blogger D'yer Mak'er said...

wow..seems exceedingly romantic isn't it??.."missin me a lot" i'm dyin..waitin in the middle of the road for you...that's what you wanted to hear???....but really fell for all this stuff...i mean you really thought all this to be true..come on...wake up!!!...n' not only you..also mirage!! my...girls are easy believers!!!!!!!!...**my concoction theory worked!!**

2:17 AM  
Blogger D'yer Mak'er said...

@mirage -->>.. n' you're askin a frozen fossil to chill out...when all i want is some warmth!!!!!!

2:18 AM  
Blogger TripleSix said...

@strangers inc...
chalo,u didn't miss me,but i did..
a big hug frm me

kyun meri tang keech rahi hai or kyun others(stranger's inc) ke liye,devil ban rahi
just kiddin

7:56 AM  
Blogger D'yer Mak'er said...

who said i didn't miss you...i did....didn't you feel that from my presence here??...n' a bigger hug from my side...n' don't you dare tell me to let you go until i want to(wink!!!!!!)

p.s. just for the record...the facts that i wrote about 666 happens to be genuine...they ain't fake...n' don't you worry about mirage...i've a few weak nerves still in my pocket that can really take her down..any moment i want...she won't dare to pull any me...she won't!!!!!!

9:41 AM  
Blogger TripleSix said...

@stranger's inc

hug me till u nvr want to leave me...hmmmmm.....nice!!!
i have a request,dn't pull mirage's leg too much,she's a dear frnd of mine....(i know,i know...u were just kiddin)

i know all the stuff tht u wrote bout "666" was not fake,and u know wat...honestly speakin,i knew bout it,otherwise i wudn't have spent so much of time readin them....i actually read them..all the facts written by U.
take care of urself.
u can jot down ur msnger id,we can keep in touch and send loads of!!!!

11:56 AM  
Blogger Mirage said...

@D'yer M'aker: Is that a challenge...!?

4:47 AM  
Blogger Mirage said...

Oh and about believing all that stuff, naah we were actually surprised that u took out so much of ur precious time to pen down SO MANY facts!! Surprised we were, gullible we're not!

Oh n a big hug to u, coz um u need warmth rt...!? ;)

4:55 AM  
Blogger D'yer Mak'er said...

@mirage -->>..

Is that a challenge...!? first of all this attitude is not at all helpin!!!...for i never want to enter some arena where i've to face a young girl!!!!!
but i feel you've absolutely got no reasons to believe that i can't take you down(wink!!!!)

coz um u need warmth
..boy!'s hot out here!!!!!

p.s. i thought you're on some trip..break liar!!!!!!

6:28 AM  
Blogger TripleSix said...

@mirage and stranger's inc...
wats goin on?
plez dn't do ur datin business on my blog
spare my lil time....

9:28 AM  
Blogger D'yer Mak'er said...

so you know a better place???...any suggestions????

10:02 AM  
Blogger TripleSix said...

@stranger's inc....
yeah i do have...
either u do ur datin on ur own blog or on mirage's,cos i'm single and i'm gettin "j"...
na...i'm just kiddin,do whatever u feel like,feel free to even date on my blog...hahahahaha

10:41 AM  
Blogger D'yer Mak'er said...

what if i say i want more???

2:04 AM  
Blogger Gates said...

DYER!! What was that, it went over my head, because, I didn't torture my eyes with it.

Mathematics? Me? He, he

5:51 AM  
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1:26 PM  

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