Vampire Numbers
cliff
From: cl...@watson.ibm.com
If you respond to this puzzle, if possible please include your name,
address, and e-mail address. If you like, tell me a little bit
about yourself. You might also directly mail me a copy of your response
in addition to any responding you do in the newsgroup. I will assume it
is OK to describe your answer in any article or publication I may write
in the future, with attribution to you, unless you state otherwise.
Thanks, Cliff Pickover
* * *
Vampire Numbers
If we are to believe best-selling novelist Anne Rice,
vampires resemble humans in many respects, but live secret lives hidden
among the rest of us mortals. Consider a numerical metaphor for
vampires. I call numbers like 2187 vampires numbers because they're
formed when two progenitor numbers 27 and 81 are multiplied together
(27*81 = 2187).
Note that the vampire, 2187, contains the same digits as both parents,
except that these digits are subtly hidden, scrambled in some fashion.
Similarly, 1435 is a vampire number because it contains the
digits of the progenitors 35 and 41.
(35*41=1435)
These vampire numbers secretly inhabit our number system, but most have
been undetected so far. I believe there are only six four-digit
vampires in existence, but have no idea if there are any larger vampire
numbers.
What is the largest vampire number you can find lurking out there in
the world of integers?
As the numbers get larger and larger, how often do you expect to find
vampires? Do they get sparser or more frequent as one searches for
vampires up to a googol?
I will be happy to report the largest vampire number ever found
in an article I'm writing.
(If you do any computer searches, could you tell me what language
you used and what machine you used and any other interesting
features?)
Queenie
>Title: Cliff Puzzle 20: Vampire Numbers
>From: cl...@watson.ibm.com
>
>
>Vampire Numbers
>These vampire numbers secretly inhabit our number system, but most have
>been undetected so far. I believe there are only six four-digit
>vampires in existence, but have no idea if there are any larger vampire
>numbers.
I think that none of them have been detected because no one wanted to
bother to find them, this is something that would require doing
a whole lot of multiplication, and is probably better suited
to a computer.
The four-digit vampyres are ...
15 x 93 = 1395
21 x 60 = 1260
21 x 87 = 1827
27 x 81 = 2187
30 x 51 = 1530
35 x 41 = 1435
80 x 86 = 6880
Now this is only if we are strict and exclude
vampyres like
03 x 501 = 1503
03 x 510 = 1530
...
I would be tempted to include them, but the zero does leave
a question unanswered. Besides including them would
make the list of 4 digit vamps bigger than would be nice
to post to this group.
>
>What is the largest vampire number you can find lurking out there in
>the world of integers?
>
So far this, I guess I could find a bigger one if I tried hard enough.
50000 x 50219 = 2510950000
50000 x 51002 = 2550100000
50000 x 51020 = 2551000000
50000 x 51263 = 2563150000
50000 x 51902 = 2595100000
50000 x 52631 = 2631550000
50000 x 59021 = 2951050000
50000 x 59102 = 2955100000
65049 x 65244 = 4244056956
65132 x 65408 = 4260153856 /* largest possible with 32bit int...
and no I don't feel like codeing
multiple precision right now :) */
>As the numbers get larger and larger, how often do you expect to find
>vampires? Do they get sparser or more frequent as one searches for
>vampires up to a googol?
I find that near 2^32 they become very infrequent compared to
the density at small values (1 - 10000).
>
>I will be happy to report the largest vampire number ever found
>in an article I'm writing.
>
>(If you do any computer searches, could you tell me what language
>you used and what machine you used and any other interesting
>features?)
I used a C program. I just wrote it. Boy I gotta lay off the coffee!!!
The Machine is a 32bit Intel-based UNIX machine.
I didn't bother to optimize for speed, but it does a decent job
of finding vamps anyway.
If you are interested in my code, or how I coded it,
email cai...@vampyre.colorado.edu
^^^^^^^ I thought that was appropriate, don't you?
--
car...@vampyre.colorado.edu | What do 7, 11, and 4882195 have in
common? Send a self-addressed stamped envelope to 'PRIMES, PO BOX 17986,
Boulder, CO 80308, for your official prime number. Inquire within.
Shriram Krishnamurthi
> 65049 x 65244 = 4244056956
> 65132 x 65408 = 4260153856 /* largest possible with 32bit int...
> and no I don't feel like codeing
> multiple precision right now :) */
65132 x 65408 = 4260153856
65132 x 87071 = 5671108372
65132 x 89402 = 5822931064
65133 x 98496 = 6415339968
and so on.
Arturo Viso Magidin
Maybe I didn't understand the rules correctly, but it seems to me
that once you have generated vampyre numbers you can get
arbitrarily large vampyre numbers with them.
If a and b are two numbers, each written with n digits, such that
a*b is written as a permutation of the digits of a and b, then
(a*10^m) * (b*10^m) will again be a vampyre number, since
you can write it with the digits of a*10^M and b*10^M. You write
a*b and then add 2m zeroes, with by an amazing coincidence are the
number of zeroes you have added to a and b together.
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
mag...@uclink.berkeley.edu
mag...@math.berkeley.edu
Queenie
>Maybe I didn't understand the rules correctly, but it seems to me
>that once you have generated vampyre numbers you can get
>arbitrarily large vampyre numbers with them.
I am not sure who's rules you are following. Perhaps you can
post again and tell us all that 2 + 2 still equals 4 even for
extrodinarily large values of 2.
c'mon I think that the fun is in finding numbers of distinction.
Did you know that 1 approximated to ten decimal places is
1.0000000000 ?
Give us all a break.
--
car...@vampyre.colorado.edu | What do 7, 11, and 438479857 have in
Arturo Viso Magidin
Queenie <cai...@ucsu.Colorado.EDU> wrote:
>
>I am not sure who's rules you are following. Perhaps you can
>post again and tell us all that 2 + 2 still equals 4 even for
>extrodinarily large values of 2.
>
>c'mon I think that the fun is in finding numbers of distinction.
>
>--
Ok, here's the original post:
-------------------------BEGIN QUOTED ARTICLE----------------------------------
From cl...@watson.ibm.com Mon May 2 14:06:56 PDT 1994
Article: 71190 of sci.math
Path: agate!howland.reston.ans.net!EU.net!Germany.EU.net!Munich.Germany.EU.net!ibm.de!aixssc.uk.ibm.com!watnews.watson.ibm.com!watson.ibm.com!cliff
From: cl...@watson.ibm.com (cliff)
Newsgroups: sci.math
Subject: Vampire Numbers
Date: 28 Apr 1994 20:43:10 GMT
Organization: A
Lines: 43
Distribution: world
Message-ID: <2pp74u$g...@watnews1.watson.ibm.com>
NNTP-Posting-Host: cliff.watson.ibm.com
Title: Cliff Puzzle 20: Vampire Numbers
From: cl...@watson.ibm.com
Vampire Numbers
If we are to believe best-selling novelist Anne Rice,
vampires resemble humans in many respects, but live secret lives hidden
among the rest of us mortals. Consider a numerical metaphor for
vampires. I call numbers like 2187 vampires numbers because they're
formed when two progenitor numbers 27 and 81 are multiplied together
(27*81 = 2187).
Note that the vampire, 2187, contains the same digits as both parents,
except that these digits are subtly hidden, scrambled in some fashion.
Similarly, 1435 is a vampire number because it contains the
digits of the progenitors 35 and 41.
(35*41=1435)
These vampire numbers secretly inhabit our number system, but most have
been undetected so far. I believe there are only six four-digit
vampires in existence, but have no idea if there are any larger vampire
numbers.
What is the largest vampire number you can find lurking out there in
the world of integers?
As the numbers get larger and larger, how often do you expect to find
vampires? Do they get sparser or more frequent as one searches for
vampires up to a googol?
-------------------------END QUOTED MATERIAL-------------------------
Of course I agree that the only interest is in finding
non-trivially large vampyre numbers. Please point out the exact
place in this post were it is asked that the two numbers we
are multyplying together must not be both multiples of 10, or that
we must factor out as many powers of 10 as possible from both numbers.
Once you do that, I'll be happy to give you a break.
My point was that the definition of vampyre number is lacking unless
you specify that the trivial way of extending vampyre numbers which
I pointed out is ruled out.
Happy now?
Kaithbradon
tina...@gmail.com
steve...@gmail.com
Python
> My Name is Steve Jones from Canada, i turn to a vampire any time i want to, I become a real vampire because of how people treat me, This world is a wicked world and not fair to any body. At the snack of my finger things are made happened. Am now a powerful vampire and no one step on me without an apology goes free. I turn to human being also at any time i want to. And am one of the most dreaded and respected person in my country. i am now also very famous and rich with the help of the VAMPIRES EMPIRE. i get what ever a want. i become a vampire through the help of my friend who introduce me into a vampire Kingdom by given me their email: jamessucces...@gmail.com, if you want to become a powerful and a real vampire kindly contact the vampire kingdom on their email: jamessucces...@gmail.com for help. it is real. Contact them today. jamessucces...@gmail.com
who could join your Kingdom.
John Gabriel is a vampire of common sense, he can draw a conclusion from
empty, void statement such as "[f(x+h)-f(x)]/h - f'(x) is a function of
x,h"
Adjunk Crank Lekturer Wolfgang Mueckheim can suck students' blood at
Hochschule Augsburg, Germany, by drawing conclusions from the fact
that any matematical object is a member of a finite set.
Demented Arab Karzhedin can demonstrate fallacies for ages by confusing
diophantian equation with real domain equations. He is sucking blood
from common decency.
David Petry may enjoy you too, he decided to avoid studying math because
he mislead himself into thinking that nobody in math was concerned with
effectiveness, so he learnt nothing and spent a few decades rantings in
the void. He is sucking blood from the elementary education he avoided.
Archimeded Plutonium, aka Perelmann is another kind of vampire, but he
is sucking blood out of himself.
James Waldby
> steve...@gmail.com wrote:
>> My Name is Steve Jones from Canada, i turn to a vampire any time i want
>> to, I become a real vampire because of how people treat me, This world
>> is a wicked world and not fair to any body. At the snack of my finger
>> things are made happened. Am now a powerful vampire and no one step on
>> me without an apology goes free. I turn to human being also at any time
>> i want to. And am one of the most dreaded and respected person in my
>> country. i am now also very famous and rich with the help of the
> You've posted in the right place Steve. We do have a few vampires around
> who could join your Kingdom.
>
> John Gabriel is a vampire of common sense, he can draw a conclusion from
> empty, void statement such as "[f(x+h)-f(x)]/h - f'(x) is a function of
> x,h"
>
> Adjunk Crank Lekturer Wolfgang Mueckheim can suck students' blood at
> Hochschule Augsburg, Germany, by drawing conclusions from the fact that
> any matematical object is a member of a finite set.
>
> Demented Arab Karzhedin can demonstrate fallacies for ages by confusing
> diophantian equation with real domain equations. He is sucking blood
> from common decency.
> Archimedes Plutonium, aka Perelmann is another kind of vampire, but he
entry in [1], which show some other names or aliases the creature has
used: "Archimedes Plutonium (current legal name, born Ludwig Poehlmann
in 1950, raised as Ludwig Hansen, also known as Ludwig van Ludvig and
Ludwig Plutonium)"
[1] https://en.wikipedia.org/wiki/Usenet_personality#Eccentric_believers
--
jiw
Sergio
Mitch Raemsch
FromTheRafters
Zero is a very special number.