HDTenEightyP/NetNews huggingface dataset:
From: michaelg@Xenon.Stanford.EDU (Michael Greenwald)
Subject: Re: factoid about new prime
Organization: CS Department, Stanford University, California, USA
Date: 10 Apr 92 16:06:54 GMT

martin@lyra.cis.umassd.edu (Gary Martin) writes:

>In article <1992Apr9.111809.19221@linus.mitre.org> bs@faron.mitre.org (Robert D. Silverman) writes:

>   4 times as big as P does NOT equal 4P. Size is measured by number of
>   bits. 4 times as big means 4 times as many bits. CNN got it RIGHT.
>   Most people here are getting it wrong.
>   --
>What are the chances that CNN understood why what they said was right?
>(Particularly considering that there are people here who don't.)

Well, I was surprised that Monty Hall apparently understood why the
solution to the Monty Hall problem was right.  Sometimes people aren't
as dumb as they seem.  I won't be surprised again, even if the
newscaster in question is offering to trade a live goat for the prime
number behind curtain number 2^(2^32) + 1.
From: kwhyte@zarquon.uchicago.edu (Kevin Whyte)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 6 Apr 92 21:09:50 GMT
Organization: Dept. of Mathematics, U. of Chicago

In article <sundquis.702591357@s6.math.umn.edu> sundquis@s6.math.umn.edu (Thomas Sundquist) writes:
>>   >>No, Erdos only offers money for his own problems.
>>   >Pardon my ignorance. Who is this Erdos dude?
>
>>   You're joking right???  April 1 is tomorrow, not today, right???
>>   This must be a joke. How can anyone who reads or posts to this newsgroup
>>   not know who Paul Erdos is???
>>   I can understand Joe Blow off the street not knowing, but how can anyone
>>   with an interest in math [evidenced by the fact that he reads this group]
>>   Bob Silverman
>>   These are my opinions and not MITRE's.
>>   Mitre Corporation, Bedford, MA 01730
>
>>Come on, Bob, as a reader of this group you must have noticed that its
>>contributors range from the professional to the not-so-professional.
>>Why not just answer the question? After all, the poster says "Pardon
>>my ignorance", and then he does not deserve to be run over like that.
>>Stein 
>
>My thoughts exactly.	Tom

  Am I the only one who thought Bob's response was tounge-in-cheek?
Kevin
Newsgroups: sci.math
From: michaelg@Xenon.Stanford.EDU (Michael Greenwald)
Subject: Re: Fermat's Last Theorum
Organization: CS Department, Stanford University, California, USA
Date:  8 Apr 92 17:50:28 GMT

danwell@IASTATE.EDU (Daniel A Ashlock) writes:

>In article <1992Apr8.004108.2697@augean.eleceng.adelaide.edu.AU>,
>dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
>> 
>> What's tantalizing about FLT is this fabled note that Fermat wrote before
>> he died saying that he found an "elegant proof."
>> 
>> There are two possibilities:
>> 
>>                   (a) he really found the proof, which is now lost
>>                   (b) he had a mental abberation and was mistaken
>> 
>> Out of curiosity, I was wondering whether the maths community today
>> generally regards (a) or (b) a being the most likely?

>   (b), except that, being the charitable sorts we are, we referred to his
>"mental abberation" as a "mistake".  He may have done something very straight
>foreward like only prove the theorem for a few n and then mistakenly believed
>the proof generalized.

Two things that should be added are 
    (a) Fermat made other mistakes (some not discovered until after his death)
    (b) Fermat was candid about mistakes that he did discover.

The original post implied that perhaps at some time most
mathematicians believed that Fermat >did< have a proof, but it was
actually lost.  I'm not sure that was ever >widely< believed.  ("Not
sure" means "I don't know, but my guess is that it wasn't") -- I'm
curious, though.  I would like someone who knows better to clarify the
point, please.

Thanks.
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Fermat's Last Theorem
    <1992Apr9.133316.24615@linus.mitre.org> 
    <1992Apr10.013258.4518@augean.eleceng.adelaide.edu.AU>
Date: Fri, 10 Apr 1992 13:25:37 GMT
Organization: University Of Kentucky, Dept. of Math Sciences
X-Bytes: 

In article <1992Apr10.013258.4518@augean.eleceng.adelaide.edu.AU> dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
>In article <1992Apr9.133316.24615@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
>>You are probably not a professional sports player, yet I'm sure you
>>know who the greatest pros are. Why do you know? Because you are
>>interested in sports and follow them! Why should not the same thing
>>apply in mathematics???
>>--
>>Bob Silverman
>
>OK Bob here's a little general knowledge quiz for you. Who are the greatest
>pros of the 20th century in the following sports:
>
>a) Cricket
>b) Baseball
>c) Golf
>d) Atheletics
>e) Gymnastics
>f) Ice skating
>h) Bungee jumping
>i) Tiddly Winks
>j) Female mud wrestling
>k) Barefoot boxing
>l) Fartlek
>
>?????

Fartlek is not a sport; it is a type of training used by distance runners.

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu
From: sam@wet.UUCP (Sam Needham)
Newsgroups: sci.math
Subject: Re: An elementary, "naturally occurring" problem
Date: 7 Apr 92 07:45:32 GMT
Organization: Wetware Diversions, San Francisco

In article <1992Apr1.201733.25777@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
-In article <1992Apr1.183035.14916@Princeton.EDU> carabalo@phoenix.Princeton.EDU (David G. Caraballo) writes:
-:The following problem and more general analogs in 2 or more dimensions have
-:occurred more than once (in some form) during the course of my research.  The
-:problem is elementary, but I found it interesting that problems of this type
-:kept occurring "naturally".  Here's the simplest example:
-:
-:Prove or disprove that there exists a bijection f:[0,1] -> [0,1] that is
-:not continuous at any point. 
- 
-Doesn't the following function do it?
-f(x) = 1-x  if x is irrational.
-f(x) = x if x is rational.
-Bob Silverman

Continuous at x = 0.5.

The proof that there is no such function uses, I think, the Baire Category 
Theorem. Suppose f: [0,1] to [0,1] is discontinuous everywhere and f(a) =
0.5; then the family

	[0,1] minus inverse-image-of-f( 0.5 - 1/n, 0.5 + 1/n) (n>=3)

has union [0,1] but none of them contains an open neighbourhood of a. 
This doesn't need all the strength of the question.


					Sam

(If I'm wrong, I don't want to know. The BCT is all I have left of graduate
analysis, and that's only because it's logic).
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Generalizing Mersenne Primes
Date: 7 Apr 92 07:34:50 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.



As long as we are discussing Mersenne primes, there is at least one 
generalization of this notion that I would like to know more about.

Let p be a prime. Let me call a prime of the form (p^r-1)/(p-1) a
p-Mersenne prime. For p=2, we recover the notion of a Mersenne prime.
Such primes exist for p>2. For example, 13=(3^3-1)/(3-1) is a 
3-Mersenne prime.

Another generalization of the notion of Mersenne prime is the notion of
a Mersenne prime power, i.e. a prime power of the form 2^n-1. But now
that we have the notion of a p-Mersenne prime, we can instead define
a p-Mersenne prime power to be a prime power of the form (p^r-1)/(p-1).

For example, 8=(7^2-1)/(7-1) is a 7-Mersenne prime power. And 
121=(3^5-1)/(3-1) is a 3-Mersenne prime power.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math,sci.crypt
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: factorial puzzle
Date: Fri, 10 Apr 1992 13:36:12 GMT
Organization: University Of Kentucky, Dept. of Math Sciences
X-Bytes: 

In article <4782@umriscc.isc.umr.edu> ecarsten@next1.cs.umr.edu (Edward Carstens) writes:
>
>How many zeros are at the end of 1000! ?
>
>No, the answer isn't 3.  The exclamation represents factorial of course. :-)
>
>-Ed Carstens
>Creator of JugglePro

You need to count the numbers of tens that divide 1000!.  To do this,
you can count the number of times 2 and 5 divide 1000!.  There is a
formula to do this, which I believe is 

SUM(i=1, , [1000/p^i]), where [x] is the greatest integer function.
I mean that this formula counts the number of times a prime p
divides 1000.  I am quoting from memory, but you can probably
find the formula in an analytic number theory textbook, or in a 
group theory book, since this formula also gives the order
of a p-Sylow subgroup of the symmetric group on 1000 letters. 

CHarles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu
From: rusin@mp.cs.niu.edu (David Rusin)
Newsgroups: sci.math
Subject: Re: Mersenne Composites
Date: 8 Apr 92 14:55:15 GMT
Article-I.D.: mp.1992Apr8.145515.23147
Organization: Northern Illinois University

In article <a_rubin.702588553@dn66> a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:
>In <1992Apr3.185550.20987@mp.cs.niu.edu> rusin@mp.cs.niu.edu (David Rusin) writes:
>
>> ... the only
>>restriction on the multiplicative group of a field is that there be at most
>>n solutions to x^n=1 (obviously). ...
>
>References would be appreciated.

Everything I know about this question (not much) started with the relevant
section of Fuchs, "Infinite Abelian Groups" (Vol II), p 312 et seq (especially
the notes at the end of the chapter). Relying now not on my poor memory but
on this source we see:

Given any infinite abelian  A  with an element of order 2 and a torsion subgroup
embeddable in  Q/Z,  there is a field  K  whose multiplicative group is
isomorphic to   A x F   for some free abelian group F.

On the other hand, there is no way to characterize exactly the groups  A
which occur as the multiplicative subgroup of some  K  (without the extra
free factor, that is). This is a result from Logic.

dave rusin@math.niu.edu
From: rose@fsu1.cc.fsu.edu (Kermit Rose)
Newsgroups: sci.math
Subject: Integer programming
Date: 2 Apr 92 18:02:34 GMT
Article-I.D.: mailer.1992Apr2.130234.24964
Reply-To: rose@fsu1.cc.fsu.edu
Organization: Florida State University
News-Software: VAX/VMS VNEWS 1.3-4

Pase@cray.com asked about solving the standard linear algebra problem when 
the coficients are integers instead of real or rational numbers.  The 
answer is quite simple.  In regular matrix inversion  you repeatedly apply 
3 operations (1) interchange of two rows. (2) replacement of a row with the 
row minus a multiple of another row. (3) division of a row by a constant.

If we have integers coeficients, then the first two operations are still 
valid, and lead to a row reduced echeleon matrix. Thus we can still reduce
the N equations to a series of equations that are easily solvable because  
each equation in the series introduces one more variable.

Kermit@FSU


This is the signature file of Kermit Rose.

Believing in dichotomies leads to hardening of your logic.

What determines the existence of Free Will?

Peace is the way to peace.  Hostility is the way to hostility.
From: cliff@WATSON.IBM.COM
Newsgroups: sci.math
Subject: Chaos and Graphics
Date: 14 Apr 92 15:03:13 GMT
Article-I.D.: ucbvax.9204141503.AA19472

The latest issue of "Computers and Graphics" is a special issue
on chaos and fractals.  Topics include:

- Synthesizing extraterrestrial terrain
- Chaos and graphics of genetic sequences
- The Mandelbrot set
- Chaotic Attractors
and more, with lots of nice color illustrations.

Inquiries regarding this special issue can be made via internet at
PPI@PERGAMON.COM

The issue is volume 16, Number 1, 1992.
Newsgroups: sci.math,sci.crypt
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: New Mersenne Prime
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Wed, 1 Apr 1992 18:24:46 GMT

In article <1992Mar29.145006.14491@swdsrv.edvz.univie.ac.at> pm@katz.cc.univie.ac.at () writes:
:Here are some more questions concerning Mersenne primes in general and
:the new one in particular:
:
:(1) What made Cray check that particular prime? Was it just one prime in a 
:    long series of tests, or is there any reason to suspect a Mersenne prime 
:    before doing the actual testing?
 
Just a lucky guess. 
There is NO reason to suspect a Mersenne prime other than that the absence of
small factors makes it slightly more likely to be prime.

:
:(2) A closely related question: how many primes can be excluded by means
:    simpler than the Lucas test? The simplest theorem about factors of
 
About 50 to 55% can be excluded by finding a small prime factor.

:    Mersenne numbers is given in Hardy and Wright and states, if I recall
:    correctly, that M_p for p = 4n + 3 and 2p + 1 prime is divisible by
:    2p + 1. Are there many more theorems of a similar nature, and, if you have

The theorem works because 2 is a primitive root. Any prime that has 2 as a
primitive root must be congruent to 1 or -1 mod 8. Here, we have 2p+1 = 8n+7.

One can construct similar theorems using higher reciprocity laws. They tend
to have limited value.

:    exhausted them all, for how many primes do you have to do the actual
:    checking?
 
	Just under 50% of the primes need be checked via Lucas-Lehmer.

:(3) How long did the calculation take? I hear some rumours about nineteen
:    hours, but it is not clear whether this refers to the testing of several
 
This is for one number. They had in fact tried 84 other numbers near 756K
before they found the prime.

:    primes, or to 756839 alone. I am particularly interested in this
:    question since I wrote a little program of my own for checking Mersenne
:    primes, and of course I want to know how it compares to other people's
:    efforts. I am currently verifying the 756839 test, and I expect the
 
It's already been independently verified.

:    answer on Wednesday at 8 a.m. sharp, Central European Daylight Saving
:    Time. I am running the program on an IBM RISC/6000-550 workstation, and
:    I estimate the calculation to take 112 hours. If the Cray people needed
:    19 hours for the single test then it seems my program is reasonably fast:
:    The cycle time of the RS/6000 is six times the cycle time of the Cray 2,
:    and the calculation takes roughly six times nineteen hours.
 
May I ask what variant of FFT you are using for your multiplies???

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: reus@klein.euromath.dk (Jens Peter Reus Christensen)
Newsgroups: sci.math
Subject: Re: gamma function
Date: 7 Apr 92 09:43:08 GMT
Organization: University of Copenhagen, Dept. of Math.

The integral of  t^(z-1).exp(-t)dt  from 0 to infinity. Only valid for
the real part of z > 0 .

--
|--------------------------------------------------------------------------|
|  Jens Peter Reus Christensen   |                                         |
|  Associate professor, Dr. Phil.|                                         |
|  Department of mathematics     | e-mail:          reus@euromath.dk       |
|  University of Copenhagen      |                  reus@danmat.euromath.dk|
|  Universitetsparken 5          | phone:           +45 3135 3133 ext. 458 |
|  DK-2100 Copenhagen            | fax:                      +45 3135 4254 |
|--------------------------------------------------------------------------|
|  Disclaimer: Except when explicitly stated otherwise any message         |
|  with this signature is the authors purely private responsibility.       | 
|--------------------------------------------------------------------------|
|  Motto : The first to present his case seems right, till another comes   |
|  forward and questions him. PROVERBS Chapter 18,v 17 .                   |
|--------------------------------------------------------------------------|
From: ravela@piglet.cs.umass.edu (Srinivas Ravela)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 7 Apr 92 04:56:14 GMT
Organization: University of Massachusetts, Amherst

In article <sundquis.702591357@s6.math.umn.edu> sundquis@s6.math.umn.edu (Thomas Sundquist) writes:
>>   >>No, Erdos only offers money for his own problems.
>>   >Pardon my ignorance. Who is this Erdos dude?
>
>>   You're joking right???  April 1 is tomorrow, not today, right???
>>   [...]
>>   Bob Silverman
>>   These are my opinions and not MITRE's.
>>   Mitre Corporation, Bedford, MA 01730
>
>>Come on,[...] 
>>Stein 
>
>My thoughts exactly.	Tom


Second that. I don't see why one should not "know". I think 
answers like the one Bob has given just discourage people from asking
any. What's the likelihood you know Bob? (You never answered the
question anyway). Pl. I request netters to be more considerate and 
if you do feel compelled to comment (in the nature and tone above)
or air your frustration I suggest use of alternate techniques 
 (Count a 10 perhaps).

Ravela
.
 
Newsgroups: sci.math
From: rscott@csws11.ic.sunysb.edu (Robert Scott)
Subject: FERMAT'S LAST THEOREM
Organization: State University of New York at Stony Brook
Date: Wed, 15 Apr 1992 14:10:50 GMT

TORD MALMGREN WRITES:

>he have mentioned it in those letters to his friends? 350 years of
>mathematicians as clever, not to say more clever than he, and with
>more knowledge, more powerful methods haven't been able to solve it,
>so if you ask me; he goofed or boosted or tried to get into history books...

I CERTAINLY USED TO BE ONE OF THOSE WHO LEANED STRONGLY TOWARDS THE THEORY
THAT FERMAT SIMPLY MADE A MISTAKE.

RECENTLY, HOWEVER, I CAME ACROSS A CASE (NOT IN THE FIELD OF NUMBER THEORY)
WHERE FERMAT WAS RIGHT, AND THE PREVAILING WISDOM OF 350 SUCCEEDING YEARS'S
WORTH OF CLEVER MATHEMATICIANS (AND PHYSICISTS) WAS WRONG.

I AM NO LONGER QUITE SO CERTAIN THAT FERMAT DIDN'T HAVE A VALID PROOF OF THE
"LAST THEOREM", AS WELL.


-JAMES DOLAN (RSCOTT@LIBSERV1.IC.SUNYSB.EDU)


Xref: sparky sci.math:5945 comp.theory:1080
From: djimenez@ringer.cs.utsa.edu (Daniel Jimenez)
Newsgroups: sci.math,comp.theory
Subject: Re: factorial function
Date: 11 Apr 92 06:40:11 GMT
Distribution: usa
Organization: University of Texas at San Antonio

In article <1992Apr11.035328.19005@newserve.cc.binghamton.edu> kym@bingvaxu.cc.binghamton.edu (R. Kym Horsell) writes:
>In article <1992Apr11.005805.12761@linus.mitre.org> bs@faron.mitre.org (Robert D. Silverman) writes:
>>In article <1992Apr10.201515.14401@ringer.cs.utsa.edu> djimenez@ringer.cs.utsa.edu (Daniel Jimenez) writes:
>>:What I'd really like would be a simple O(log n) algorithm
>>:for n!, but I suspect there isn't one out there.
>> 
>>It's easy to show that an O(log n) algorithm is impossible.
>>n! is about (n/e)^n so log(n!) is about n log n. It takes just
>>this long to merely write down the answer.
>
>I'm not sure whether the original poster had in mind O(log n) ARITHMETIC
>operations or BIT operations.
>
>-kym

Arithmetic.  As many have pointed out, n! takes O(n) bit operations
just to do anything to, like print or add.  I don't care about this.
Besides just wondering whether such an algorithm exists, and just
hasn't been discovered for lack of interest, this algorithm may
actually have some "practical" use.

For example, n^n (an upper bound for n!) would take far too many bit
operations and memory cells to contemplate, for a large n.  But
n^n mod 100000 is a simple operation you can do on your home computer
in O(log n) time, and will give you the last few digits of n^n.

If we can calculate n! mod 100000, we can know the last few digits
of n!, assuming the algorithm lends itself to modulus like
exponentiation does.

Practical?  About as practical as calculating the next Mersenne prime,
but what do you want?
-- 
Daniel Jimenez
From: rose@fsu1.cc.fsu.edu (Kermit Rose)
Newsgroups: sci.math
Subject: how to solve a = p (1+r/n)**nt   for n
Date: 3 Apr 92 17:22:40 GMT
Article-I.D.: mailer.1992Apr3.122240.25582
Reply-To: rose@fsu1.cc.fsu.edu
Organization: Florida State University
News-Software: VAX/VMS VNEWS 1.3-4

a = p (1+r/n)**nt = p ([1+r/n]**n)**t  aproximately = p exp(rt) for large n
(a/p)**(1/t) = (1+r/n)**n aproximately = exp(r) for large n.
(a/p)**(1/rt) = (1+r/n)**(n/r)  
So if you have a table of f(h) = (1+h)**(1/h) approaches e as h aproaches 
0, you can estimate f inverse of [(a/p)**(1/rt)]. This would give a number 
equal to r/n.   Invert and then multiply by r to get n.

Kermit@FSU or rose@fsu1.cc.fsu.edu.bitnet
If you want to be sure I see your response, please e-mail me.
-----------------------------------------------------------------------
This is the signature file of Kermit Rose.

Believing in dichotomies leads to hardening of your logic.

What determines the existence of Free Will?
I strive to believe only what is true. I have faith that whatever is 
true will also be logically consistent and knowing truth will increase my 
capacity to be kind.
Peace is the way to peace.  Hostility is the way to hostility.
From: maylis@marylin.Greco-Prog.FR (Maylis DELEST)
Newsgroups: sci.math
Subject: Re: polyominoes, anyone?
Date: 14 Apr 92 15:15:13 GMT
Organization: Laboratoire Bordelais de Recherche en Informatique

In article 
<1992Apr11.033700.8101@ux1.cso.uiuc.edu>  marty@amaterasu.physics.uiuc.edu
 (Marty Gelfand) writes:

> If I'm not mistaken polyominoes also go by the name "lattice animals" in
> the physics literature...and that might be a place to look for the current
> status of the asymptotics at large n.  I don't think exact results are
> available unless the shape is restricted in various ways.  --Marty G.

You are right a lot of Physics literature exist about polyominoes or animals
and you are right also for general polyominoes there are only
assymptotic results according to the area.
Recently two surveys were made on this subject: one by A.J. Guttman
(Melbourne University, Australia) in the J. of Phys. A, this is 
essentially about asymptotic results and
one by me which can be found in J. of Math. Chem. 91 which treat with exact
enumeration.
Our group of "Combinatoire Enumerative" 
in Bordeaux had obtained several results on the enumeration of
polyominoes having some properties according to several statistics (perimeter,
area,...).
Be free to ask me reprints if you need

On the other hand about tilling, I am in touch with several person working on it
ask to db@litp.ibp.fr, or Pr. Mazoyer in Ecole Normale Superieure de Lyon, LYON

Maylis DELEST
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Newsgroups: sci.math
Subject: Re: fun with primes
Date: 7 Apr 92 20:47:03 GMT
Article-I.D.: dn66.a_rubin.702679623
Organization: Beckman Instruments, Inc.

In <f!cHf9kj6@cs.psu.edu> sibley@math.psu.edu (David Sibley) writes:

>In article 702587236@dn66, a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:
>>
>>The best one I can remember is: in any Noetherian integral domain D which
>>is not a field, there are infinitely many primes.
>>
>>Proof sketch:
>>
>> ... (omitted stuff)
>>
>>(3)  Suppose there are only finitely many primes; let x be the product of
>>all of them plus 1.  If x is 0, then each p is a unit, a contradiction.  If
>>p divides x, then p divides 1, and p is a unit, a contradiction.  Hence, in
>>any factorization of x (guaranteed by (1)), no prime can occur, again, a
>>contradiction.  Done.
>>

>Nope. x can be a unit and therefore have no prime factors.

OOPS, you're right.
--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
Ich bin ein Virus.  Mach' mit und kopiere mich in Deine .signature.