Mersenne Digest         Tuesday, May 18 1999         Volume 01 : Number 561




----------------------------------------------------------------------

Date: Tue, 18 May 1999 02:31:24 -0400
From: [EMAIL PROTECTED]
Subject: Mersenne: Re: Mersenne Digest V1 #560 

I can see two possible ways offhand, neither of which I have tested. 

1. Rather than watching stdout, check for prime.spl or whatever the
spool file is named existing and having a size > 0, then spawn
pppd. This is a simpler script, but you'll need to adjust the retry
interval so that it contacts the server before the ppp link idles out.

2. Use diald, or a similar demand-dialing daemon and do nothing, it
will automatically connect whenever you use any network
socket. Beware, however, that demand-dialed analog connections usually
take so long to connect that the system call will probably time out
the first try. Again, the solution is to keep a relatively small retry
interval in mprime.

>Hi, I have a question to the linux/mprime experts:
[...]

>Eventually, I got that to work. My question is whether there is any way
>to bring down/up the ppp0 interface whenever mprime needs to contact
>PrimeNet server automatically?
>
>The only way I can think of is having a script monitor the optional
>STDOUT of mprime and then checking whether it needs to contact the
>server.
>
>If there is a better solution, please point me to it.

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------------------------------

Date: Tue, 18 May 1999 10:17:42 GMT
From: "Brian J Beesley" <[EMAIL PROTECTED]>
Subject: Re:  Mersenne:  Repeating LL remainders

> >I think we should check the math first. I have a sneaky suspicion that looping
> >won't occur in the relevant region (the first 2^n-3 iterations) unless n is 
> >composite - which may be interesting, but doesn't help us eliminate Mersenne
> >numbers as candidate primes. But my math is inadequate to prove this 8-(
> 
> I think that you mean n-2 iterations, but you may be right.

Yup. Brain failure again. I think I must have been confused with the
idea that the sequnce _must_ recur within 2^n-3 iterations - there
are only 2^n-1 different values of the residual, and 2 of them are
special - see below

>  It's hard to
> say, without any evidence, or solid math.

Chris Nash's excellent contribution isn't an actual proof, but it looks
solid enough to make me _extremely_ sceptical about the value
of searching for a recurrence, so far as testing Mersenne numbers
for primality is concerned. If you did find an example, you'd be well
worth your "15 minutes of fame"!
> 
> Just a side note, but all l_n values are 2 after n-1 iterations on a mersenne
> prime.  Maybe lends some small bit of evidence against that...

Yes but the recurrence _starts_ after n iterations. (n-2)th is 0,
(n-1)th is -2, all subsequent values are +2

Also, if the sequence ever reaches +1 or -1 it immediately
starts recurring, 1^2 - 2 = -1, (-1)^2 - 2 = -1, ...

This is why we can reduce the maximum recurrence period
from 2^n-1 to 2^n-3 since both -1 and +2 have two "precursors".


Regards
Brian Beesley
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------------------------------

Date: Tue, 18 May 1999 13:10:12 -0700
From: Lang Pal <[EMAIL PROTECTED]>
Subject: Mersenne: coincidence

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For those who think statistical methods could be useful treating of
the Mersenne problem (during the last weeks I have read some letters
of this kind in the Digests) I draw the attention to the following
coincidence:
Browsing among the lines in the book of
 N.J.Sloane ( Mathematics Research Center Bell Telephone
Laboratories.Inc.Murray Hill,New Jersey)
entitled:
        "A Handbook of Integer Sequences" (Academic Press, New York
and London,1973)
I found
on page 50, under Nr.248.  the Mersenne primes (on account of
editorial aspects beginning with the number "1"), and
on page 68. under Nr.536.  another sequence, namely " Partitions into
parts of 2 kinds"
with two references i.e.
      - R52 = Royal Society Math. Tables Vol.4.Tables of partitions by
Gupta and others .Cambridge Univ. Press, London and New York,1958, 90,

and
       -RCI = Riordan: Combinatorial Identities, Wiley, New York 1958,
199
( The first 38 elements of the ulterior sequence are:


1,2,5,10,20,36,65,110,185,300,481,752,1165,1770,2665,3956,5822,8470,12230,17490,24842,35002,

49010,68150,94235,129512,177087,240840,326015,439190,589128,786814,1046705,1386930,

1831065,2408658,3157789,4126070.)

If we count the correlation  coefficient of these first 38 elements of
the sequences (the 37 known Mersenne primes and the number "1", and
the quoted partition function)
            the result would be over 0,96953 with an F-test = 0,9441.
If we count again with only 37 - 37 integer (omitting the beginner
number "1")
            the result would be over 0,96952 with an F-test = 0,9391

These results seem to be surprisingly high, even if we are aware of
the relation between the sum of divisors and the partition function
dealt by Combinatorial Analysis (Partition Theory). However it might
be merely a coincidence, the sequences only ran across each other?


Best regards


La'ng Pa'l

(Paul La'ng)

Budapest, Hungary

PS.: As I am also anxious to get knowledge of the 38th amd the 39th
Mersenne prime and then to see the distances, and the modified
correlation coefficient, I quote also the next ten elements of the
mentioned partition sequence, as follows:

5374390,
6978730,9035539,11664896,15018300,19283830,24697480,31551450,40210481,51124970


Regards

La'ngPa'l



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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML>
For those who think statistical methods could be useful treating of the
Mersenne problem (during the last weeks I have read some letters of this
kind in the Digests) I draw the attention to the following coincidence:
<BR>Browsing among the lines in the book of
<BR>&nbsp;N.J.Sloane ( Mathematics Research Center Bell Telephone 
Laboratories.Inc.Murray
Hill,New Jersey)
<BR>entitled:
<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; "A Handbook of Integer Sequences"
(Academic Press, New York and London,1973)
<BR>I found
<BR>on page 50, under Nr.248.&nbsp; the Mersenne primes (on account of
editorial aspects beginning with the number "1"), and
<BR>on page 68. under Nr.536.&nbsp; another sequence, namely " Partitions
into parts of 2 kinds"
<BR>with two references i.e.
<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - R52 = Royal Society Math. Tables Vol.4.Tables
of partitions by Gupta and others .Cambridge Univ. Press, London and New
York,1958, 90,
<BR>and
<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -RCI = Riordan: Combinatorial
Identities, Wiley, New York 1958, 199
<BR>( The first 38 elements of the ulterior sequence are:
<BR>&nbsp;
<P>1,2,5,10,20,36,65,110,185,300,481,752,1165,1770,2665,3956,5822,8470,12230,17490,24842,35002,
<BR>49010,68150,94235,129512,177087,240840,326015,439190,589128,786814,1046705,1386930,
<BR>1831065,2408658,3157789,4126070.)
<P>If we count the <B>correlation&nbsp; coefficient </B>of these first
38 elements of the sequences (the 37 known Mersenne primes and the number
"1", and the quoted partition function)
<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
the result would be <B>over 0,96953 </B>with an <B>F-test = 0,9441.</B>
<BR>If we count again with only 37 - 37 integer (omitting the beginner
number "1")
<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
the result would be over 0,96952 with an F-test = 0,9391
<P>These results seem to be surprisingly high, even if we are aware of&nbsp;
the relation between the sum of divisors and the partition function dealt
by Combinatorial Analysis (Partition Theory). However it might be merely
a coincidence, the sequences only ran across each other?
<P>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Best regards
<P>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
La'ng Pa'l
<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
(Paul La'ng)
<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Budapest, Hungary
<P>PS.: As I am also anxious to get knowledge of the 38th amd the 39th
Mersenne prime and then to see the distances, and the modified correlation
coefficient, I quote also the next ten elements of the mentioned partition
sequence, as follows:
<P>5374390, 
6978730,9035539,11664896,15018300,19283830,24697480,31551450,40210481,51124970
<P>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Regards
<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
La'ngPa'l
<P>&nbsp;</HTML>

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Date: Tue, 18 May 1999 07:13:27 -0400
From: "Pierre Abbat" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Linux Mprime how to Auto Dialup?

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> The only way I can think of is having a script monitor the optional
> STDOUT of mprime and then checking whether it needs to contact the
> server.

I use the attached Tcl script to keep the last 25 lines of the output of mprime
in a file. You could put some commands in your crontab to check this file for
"done" and "server", and if it has "server" but not "done", connect to the Net,
but if it has "done", disconnect.

phma
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  name="runtail"
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Content-Disposition: attachment; filename="runtail"

#!/usr/bin/tclsh

# Reads standard input and writes the last n lines to a file.
# Usage: runtail n file

proc outem {} {
  global n ;
  global file;
  global line ;
  set f [open $file w];
  for {set i 0} {$i < $n} {incr i} {puts $f $line($i)};
  close $f;
  }

proc scroll {str} {
  global n;
  global line;
  for {set i 1} {$i < $n} {incr i} {set line([expr $i - 1]) $line($i)};
  set line([expr $n - 1]) $str;
  }

foreach {n file} $argv {}
for {set i 0} {$i < $n} {incr i} {set line($i) ""}

while {1} {
  scroll [gets stdin];
  outem;
  }


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------------------------------

Date: Tue, 18 May 1999 13:31:37 +0200 (MET DST)
From: [EMAIL PROTECTED]
Subject: Re: Mersenne:  Repeating LL remainders

Chris Nash <[EMAIL PROTECTED]> wrote:

> Define L(n)=(2+sqrt(3))^n+(2-sqrt(3))^n. It turns out that what we usually
> call *the* Lucas sequence is just
>
> S(n)=L(2^n).

      Yes.  We can check S(0) = L(1) = 4 and S(n+1) = S(n)^2 - 2
from the definitions.  So S defines the familiar Lucas sequence.

> The whole point of the proof is to show that the set of elements a+b.sqrt(3)
> (a, b mod N) that form a closed group under multiplication has the maximal
> order, N^2-1, and thus N is prime. The Lucas sequence does this with a
> little jiggery-pokery, because it is sufficient to show that L(N+1) is zero,
> while L((N+1)/q) isn't for any prime factor q of N+1. For Mersenne numbers
> the only factor to worry about is 2, so the test collapses into its briefer
> form.

> So the question becomes one of solving (2+sqrt(3))^n has zero surd part, and
> in fact prove that the group does not have order N^2-1. The sequence L(n)
> "will" recur in that case. However, it is not difficult to prove that the
> "first" recurrence, ie the point where L(x)=L(1), will generally occur quite
> late in the sequence unless N has all small factors - in which case, we
> would have eliminated this N by trial factoring.

> Remember too, this is late in the "L" sequence, not in the S sequence!
> Suppose for instance it occurred between L(2^(n-3)) and L(2^(n-2)) - which,
> even assuming the "first" recurrence is equally likely anywhere, would occur
> with probability 50%. The S-sequence would not even see it.

    We can illustrate working modulo M23 = 8388607 = 47 * 178481.
3 is a quadratic reside modulo 47 (e.g, 12^2 == 3 mod 47),
so 2 + sqrt(3) is in the base field of order 47.
The multiplicative order of 2 + sqrt(3) divides 47-1, and turns out to be 23.

    3 is a quadratic nonresidue modulo q = 178481.  The order of 2 + sqrt(3)
divides q + 1 = 178482 = 2 * 3 * 151 * 197 and turns out to be 178482.

    The least common multiple of these orders is
2 * 3 * 23 * 151 * 197.  So L(2 * 3 * 23 * 151 * 197) == L(0) mod M23.

    For the L sequence, we need two powers of 2 whose difference is
divisible by 2 * 3 * 23 * 151 * 197.
The orders of 2 modulo 3, 23, 151, 197 are 2, 11, 15, 196, respectively.
The order of 2 modulo 3 * 23 * 151 * 197 is the least common multiple
of these orders, namely 2^2 * 3 * 5 * 7^2 * 11 = 32340.
To include a factor of 2, we need L(2^32341) == L(2^1) mod M23.
That is, S(32341) == S(1) mod M23.
This is far more than 23 LL steps before the sequence repeats.

    EXERCISE: Repeat this analysis modulo M11 = 23 * 89.
              Find the period modulo M29 = 233 * 1103 * 2089, after getting
              the individual periods for each prime factor.


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Date: Tue, 18 May 1999 07:13:21 -0500
From: Curtis Cooper <[EMAIL PROTECTED]>
Subject: Mersenne: Monitor Flicker on Dell P-II 450 MHz

Has anyone noticed monitor flicker on a Dell OptiPlex GX1p
P-II 450 MHz?  We have installed ntprime on 16 of these
computers and noticed the monitor flicker on each one.
We know that the video chip is integrated on the motherboard
so we cannot move the video card to a different slot away
from the CPU, as has been suggested when this problem has
come up in the past.  The refresh rate for the monitor was set
at the maximum value of 85 MHz.

Is there a solution to this monitor flicker problem?

Thanks for any help.

Curtis Cooper and Vince Edmondson





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Date: Tue, 18 May 1999 09:56:00 -0400
From: "Louis Towles" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Monitor Flicker on Dell P-II 450 MHz

Let me guess with a ATI rage on the motherboard?

All you can do is set them to factor (this doesn't create flickering) - we
have many gateway e3200 (with various PII chips in them) that all suffer
from this problem - but on the positive side our latest 3200 series (a PIII
450) is just fine!

Louis Towles
[EMAIL PROTECTED]


- ----- Original Message -----
From: Curtis Cooper <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, May 18, 1999 8:13 AM
Subject: Mersenne: Monitor Flicker on Dell P-II 450 MHz


> Has anyone noticed monitor flicker on a Dell OptiPlex GX1p
> P-II 450 MHz?  We have installed ntprime on 16 of these
> computers and noticed the monitor flicker on each one.
> We know that the video chip is integrated on the motherboard
> so we cannot move the video card to a different slot away
> from the CPU, as has been suggested when this problem has
> come up in the past.  The refresh rate for the monitor was set
> at the maximum value of 85 MHz.
>
> Is there a solution to this monitor flicker problem?
>
> Thanks for any help.
>
> Curtis Cooper and Vince Edmondson
>
>
>
>
>
> ________________________________________________________________
> Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm

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------------------------------

Date: Tue, 18 May 1999 10:53:29 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Mersenne: [Mersenne] Prime95 gets CPU time

When I have something running that should grab all of the CPU cycles,
Prime95 still gets about 3% of them.  Is this because W95/98 won't let any
one program hog all of the CPU?


+------------------------------------------+
| Jud McCranie [EMAIL PROTECTED] |
+------------------------------------------+

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Date: Tue, 18 May 1999 08:08:50 -0700
From: Joe Decker <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Monitor Flicker on Dell P-II 450 MHz

Curtis Cooper wrote:
> Has anyone noticed monitor flicker on a Dell OptiPlex GX1p
> P-II 450 MHz?  We have installed ntprime on 16 of these
> computers and noticed the monitor flicker on each one.
> We know that the video chip is integrated on the motherboard
> so we cannot move the video card to a different slot away
> from the CPU, as has been suggested when this problem has
> come up in the past.  The refresh rate for the monitor was set
> at the maximum value of 85 MHz.
> 
> Is there a solution to this monitor flicker problem?

Not easily.  This precise model is common where I work right
now, and I'm running prime95 on 3 such machines.  In every case
the problem is quite visible.

In one case (not a personal workstation), I just left it on, 
in another, we put in a separate monitor card and that worked 
around the problem (needed a particular video card in that
machine anyway), in a third, I worked with the user of 
that machine and set up prime95 not to run during the hours
she was likely to be working.

The problem is not only prime95, although it is far more
pronounced with that than any other program I tried.  For
example, writing a small infinite loop in JavaScript and
running that under Netscape causes similar but more minor
interference.

Having a faster refresh rate doesn't help.  The effect is
still undiminished at 120 MHz. monitor refresh rate.

I did call Dell for a workaround, and tried a number of
things they suggested, but it looks to me that the processor
is directly affecting the video signal (by either modulating
the power supply or, more likely, via induction through some
unintentional antenna on the PC board.)

- --Joe
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Date: Tue, 18 May 1999 12:06:56 -0400
From: Joth Tupper <[EMAIL PROTECTED]>
Subject: Re:  Mersenne:  Repeating LL remainders

Message text written by "Brian J Beesley"
>> >I think we should check the math first. I have a sneaky suspicion that
looping
> >won't occur in the relevant region (the first 2^n-3 iterations) unless n
is 
> >composite - which may be interesting, but doesn't help us eliminate
Mersenne
> >numbers as candidate primes. But my math is inadequate to prove this 8-(
> 
> I think that you mean n-2 iterations, but you may be right.

Yup. Brain failure again. I think I must have been confused with the
idea that the sequnce _must_ recur within 2^n-3 iterations - there
are only 2^n-1 different values of the residual, and 2 of them are
special - see below

<

...I wonder if the LL sequence for a biggish MP would give a decent
pseudo-random series.

That is, I wonder if the series would be "better" than the usual
linear-congurential series (or sum of three).

Might win some support if there are still random number chasers out there.

Joth
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Date: Tue, 18 May 1999 10:36:49 -0600
From: "Blosser, Jeremy" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Monitor Flicker on Dell P-II 450 MHz

- -----Original Message-----
From: Joe Decker [mailto:[EMAIL PROTECTED]]
Sent: Tuesday, May 18, 1999 10:09 AM
To: Curtis Cooper
Cc: [EMAIL PROTECTED]
Subject: Re: Mersenne: Monitor Flicker on Dell P-II 450 MHz


Curtis Cooper wrote:
> Has anyone noticed monitor flicker on a Dell OptiPlex GX1p
> P-II 450 MHz?  We have installed ntprime on 16 of these
> computers and noticed the monitor flicker on each one.
> We know that the video chip is integrated on the motherboard
> so we cannot move the video card to a different slot away
> from the CPU, as has been suggested when this problem has
> come up in the past.  The refresh rate for the monitor was set
> at the maximum value of 85 MHz.
> 
> Is there a solution to this monitor flicker problem?

Not easily.  This precise model is common where I work right
now, and I'm running prime95 on 3 such machines.  In every case
the problem is quite visible.

In one case (not a personal workstation), I just left it on, 
in another, we put in a separate monitor card and that worked 
around the problem (needed a particular video card in that
machine anyway), in a third, I worked with the user of 
that machine and set up prime95 not to run during the hours
she was likely to be working.

The problem is not only prime95, although it is far more
pronounced with that than any other program I tried.  For
example, writing a small infinite loop in JavaScript and
running that under Netscape causes similar but more minor
interference.

Having a faster refresh rate doesn't help.  The effect is
still undiminished at 120 MHz. monitor refresh rate.

I did call Dell for a workaround, and tried a number of
things they suggested, but it looks to me that the processor
is directly affecting the video signal (by either modulating
the power supply or, more likely, via induction through some
unintentional antenna on the PC board.)

- --Joe
________________________________________________________________
Sounds to me more like a "dirty" motherboard or power supply. Chances are
that the computer is emitting a lot of RF at high CPU load whether due to a
"dirty" (ie leaking) motherboard of a bad power supply. So I'd imagine it
doesn't satisfy some FCC Class whatever spec or something. I'd have Dell
replace the thing.

I suppose you could test the theory out by tuning a radio to some station
and seeing how close you can get to the computer without it messing with
your reception. (just kidding)

Good luck.
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------------------------------

Date: Tue, 18 May 1999 12:41:42 -0500
From: "David L. Nicol" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Learning FFT

Steve Johnson wrote:
> 
> Some time ago someone on the list mentioned that would like to know
> about FFT.  I recently picked up a book that presented Fourier
> Transforms (including FFT) in a very easy to understand format.
> 
> It is called "Who is Fourier? A Mathematical Adventure". 
> 
> Although the book starts out a little simplistic, one is able to skim
> the book until unfamiliar concepts are found, and then study the book in
> detail from that point forward.
> 
> Steve Johnson


Amazon price $25

http://www.amazon.com/exec/obidos/ISBN%3D0964350408/tipjartransactioA

Any comissions from sales from this link will be given to Steve Johnson
________________________________________________________________________
  David Nicol 816.235.1187 UMKC Network Operations [EMAIL PROTECTED]
           "The more wailing, the better" -- David B. Luby
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Date: Tue, 18 May 1999 14:55:34 -0300 (EST)
From: "Nicolau C. Saldanha" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Back to the maths of primes for a sec....

On Mon, 17 May 1999, Chris Nash wrote:

(talking about how maple decides that a number is "probably composite")

> The test is now tougher. If MAPLE now identifies a probable prime, it tests
> again, to another base, and if that also passes, it performs a test using a
> Lucas sequence. Again these are probable prime tests, so it is possible (and
> likely) composites exist that pass all three. I think Carl Pomerance himself
> has offered a cash prize for anyone who could find a counterexample to the
> "twice SPRP, one Lucas sequence" test - an indication that it is not an easy
> task of mere computation.

Do you have more precise information, or do you know where we can find it?
(the help function inside maple gives only a very superficial explanation)
Strong pseudoprime wrt which base? Probably not random, or the search
for a counterexample becomes meaningless. And which Lucas sequence?

http://www.mat.puc-rio.br/~nicolau

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Date: Tue, 18 May 1999 20:37:35 +0200 (MET DST)
From: [EMAIL PROTECTED]
Subject: Re: Mersenne: Back to the maths of primes for a sec....

"Nicolau C. Saldanha" <[EMAIL PROTECTED]> writes

> Do you have more precise information, or do you know where we can find it?
> (the help function inside maple gives only a very superficial explanation)
> Strong pseudoprime wrt which base? Probably not random, or the search
> for a counterexample becomes meaningless. And which Lucas sequence?
> 
     Assuming you have maple installed, you can see
its procedures (sans comments):

interface(verboseproc=3);
eval(isprime);
;quit;


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Date: Tue, 18 May 1999 12:55:15 -0700
From: Michael Gebis <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Linux Mprime how to Auto Dialup? 

Warning: My comments are not math related; feel free to delete this
message and curse my name for overstepping the mailing list charter.
Sorry.

>>>>> "Greg" == Greg Czajkowski <[EMAIL PROTECTED]>
>>>>> wrote the following on Mon, 17 May 1999 23:12:06 -0500

  Greg> Hi, I have a question to the linux/mprime experts:

  Greg> I just installed RedHat 6.0, (it's awesome) but the only
  Greg> connection that machine has to the internet is PPP.

  Greg> Eventually, I got that to work. My question is whether there
  Greg> is any way to bring down/up the ppp0 interface whenever mprime
  Greg> needs to contact PrimeNet server automatically?

The more generic approach is to set up demand dialing.  There are
several ways to do this[1].  One way is to use a recent pppd and use
the "demand" option.  Once properly configured, your linux box will
automaticially dial whenever it needs to, and hang up when the
connection has been idle.  It's really quite nifty.

The details of configuration are FAR outside the the charter of this
mailing list; however, the ppp package comes with extensive
documentation, and the miscellaneous linux newsgroups should be able
to help you out, too.  A good start would be to get the ppp package.
It looks like the home of ppp is at:

ftp://cs.anu.edu.au/pub/software/ppp/

You may wish to check out the ppp documentation that came with RedHat
6.0 to see if you already have a ppp that supports the demand option.
(Probably in /usr/doc/ppp_somethingorother)

[1] Another method I don't mention is "diald".  My ignorance of diald
is overwhelming.  If you want to investigate, try the home page at:

http://diald.unix.ch/

Good luck,
Mike Gebis
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Date: Tue, 18 May 1999 12:53:47 -0700
From: "John R Pierce" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: [Mersenne] Prime95 gets CPU time

> When I have something running that should grab all of the CPU cycles,
> Prime95 still gets about 3% of them.  Is this because W95/98 won't let any
> one program hog all of the CPU?

its possible the nominally CPU bound application is causing at least *some*
page swapping, this would free CPU cycles for a background process when the
page swapper is waiting on the disk IO.

But, yes, win95/98 does try to give even idle priority processes a % or 2 of
CPU time.

- -jrp


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Date: Tue, 18 May 1999 12:57:42 -0700
From: "John R Pierce" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Monitor Flicker on Dell P-II 450 MHz

> Sounds to me more like a "dirty" motherboard or power supply. Chances are
> that the computer is emitting a lot of RF at high CPU load whether due to a
> "dirty" (ie leaking) motherboard of a bad power supply. So I'd imagine it
> doesn't satisfy some FCC Class whatever spec or something. I'd have Dell
> replace the thing.

As the original poster said, he's running on identical 16 Dell Optiplex
systems, they ALL have this problem.  This is a highly integrated business
system with the graphics on the motherboard.  There's no indication that the
EMI is leaking from the case, indeed, the Optiplex cases that I've seen are
very well shielded, with metal braid seals on all joints, etc.


- -jrp

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Date: Tue, 18 May 1999 14:52:00 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Monitor Flicker on Dell P-II 450 MHz

> > Sounds to me more like a "dirty" motherboard or power supply.
> Chances are
> > that the computer is emitting a lot of RF at high CPU load
> whether due to a
> > "dirty" (ie leaking) motherboard of a bad power supply. So I'd
> imagine it
> > doesn't satisfy some FCC Class whatever spec or something. I'd have Dell
> > replace the thing.
>
> As the original poster said, he's running on identical 16 Dell Optiplex
> systems, they ALL have this problem.  This is a highly integrated business
> system with the graphics on the motherboard.  There's no
> indication that the
> EMI is leaking from the case, indeed, the Optiplex cases that
> I've seen are
> very well shielded, with metal braid seals on all joints, etc.

So basically, it's just a poorly designed box.  That's what you get for
buying Dell, but that's just my opinion :-)

If the problem were pervasive in many applications, I'd waste no time in
calling Dell and asking for a fix.  As it is, if only FPU intensive apps
cause the problem, they probably wouldn't care.

Possible fixes:  If it's a noisy power signal getting to the graphics chips,
too bad.  If it's radiated interference, maybe some good copper braiding
around the CPU would help, tied to ground.  Or around the graphics
circuitry.  But again, if the problem is interference on the wiring, you're
SOL.  Send 'em back and get Compaqs! :-)

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Date: 18 May 1999 14:49:57 -0700
From: Mark James <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Linux Mprime how to Auto Dialup?

Greg Czajkowski <[EMAIL PROTECTED]> writes:

> Hi, I have a question to the linux/mprime experts:
> 
> I just installed RedHat 6.0, (it's awesome) but the only connection
> that machine has to the internet is PPP.
> 
> Eventually, I got that to work. My question is whether there is any way
> to bring down/up the ppp0 interface whenever mprime needs to contact
> PrimeNet server automatically?
> 
> The only way I can think of is having a script monitor the optional
> STDOUT of mprime and then checking whether it needs to contact the
> server.
> 
> If there is a better solution, please point me to it.

Before I got my cable modem, I used a package called diald.  

   http://www.loonie.net/~eschenk/diald.html

Diald provides on demand Internet connectivity for Linux, giving you
complete automated control over your SLIP or PPP links. When you need
a connection it's there. When you don't, it's not. You'll never need
to run a "ppp-on" or "ppp-off" script again.

     M.
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Date: Tue, 18 May 1999 15:47:36 -0600
From: "Blosser, Jeremy" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Monitor Flicker on Dell P-II 450 MHz

>-----Original Message-----
>From: Aaron Blosser [mailto:[EMAIL PROTECTED]]
>Sent: Tuesday, May 18, 1999 3:52 PM
>To: Mersenne@Base. Com
>Subject: RE: Mersenne: Monitor Flicker on Dell P-II 450 MHz
>
>
>> > Sounds to me more like a "dirty" motherboard or power supply.
>> Chances are
>> > that the computer is emitting a lot of RF at high CPU load
>> whether due to a
>> > "dirty" (ie leaking) motherboard of a bad power supply. So I'd
>> imagine it
>> > doesn't satisfy some FCC Class whatever spec or something. 
>I'd have Dell
>> > replace the thing.
>>
>> As the original poster said, he's running on identical 16 
>Dell Optiplex
>> systems, they ALL have this problem.  This is a highly 
>integrated business
>> system with the graphics on the motherboard.  There's no
>> indication that the
>> EMI is leaking from the case, indeed, the Optiplex cases that
>> I've seen are
>> very well shielded, with metal braid seals on all joints, etc.
>
>So basically, it's just a poorly designed box.  That's what you get for
>buying Dell, but that's just my opinion :-)
>
>If the problem were pervasive in many applications, I'd waste 
>no time in
>calling Dell and asking for a fix.  As it is, if only FPU 
>intensive apps
>cause the problem, they probably wouldn't care.
>
>Possible fixes:  If it's a noisy power signal getting to the 
>graphics chips,
>too bad.  If it's radiated interference, maybe some good 
>copper braiding
>around the CPU would help, tied to ground.  Or around the graphics
>circuitry.  But again, if the problem is interference on the 
>wiring, you're
>SOL.  Send 'em back and get Compaqs! :-)
>

Actually, I went and looked at the newsgroups and a few people posted about
an apparently bad batch of 1226H monitors, and suggest sending them back and
getting the P-990's instead. So if you have this monitor, perhaps that is
the problem there...

I'm still led to believe that its a bad power supply of a bad batch of caps
that are on the motherboard or something. Having a "highly integrated
business machine" that is "very well shielded" does not mean anything in
this case.

Actually, thinking about it, I'm very inclined to say its a bad power
supply. I'd suggest checking it for fun's sake and seeing how far out of
spec they are. It seems the problem only shows up when the CPU is under a
heavy load, thus drawing more power, and thus drawing the voltage from the
P/S all wacky.

In any case, I'd call Dell and get them to replace the systems or send 'em
back or something. Especially since they are "highly integrated busines s
machines" :)
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Date: Tue, 18 May 1999 17:28:38 -0500
From: Gary & Cindi Diehl <[EMAIL PROTECTED]>
Subject: Mersenne: Fourier Transform for MVS?

Does anybody have any source code to do large-number FFT in MVS 390
Assembler for IBM Mainframes?

I would like to use FFT to test Mersenne Primes on my 390 CPU but lack
the code, and I don't have any high-level language compilers.  I just
have Assembler.

Any help would be appreciated.

Gary Diehl

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Date: Tue, 18 May 1999 15:42:06 -0700
From: "Gilmore, John (AZ75)" <[EMAIL PROTECTED]>
Subject: Mersenne: 10000000-, 100000000-, and 1000000000-digit primes

On the theory that at least one other person is interested in the
computational effort required to go after the EFF prizes for the larger
prime numbers, I made some rough extrapolations from George's "Status" table
and came to the following conclusions (generally to one significant figure):


Ten-million-digit prime
On the order of M33000000, FFT size 1408, 7 P-90 seconds per iteration, 8
P-90 years per exponent.

One-hundred-million digit prime
On the order of M330000000, FFT size 3072, 80 P-90 seconds per iteration,
and 800 P-90 years per exponent.  If I postulate the existance of a 900Mhz
Pentium, the computation time for a LL test drops to merely 80 years per
exponent.

And, finally, the giga-digit prime:
M3300000000, FFT size 4736, this time postulating a 90Ghz Pentium (three
orders of magnitude faster than the current reference), the single iteration
time is a "mere" 0.8 seconds per iteration, but since the algorithm requires
~3 billion passes, the per-exponent test time is still 80 years.

These times are all PER EXPONENT; historical evidence suggests many
exponents would have to be tested for each prime found.

I would imagine the EFF folks could probably put a dollar in a savings
account now, and it will grow  via interest to fund the largest prize by the
time it's claimed.  ;-)

Regards,

John Gilmore
(Not the one at EFF)
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End of Mersenne Digest V1 #561
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