Mersenne Digest Sunday, October 24 1999 Volume 01 : Number 651
----------------------------------------------------------------------
Date: Thu, 21 Oct 1999 23:47:47 -0400 (EDT)
From: Chip Lynch <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: Schlagobers, Louisville style
On Thu, 21 Oct 1999 [EMAIL PROTECTED] wrote:
> I used to have a girlfriend from Louisville (Kentucky), but must admit
> that I've forgotten her number...
>
> Seriously, I think you mean "Liouville" numbers.
I thought that sounded odd. I myself am from Louisville (and if you find
your girlfriend's number, I'll be glad to look for patterns in it)...
Speaking of which...
> But while watching the movie Pi, it occurred to me that since the number
> Pi has *nothing* to do with base 10, there would be no repitition in the
> digits in any approximation of it in base 10 (or any other integer base,
> for that matter). The sequence of digits *should* be completely random,
> and it's goofy for people to try to look for patterns. I mean hey, if
> it's what you gotta do, go for it, but I think time would be better
> spent on other things.
There's no reason for it to be COMPLETELY random. Plenty of trancendental
numbers have easy to view patterns (aka the Liouville numbers above)... Or
eaiser, a number like .101001000100001 (...) which also happens to be
easily describable, but only noticeable in certain bases (this probably
looks stupid in base 3, but I haven't the desire to find out right now).
I remember some notes on interesting patterns in Pi that led one to
believe that certain statistical events were NOT ocurring. For example,
in a completely random set of (base 10) digits, one would expect a string
of, say, 100 of the SAME digit to appear in the first so many digits of
the number, however this doesn't happen in Pi and, furthermore, certain
digits appear in large clusters more often than others in the list of
'known' digits.
Does anyone have any stats on this? Personally, I imagine this is the
same sort of statistical dribble as "The Bible Code", and someone probably
got their Chi-squareds mixed up when they were doing the math, but since
I'm not strong in statistics, it would be nice to hear an 'Expert'
opinion.
- ---Chip
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Date: Fri, 22 Oct 1999 00:50:59 -0400 (EDT)
From: Lucas Wiman <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: Schlagobers, Louisville style
> > But while watching the movie Pi, it occurred to me that since the number
> > Pi has *nothing* to do with base 10, there would be no repitition in the
> > digits in any approximation of it in base 10 (or any other integer base,
> > for that matter). The sequence of digits *should* be completely random,
> > and it's goofy for people to try to look for patterns. I mean hey, if
> > it's what you gotta do, go for it, but I think time would be better
> > spent on other things.
Yech! To maintain the niceties of the list, I'll just say that I'm not a fan
of that movie.
> I remember some notes on interesting patterns in Pi that led one to
> believe that certain statistical events were NOT ocurring. For example,
> in a completely random set of (base 10) digits, one would expect a string
> of, say, 100 of the SAME digit to appear in the first so many digits of
> the number, however this doesn't happen in Pi and, furthermore, certain
> digits appear in large clusters more often than others in the list of
> 'known' digits.
Umm, would the probability of any specific series of n digits in a random sample
occurring be 10^-n? This shouldn't yeild a series of a hundred of the same digits
for some time, if the sample is random.
> Does anyone have any stats on this? Personally, I imagine this is the
> same sort of statistical dribble as "The Bible Code", and someone probably
> got their Chi-squareds mixed up when they were doing the math, but since
> I'm not strong in statistics, it would be nice to hear an 'Expert'
> opinion.
You mean the bible code isn't real, I'm shocked...
- -Lucas
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------------------------------
Date: Fri, 22 Oct 1999 11:16:05 +0000
From: "Steinar H . Gunderson" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: mprime startup at boot-time
On Thu, Oct 21, 1999 at 08:15:31PM -0400, Pierre Abbat wrote:
>Try adding the line
>
>8:2345:respawn:/usr/local/bin/mprime
>
>to /etc/inittab.
Note that this can degrade performance -- I don't know why, but it might be
more going on when all the VTs are inited, and the memory map gets more
fragmented.
I stick with the normal -m on VT1 :-)
/* Steinar */
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Date: Fri, 22 Oct 1999 05:31:30 -0400 (EDT)
From: "St. Dee" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: mprime startup at boot-time
On Thu, 21 Oct 1999, Pierre Abbat wrote:
> >Secondly, I used to feed the output to a virtual terminal, but decided that
> >having a hard copy that I could periodically check was better. I've been
> >piping all the output to a file, such as mprime -d
> >>>/home/GIMPS/tracking.txt. When it finishes reporting a result, I delete
> >everything but the result and let mprime continue on to the next LL test
> >using the same file.
>
> If you delete a file while a program is writing to it, it will keep on writing
> to the now nameless file, and will keep eating up disk space, until the program
> quits or closes the file, at which time the file will disappear.
I don't delete the file, just all of the iteration information from
completed exponents within the file. That way I have a running record of
current exponent iteration progress as well as past exponents completed
(in addition to the info contained in the results.txt file).
Kel
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------------------------------
Date: Thu, 21 Oct 1999 17:16:52 +0200
From: "Grieken, Paul van" <[EMAIL PROTECTED]>
Subject: Mersenne: difference between LL and double check
Thanks for the answers I received.
You all are right, of course, the double check was on a number in the 4 million and
the LL test in the 8 million. That explain the difference.
But I thought it only took longer to complete not that the iteration take longer. So I
can say if the number doubles it takes 4x more time to complete.
thanks to all.
bye,
Paul van Grieken
Alcatel telecom Nederland
Afd: TTAC Netwerk Elementen
Tel: 070-3079353
email: [EMAIL PROTECTED]
marklin collector
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Date: Fri, 22 Oct 1999 09:59:23 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: Schlagobers, Louisville style
- --=====================_58216264==_.ALT
Content-Type: text/plain; charset="us-ascii"; format=flowed
At 11:47 PM 10/21/99 -0400, Chip Lynch wrote:
> There's no reason for it to be COMPLETELY random. Plenty of trancendental
>numbers have easy to view patterns
Only an infinitesimally small % of them have patterns. For each one that
has a pattern there are an infinite number that don't.
+---------------------------------------------------------+
| Jud McCranie |
| |
| Programming Achieved with Structure, Clarity, And Logic |
+---------------------------------------------------------+
- --=====================_58216264==_.ALT
Content-Type: text/html; charset="us-ascii"
<html>
At 11:47 PM 10/21/99 -0400, Chip Lynch wrote:<br>
> There's no reason for it to be COMPLETELY random. Plenty of
trancendental<br>
<blockquote type=cite cite>numbers have easy to view patterns
</blockquote><br>
<br>
Only an infinitesimally small % of them have patterns. For each one
that has a pattern there are an infinite number that don't.<br>
<br>
<br>
<div>+---------------------------------------------------------+</div>
<div>| Jud
McCranie
|</div>
<div>|
|</div>
<div>| Programming Achieved with Structure, Clarity, And Logic |</div>
<div>+---------------------------------------------------------+</div>
<br>
</html>
- --=====================_58216264==_.ALT--
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------------------------------
Date: Fri, 22 Oct 1999 10:59:09 -0400 (EDT)
From: Chip Lynch <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: Schlagobers, Louisville style
On Fri, 22 Oct 1999, Jud McCranie wrote:
> At 11:47 PM 10/21/99 -0400, Chip Lynch wrote:
> > There's no reason for it to be COMPLETELY random. Plenty of trancendental
> >numbers have easy to view patterns
>
>
> Only an infinitesimally small % of them have patterns. For each one that
> has a pattern there are an infinite number that don't.
Of course! But by 'Plenty', I only meant an infinite number, which as
you've pointed out on the whole isn't that much at all. *evil grin*
- ---Chip
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------------------------------
Date: Fri, 22 Oct 1999 10:20:38 -0700
From: "Joth Tupper" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: Schlagobers, Louisville style
- ----- Original Message -----
>From: Jud McCranie
>To: Chip Lynch
>Cc: GIMPS Project Mailing List
>Sent: Friday, October 22, 1999 6:59 AM
>Subject: Re: Mersenne: Re: Schlagobers, Louisville style
>At 11:47 PM 10/21/99 -0400, Chip Lynch wrote:
>> There's no reason for it to be COMPLETELY random. Plenty of
trancendental
>>numbers have easy to view patterns
>Only an infinitesimally small % of them have patterns. For each one that
has a pattern there are an infinite number that don't.
Gotta watch those infinities. For each (positive) even integer we can
construct an infinite set of odd numbers to go with it. Here is one way:
Let 2k > 0 be given. let P(k) = k'th odd prime (so P1 = 3, P2 = 5, ...).
Consider the set of integers S(k) = {P(k), P(k)^2, P(k)^3,...}.
Clearly S(k) is infinite, and if j and k are different, then S(k) and S(j)
are disjoint.
So what?
Now, back to Jud's comment.
Well, of course! There are uncountably many transcendentals because there
are uncountably many real numbers but only countably many algebraic numbers.
Unless someone can suggest an infinite (I think we need uncountable)
collection of patterns for transcendental numbers,
the collection of transcendental numbers with patterns will be countable.
With infinitely many (but countable) patterns,
it is possible to construct 2^(aleph-null) transcendentals with patterns
(of some sort) but only using infinite series -- which may
turn up algebraic numbers in the limits. Finite linear (over rationals)
combinations of transcendentals will be transcendental but
this will keep the set with patterns countable.
A countable subset of real or complex numbers has measure 0 in the usual
measure
(Lebesgue or Haar or any other derivation where the length of an interval on
the real line is its measure
or the derived measure in the plane based on the product topology).
Sets of measure 0 represent 0% probabilities in any Borel probability
measure based on intervals.
On the other hand, remembering Littlewood, I think, finitely many instances
of transcendental
numbers with patterns will give us what we need for all practical purposes.
Having countably many available sounds like 'plenty' to me.
JT
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------------------------------
Date: Fri, 22 Oct 1999 19:01:46 +0100
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: difference between LL and double check
On 21 Oct 99, at 17:16, Grieken, Paul van wrote:
> But I thought it only took longer to complete not that the iteration
> take longer. So I can say if the number doubles it takes 4x more
> time to complete.
Very roughly, yes. There are (p-2) iterations to do for a test of
exponent p. The computer work per iteration is proportional to
N log N, where N is the FFT run length. The complication here is that
as the run length increases, the effectiveness of the computer's
cache reduces, so there are also more "wasted" cycles when the CPU
cannot work as it's waiting for operands to be fetched from memory.
Another small complication is that you can't _quite_ cover double the
range with double the FFT size. The larger FFT needs an extra bit
precision, so the range of exponents which can be covered with FFT
run length 2N is not quite twice as large as the range of exponents
which can be covered with FFT run length N.
These effects (p-2 not p, the log N factor and the FFT run length
complication) are really quite small, but the CPU cache effectiveness
fall-off _does_ have quite a noticeable effect. George's V19 code has
managed to reduce the cache fall-off somehow, this is probably the
main reason for the increase in speed over V18.
Regards
Brian Beesley
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Date: Fri, 22 Oct 1999 11:43:23 -0700
From: "Joth Tupper" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: Schlagobers, Louisville style
This follows my recent post on this topic.
Maybe, maybe not...
[snip]
>
> Finite linear (over rationals)
> combinations of transcendentals will be transcendental but
> this will keep the set with patterns countable.
>
[snip]
Finite linear combinations of transcendentals MAY be transcendental
but even this statement needs work. The conclusion that the
number of the beasts remains countable will stand.
Suppose T is a transcendental with some pattern.
Then 1 + T is transcendental and has (pretty much) the same pattern.
Clearly 1*( 1+ T) + (-1) * (T) = 1 is a Q-linear combination of
transcendentals which is NOT transcendental.
I think I will go back to sleep. ...Probably more productive!
JT
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Date: Fri, 22 Oct 1999 18:48:20 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Re: PI
Jud McCranie <[EMAIL PROTECTED]> wrote:
>At 01:36 PM 10/21/99 -0500, Herb Savage wrote:
>
>> I remember reading an interview with the Chudnovsky brothers a long time
>>ago. I think they had computed about 4 billion digits at the time. Then
>>they felt that there would be something interesting in the digits of PI if
>>you computed them out far enough.
>
>I don't know if that makes much sense. If you do get something significant
>after a finite number of digits, it is probably a statistical fluke and
>won't hold up in the long run.
Several years ago there was an episode of "Northern Exposure" in which the
female guest star played a researcher who was calculating digits of pi.
In one scene, she breathlessly describes to lovestruck John Corbett (who
played Chris, the local radio DJ) about how there are these millions of
seemingly random digits, "...and then suddenly, around the billionth digit,
there's this string of eight eights," claiming this to be some sort of
revelation from the Maker. It's probably just some screenwriter's fantasy,
but now calculate the odds of such a string appearing at random. Voila!
you'd expect a repeating sequence of eight digits on average every 10^8
digits, and a sequence of eight eights about every 10^9 - right on
"schedule," I'd say. Just another illustration about how the human mind
is preprogrammed to look for patterns in data and ascribe significance
to them. Not every lion you see on the African savanna wants to eat you,
but it's safer to assume that to be the case.
Roar,
- -Ernst
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Date: Sat, 23 Oct 1999 08:06:39 +0100
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: mprime startup at boot-time
On 22 Oct 99, at 11:16, Steinar H . Gunderson wrote:
> >Try adding the line
> >
> >8:2345:respawn:/usr/local/bin/mprime
> >
> >to /etc/inittab.
>
> Note that this can degrade performance -- I don't know why, but it might be
> more going on when all the VTs are inited, and the memory map gets more
> fragmented.
Probably.
What about constructing a file (/etc/mprime.rc) containing
sleep 1m
/usr/local/bin/mprime
& invoking it with
8:2345:respawn:/bin/sh /etc/mprime.rc
in /etc/inittab?
The 1 minute delay is to give the other stuff time to initialize. In
linux, waiting for initialization to complete (disk drive stops
hammering away) the logging on & starting mprime manually seems to
give good results in so far as mprime runs reasonably close to its
potential fastest speed. Conversely (or perhaps perversely), Windows
needs ReCache, _especially_ just after a fresh boot, to make Prime95
run at its best speed.
Regards
Brian Beesley
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Date: Sat, 23 Oct 1999 18:15:06 +0200
From: Lars Lindley <[EMAIL PROTECTED]>
Subject: Re: Mersenne: mprime startup at boot-time
"Brian J. Beesley" wrote:
>
> What about constructing a file (/etc/mprime.rc) containing
>
> sleep 1m
> /usr/local/bin/mprime
>
> & invoking it with
>
> 8:2345:respawn:/bin/sh /etc/mprime.rc
>
> in /etc/inittab?
>
I found no performance difference _at all_ between using the one
minute delay and using a direct start. .266/iter on both.
On the other hand after starting X and gimp and then exiting and
killing the mprime process letting it respawn got it down to .260...
I would figure that it is the ReCache effect of using up alot of
memory, releasing it and immediately starting mprime after.
Roughly 2%. Not much but...all the help one can get is appreciated :)
Regards,
Lars
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Date: Sun, 24 Oct 1999 00:55:41 -0700 (PDT)
From: poke <[EMAIL PROTECTED]>
Subject: Re: Mersenne: mprime startup at boot-time
Sorry, -d, not -m. I'm not that familiar with the command line arguments
of mprime. My expertise lies in the symantics of Linux.
One way to pipe to a virtual terminal AND to a file is by using a
combination of a tee and a redirect. Something like:
/usr/src/mprime -d | tee -a /home/GIMPS/tracking.txt > /dev/tty6
- -Chuck
> First, wouldn't you want to use mprime -d ? The -m flag simply brings up
> the menu.
>
> Secondly, I used to feed the output to a virtual terminal, but decided that
> having a hard copy that I could periodically check was better. I've been
> piping all the output to a file, such as mprime -d
> >>/home/GIMPS/tracking.txt. When it finishes reporting a result, I delete
> everything but the result and let mprime continue on to the next LL test
> using the same file.
>
> Just my $.02,
> Kel
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End of Mersenne Digest V1 #651
******************************
