Mersenne Digest Friday, 26 February 1999 Volume 01 : Number 514
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From: "Ernst W. Mayer" <[EMAIL PROTECTED]>
Date: Thu, 25 Feb 1999 14:17:18 -0500
Subject: Re: Mersenne: so many primes, so little time...
Spike Jones wrote:
>The mass of the earth is about 8E24 kg, and there are on the order
of 10^26 atoms of lithium per kg, so the earth became a computer
with 2E51 bits capable of an equivalent of 10^67 operations per sec
Uh, you'd better save a few E24 kg for a whopper of a heat sink and
a convective neutrino cooling fan - or are you assuming 100% efficiency,
which would appear to violate the 2nd law of thermodynamics?
>if a proton were to become a tiny supercomputer, capable of
dividing *any* two numbers, regardless of size, in one chronon
Spike, there's a flaw in your reasoning here (or better, one
humongous missed opportunity): you are using quantum theory to
set a lower limit on your cycle time, but your lithiverse is
not exploiting quantum nonlocality to speed up the factoring.
I think if you switch to a quantum factoring algorithm, the
Mersennes will be dropping like ripe wheat before a scythe...
For those who are saying, "hey - what about decoherence?":
if Spike gets to assume the speed of light is infinite (note that
the quantum algorithm need not assume this to be effective), I get
to assume there is no decoherence.
In any case, thanks for an amusing posting, Spike!
- -Ernst
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From: Blake Stacey <[EMAIL PROTECTED]>
Date: Thu, 25 Feb 1999 17:00:34 -0600
Subject: Mersenne: Chronons (was so many primes, so little time)
Spike Jones, esteemed creator of the lithiverse, cites the distance it
takes light to cross a proton, one "chronon" as the smallest possible
unit of quantized time. I beg to differ.
Just today, by a sheer coincidence, I was diddling away some time in my
10th grade Algebra II/Trigonometry class, and began to ponder this very
problem. From some quantum mechanics book somewhere, my brain dredged
up the result 10^-42 seconds as Planck time, the smallest measurable
unit of time. (For curiosity's sake, I spent a while working out a
back-of-the envelope calculation, and decided that one photon of light
should travel 3 * 10^-34 meters or so in Planck time.)
- --
Blake Stacey
Executive Director of Programming
HyperSphere Software
[EMAIL PROTECTED] :: http://fly.hiwaay.net/~bstacey
Some chairs are ergonomic.
No junk bond is ergonomic.
Therefore, some chairs are not junk bonds.
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From: Spike Jones <[EMAIL PROTECTED]>
Date: Thu, 25 Feb 1999 19:48:28 -0800
Subject: Re: Mersenne: so many primes, so little time...
Ernst W. Mayer wrote:
> ..if Spike gets to assume the speed of light is infinite (note that
> the quantum algorithm need not assume this to be effective), I get
> to assume there is no decoherence. In any case, thanks for an amusing
> posting, Spike!
That flight of fancy was in answer to a question by my mother of
all people. After I explained Lucas Lehmer, she asked: So, this
is a lot faster algorithm than factoring?
I searched for some means of avoiding a truly comical understatement,
but was nearly powerless to do so. After doing the exercise, I
came to appreciate the LL algorithm much more deeply. Plus,
it convinced my mother to sign up for GIMPS, which brings
my recruiter's total to 3. spike
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From: Spike Jones <[EMAIL PROTECTED]>
Date: Thu, 25 Feb 1999 20:17:58 -0800
Subject: Re: Mersenne: Chronons (was so many primes, so little time)
Blake Stacey wrote:
> Spike Jones, esteemed creator of the lithiverse, cites the distance it
> takes light to cross a proton, one "chronon" as the smallest possible
> unit of quantized time. I beg to differ.... my brain dredged
> up the result 10^-42 seconds as Planck time, the smallest measurable
> unit of time. ...
Great news blake! That will give the Lithiumy Way another 18 orders
of magnitude. As for errors in the original post, no one hammered
me for calling 1E15 a trillion either, but I hope all who care about
such silliness got the real point: we sometimes do not appreciate
the magnitude of the numbers we toss around, such as 2^3021377-1.
I printed out the 37th Mersenne in 2 point font, taped the 6 resulting
pages together and now it is hanging on the wall in my office. Only
those with verrrry good eyes can read the numbers. Great conversation
piece, and may result in recruiting more GIMPSers.
All of GIMPS is searching the range from about 2^(2^20) to about
2^(2^24.3). It is easy to lose a sense of the enormity of these numbers
when we toss them around like this, or see our sometimes outdated
computers grinding away on them. The number your computer is
currently working on is big, my friends. Blake, thanks for catching
the error! {8-] regards, spike
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From: "Aaron Blosser" <[EMAIL PROTECTED]>
Date: Thu, 25 Feb 1999 23:36:17 -0700
Subject: RE: Mersenne: Chronons (was so many primes, so little time)
> All of GIMPS is searching the range from about 2^(2^20) to about
> 2^(2^24.3). It is easy to lose a sense of the enormity of these numbers
> when we toss them around like this, or see our sometimes outdated
> computers grinding away on them. The number your computer is
> currently working on is big, my friends. Blake, thanks for catching
> the error! {8-] regards, spike
I actually found all of this interesting. It's been a while since I've
tried to conceptualize large numbers, and just how large they really are.
We all being mathematically minded can appreciate such things.
Last time I did something similar was my ongoing "crusade" to show just how
impossible it would be for "life" to be "accidentally" caused. You'd have a
better chance of randomly picking a single Mersenne number in the
2^(10^100)-1 (wild "butt" guess) range and having it be prime. I'm sure
we've all heard about some "amoeba" type thing moving the entire universe,
atom by atom, one angstrom every 15 billion years, over a distance of one
universe (about 30 billion light years) and then back for the next atom at
the same speed, and in that time you'd still not be likely to arrange even
so much as a protein by "chance" (not really chance since chance is a
statistical measure, not a causative force). It's an illustration by James
Coppedge that basically expands on the "million monkeys typing Shakespeare"
mental picture.
And that's just to arrange a single protein molucule. Rough estimates give
a 1 in 10^161 chance of arranging a single protein by accident, and a 1 in
10^119879 chance of "accidentally" arranging the *simplest* self-replicating
cell (life)...if anyone wants to go further with that... :-) Point
being...10^161 is a VERY large number, and so is 2^3021377-1!!
Why anyone who comprehends how big these oddsa are can believe that life
began that way is amazing. I'd sooner believe in "directed panspermia", but
that's something for talk.origins. :-)
By the way, totally changing the subject, going back to my idea of some
other prize we could offer besides the one for finding the next Mersenne
Prime...anyone come up with anything? If not, I suppose I could just donate
to that prize pool.
Aaron
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From: "Hoogendoorn, Sander" <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 11:02:47 +0100
Subject: Mersenne: Pentium III
from www.tomshardware.com
Intel's new Pentium III
The Pentium III, also known under the code name 'Katmai', does not come with
a feature that would show an immediate performance increase as in case of
the K6-3. Its basic core as well as the L2-cache architecture is identical
to the Pentium II processor. The justification for the new name lies in a
set of 70 new multimedia instructions, once known as 'KNI', now known as
'SSE' standing for 'streaming SIMD extensions'. Those new instructions
enable the CPU to perform floating-point calculations on multiple data at
the same time, which proves very helpful for 3D graphics, video encoding and
decoding and other floating point intensive applications that operate on
large sets of data.
Can this be helpfull for searching Mersenne primes???
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From: Andre De Boer <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 14:43:01 +0000
Subject: Mersenne: again linux
Hello,
Ok, when i run mprime as root the results are written.
But when i give a "find" commando in linux with mprime running, it does
take a very long time to get results from the find commando on the
screen.
The "find" commando is useless now. Does someone else has this problem
and is there way to solve it?
Thanks,
Andre de Boer
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From: Jason Stratos Papadopoulos <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 09:44:50 -0500 (EST)
Subject: Re: Mersenne: Pentium III
On Fri, 26 Feb 1999, Hoogendoorn, Sander wrote:
> The Pentium III, also known under the code name 'Katmai', does not come with
> a feature that would show an immediate performance increase as in case of
> the K6-3. Its basic core as well as the L2-cache architecture is identical
> to the Pentium II processor. The justification for the new name lies in a
> set of 70 new multimedia instructions, once known as 'KNI', now known as
> 'SSE' standing for 'streaming SIMD extensions'. Those new instructions
> enable the CPU to perform floating-point calculations on multiple data at
> the same time, which proves very helpful for 3D graphics, video encoding and
> decoding and other floating point intensive applications that operate on
> large sets of data.
>
> Can this be helpfull for searching Mersenne primes???
Only if KNI allows double precision floating point (which it almost
surely won't, since multimedia doesn't need 15-digit precision).
Now, if KNI has very fast 32-bit to 64-bit unsigned integer multiplies it
does open up the chance of a pretty fast number-theoretic DWT squaring,
but I wouldn't hold my breath that it has that, either.
jasonp
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From: "John R Pierce" <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 08:17:46 -0800
Subject: Re: Mersenne: Pentium III
> The Pentium III, also known under the code name 'Katmai', does not come with
> a feature that would show an immediate performance increase as in case of
> the K6-3. Its basic core as well as the L2-cache architecture is identical
> to the Pentium II processor. The justification for the new name lies in a
> set of 70 new multimedia instructions, once known as 'KNI', now known as
> 'SSE' standing for 'streaming SIMD extensions'. Those new instructions
> enable the CPU to perform floating-point calculations on multiple data at
> the same time, which proves very helpful for 3D graphics, video encoding and
> decoding and other floating point intensive applications that operate on
> large sets of data.
>
> Can this be helpfull for searching Mersenne primes???
probably not. While I haven't actually seen the tech ref on the KNI
instructions they are likely to be single precision vector/matrix operations
oriented towards 3D, probably operating on two 'singles' at a time.. The LL
test would benefit most from operations that used larger word sizes, perhaps a
SIMD 64 bit integer multiply-accumulate.
- -jrp
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From: "Aaron Blosser" <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 11:24:29 -0700
Subject: RE: Mersenne: Pentium III
> Only if KNI allows double precision floating point (which it almost
> surely won't, since multimedia doesn't need 15-digit precision).
> Now, if KNI has very fast 32-bit to 64-bit unsigned integer multiplies it
> does open up the chance of a pretty fast number-theoretic DWT squaring,
> but I wouldn't hold my breath that it has that, either.
Anyone interested can read the PDF on Intel's entire instruction set at
ftp://download.intel.com/design/PentiumII/manuals/24319102.PDF
It's pretty big, 6MB. The normal instructions are using the same PII core,
so don't expect a speed improvement beyond the obvious boost to 500MHz (and
faster once .18 fabs come online).
As for the new instructions, you can always get slightly better performance
by optimizing your assembly to use the SIMD stuff, though you won't get a
HUGE boost from that. Otherwise, there are new instructions for multiple
integer ops that *may* help.
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From: Andrew Isaacson <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 14:54:12 -0500
Subject: Re: Mersenne: Pentium III
On Fri, Feb 26, 1999 at 08:17:46AM -0800, John R Pierce wrote:
> probably not. While I haven't actually seen the tech ref on the KNI
> instructions they are likely to be single precision vector/matrix operations
> oriented towards 3D, probably operating on two 'singles' at a time.. The LL
> test would benefit most from operations that used larger word sizes, perhaps a
> SIMD 64 bit integer multiply-accumulate.
There are some documents on the KNI instructions at
http://www.tbcnet.com/~clive/knirough.html
Basically, KNI (also known as SSI, Streaming SIMD Instructions) allow
the application to execute one instruction (divide or add, for
example) on 4 single-precision floats simultaneously. There are some
instructions which can pertain to integer values, like XOR, AND, and
the like, but for the most part these are aimed at making 3D games go
faster.
A KNI-enhanced version of DES or RC5 will fly, I think, because of the
ability to XOR 128 bits at once. Also, the PSHUFW instruction allows
you to transpose words in one cycle, which is great for RC5 if I
understand correctly.
Also interesting are the uncached instructions, which load and store
directly from memory without polluting the L1 or L2 cache. (There's
no point in using the cache if you're writing 4MB of screen data,
because you're not going to go back and read any of that data before
it gets blown out of the cache anyways.)
I don't see much application to Mersenne searching, though.
- -andy
- --
Andy Isaacson [EMAIL PROTECTED] [EMAIL PROTECTED] Fight Spam, join CAUCE:
http://www.csl.mtu.edu/~adisaacs/ http://www.cauce.org/
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From: David L Nicol <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 14:13:04 -0600
Subject: Mersenne: Geocentrism
Aaron Blosser wrote:
> ....
> And that's just to arrange a single protein molucule. Rough estimates give
> a 1 in 10^161 chance of arranging a single protein by accident, and a 1 in
> 10^119879 chance of "accidentally" arranging the *simplest* self-replicating
> cell (life)...if anyone wants to go further with that... :-) Point
> being...10^161 is a VERY large number, and so is 2^3021377-1!!
Lucky us. Earth is the cradle of life
in the universe! There are a lot of planets and it had to happen
somewhere, sooner or later.
________________________________________________________________________
David Nicol 816.235.1187 UMKC Network Operations [EMAIL PROTECTED]
++++ stop the execution of Mumia Abu-Jamal ++++
++++ more info: http://www.xs4all.nl/~tank/spg-l/sigaction.htm ++++
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From: Blake Stacey <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 16:16:09 -0600
Subject: Mersenne: Re: Chronons
In response to the chance origin of life posting, I think that seems
a lot more likely than a randomly picked Mersenne number turning out to
be prime. Follow me here.
The entire Darwinian theory is based on the concept that better
adapted things pass on hereditary information better, more or less.
Consider the monkey-typing-Shakespeare randomly analogy. It is
fantastically improbable that a random assortment of letters will be any
one of the sonnets. However, imagine writing a computer program that
randomly picks a letter, compares it to the nth letter in a given
sonnet, and keeps it if the letter matches but throws it out if it
doesn't match. This vastly improves the odds, and is a much better
approximation to the phenomenon we're trying to explain.
In terms of Mersenne numbers, the probability of protolife arising
from chemical soup isn't of the order of a random Mersenne number being
prime--it's on the order of a Mersenne prime being prime.
My apologies for the off-topic-ness; I tried to tie it back at the
end.
- --
Blake Stacey
Executive Director of Programming
HyperSphere Software
[EMAIL PROTECTED] :: http://fly.hiwaay.net/~bstacey
"Think for yourself."
- --The Beatles
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From: "Yves & Lucile Gallot" <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 23:21:42 +0100
Subject: Re: Mersenne: Pentium III
>Intel's new Pentium III
>
>Can this be helpfull for searching Mersenne primes???
I just downloaded the manuals from Intel's site.
SIMD integer instructions is just a new name for MMX instructions.
The KNI are called SIMD floating-point instructions. The principal data type
of the Streaming SIMD Extensions are a packed single-precision
floating-point operand, specifically four 32-bit single-precision (SP)
floating-point numbers. Only Single-FP operations are available.
Double precision FP are required for FFT-multiplications : I don't think
that the PIII can be useful for the prime search (except because of its
frequency).
But some new instructions of the PIII can probably improve a little bit the
programs: the prefetch instructions. We can control prefetch and then fetch
data into all cache levels before using them. The bottleneck of memory I/O
can now be controlled easily ...
Yves
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From: Chip/Sandy Kerchner <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 18:54:28 -0500
Subject: Re: Mersenne: Pentium III
>
> > The Pentium III, also known under the code name 'Katmai', does not come with
> > a feature that would show an immediate performance increase as in case of
> > the K6-3. Its basic core as well as the L2-cache architecture is identical
> > to the Pentium II processor. The justification for the new name lies in a
> > set of 70 new multimedia instructions, once known as 'KNI', now known as
> > 'SSE' standing for 'streaming SIMD extensions'. Those new instructions
> > enable the CPU to perform floating-point calculations on multiple data at
> > the same time, which proves very helpful for 3D graphics, video encoding and
> > decoding and other floating point intensive applications that operate on
> > large sets of data.
> >
> > Can this be helpfull for searching Mersenne primes???
>
> Only if KNI allows double precision floating point (which it almost
> surely won't, since multimedia doesn't need 15-digit precision).
> Now, if KNI has very fast 32-bit to 64-bit unsigned integer multiplies it
> does open up the chance of a pretty fast number-theoretic DWT squaring,
> but I wouldn't hold my breath that it has that, either.
It can multiply four simulatenous 32-bit numbers in 2 clock cycles. It uses
128-data (instead of overlaying 64-bit data on the floating point unit as the MMX
does). I believe that these instructions can be useful with a creative approach
to number theory problems. Look at this.
http://www.tbcnet.com/~clive/knirough.html
Chip Kerchner
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From: "Aaron Blosser" <[EMAIL PROTECTED]>
Date: Fri, 26 Feb 1999 20:31:49 -0700
Subject: RE: Mersenne: Re: Chronons
> In response to the chance origin of life posting, I think that seems
> a lot more likely than a randomly picked Mersenne number turning out to
> be prime. Follow me here.
> The entire Darwinian theory is based on the concept that better
> adapted things pass on hereditary information better, more or less.
> Consider the monkey-typing-Shakespeare randomly analogy. It is
> fantastically improbable that a random assortment of letters will be any
> one of the sonnets. However, imagine writing a computer program that
> randomly picks a letter, compares it to the nth letter in a given
> sonnet, and keeps it if the letter matches but throws it out if it
> doesn't match. This vastly improves the odds, and is a much better
> approximation to the phenomenon we're trying to explain.
> In terms of Mersenne numbers, the probability of protolife arising
> from chemical soup isn't of the order of a random Mersenne number being
> prime--it's on the order of a Mersenne prime being prime.
> My apologies for the off-topic-ness; I tried to tie it back at the
> end.
The methodology you described includes a fatal flaw because, by introducing
an outside force, you've just removed the randomness.
In the monkey experiment, you have the end product, the Shakespeare sonnet,
and an intelligent force of some sort, the computer, matching the random
results to the desired end product.
Is there some outside force that is overseeing the random throwing together
of amino-acids to produce proteins? If so, it's not a very random
process...in fact it's not an accidental process at all. An outside,
intelligent force is guiding it, which is *exactly* the point that
abiogenesis tries to *avoid*. :-)
Besides, I wouldn't even argue about evolution since it's too touchy. We
all have our opinions on that, and I'd just as soon let those be. But how
the very *first* amino acids, proteins, or cells came about is something
else. You can't build a cell by natural selection, or any other
"stair-stepping" process. You either get it *all* right, or it's all wrong.
Trying to get back OT, there are 37 known Mersenne Primes below 2^3021377-1.
How many "potential" primes are there, i.e. how many exponents between 2 and
3021377 are prime? Darn, I can't find that...
Well, there's 100,008 primes up to 1,299,827 and there's 34 Mersenne Primes
in that exponent range.
Therefore, if we pick a Mersenne number at random, we have 34 chances in
~1.3*10^6 of picking a Mersenne prime. Those are even better odds than
winning the lottery (6 numbers from 1-50 giving about a 1 in 11.44 billion
chance in any order).
On the other hand, try the odds of flipping a coin 450 times in succession
and getting heads each time. 1 in 2^450 is a zero chance.
And I haven't even brought up, as I did in an email, the fact that proteins
consist of *only* left-handed amino acids, whereas amino-acids produces in
lab experiments contain equal amounts of left- and right-handed ones.
What's the odds of a protein containing 450 only-left-handed amino acids
now? Even more ridiculously small.
Now, what are the odds of enough of these amazingly rare proteins existing
close enough to each other and magically combining to form a
self-replicating cell? Even more staggeringly impossible.
Given all the obstacles to a single protein forming, much less a single
cell, I'm amazed that they still teach this stuff to kids in school without
even trying to explain just how such a miracle happened. The only
explanation you'll get from anyone is that there was a primordial soup, got
hit by lightning or some such, and boom, life.
The Nova show on the subject went on to explain that this first cell
promptly started to feed on bacteria. Whoa! Where'd this bacteria come
from? Like before the first cell formed, bacteria had already managed to
put itself together too? The book "Darwin's Black Box" by Behe certainly
shows that a bacterium is no simple machine either.
I'm seriously OT now...I promise...no more! :-)
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End of Mersenne Digest V1 #514
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