cles per second).
+-------+
| Jud McCranie [EMAIL PROTECTED] or @camcat.com |
| |
| "We should regard the digital computer system as an |
| instrument to assist the number theorist in investigating |
| the properties of his universe -
ology in the military is about 5 years ahead of what is
commercially available. Anyhow, GIMPS will get to exponents around 5,200,000
before too long, and that will help confirm or deny it.
+---+
| Jud McCranie [EMAIL PROTECTED] or @camcat.
.
I think already about 1/4 of the exponents in this range have been tested, and
I'm working on a larger exponent (so they must all be assigned). So it
shouldn't be more than about 2 months before they're finished, my rough
estimate.
+--
around 5,200,000 even though
it is
closer to 5,300,000.
+------+
| Jud McCranie [EMAIL PROTECTED] |
+--+
ck speeds
are
higher.
+------+
| Jud McCranie [EMAIL PROTECTED] or @camcat.com |
| |
| Where a calculator on the ENIAC is equipped with 19,000 |
| vacuum tubes and weighs 30 tons, computers in the future |
|
At 12:59 AM 10/17/98 -0400, Foghorn Leghorn wrote:
>
>Second, I see that there are now some composite exponents in the ECM
>factoring page. Why are none of them even? Is there a technical reason
>that makes them less interesting?
Composite exponents have algebraic factors. For even n, 2^n-1 is
that ) ?
>
>Phil Brett
The regular FPU must be compatible as Intel's. The 3D Now instructions are
probably shorter, but they probably don't matter anyway.
+-+
| Jud McCranie [EMAIL PROTECTED] |
|
, on a Pentium at least, it is faster to use the FPU
than do it with the double-precision integers.
+---------+
| Jud McCranie [EMAIL PROTECTED] |
| |
| You'll never need more than 640 megs of memory. |
+-+
ms possible
that we would have 128-bit arithmetic and data, but 64-bit addressing and
instructions.
+------+
| Jud McCranie [EMAIL PROTECTED] or @camcat.com |
| |
| Where a calculator on the ENI
ing a 16 bit selector for a
'segment descriptor', which contained the location within a 24 bit address
space, size (still less than 64K), and attributes (for Virtual Memory support)
of a segment.
+------+
|
es where it helps. To take an
example that is familiar to us, if you double the data width you make testing
Mersenne numbers more than twice as fast.
+------+
| Jud McCranie [EMAIL PROTECTED] or @camcat.com |
|
e universe is
right, using the 10^78 figure.
+---------+
| Jud McCranie [EMAIL PROTECTED] or @camcat.com |
| |
| "... we live in a world that obeys meticulously the |
| laws of mathematics.
isk space. This is somewhat
more
than we have now, but it won't be long before we do. 62 bits are
sufficient to
address each byte of disk space. 64 bits is enough to address each byte of 1
billion 16GB disks.
+-----+
| Jud McCra
xcept
for
>global economics.
>
128-bit FP is/would be useful in scientific and mathematical calculations.
+---------+
| Jud McCranie [EMAIL PROTECTED] |
| |
| You'll never need more than 640 megs of memory. |
+-+
ive a better result.
I think you just disproved yourself. On the second example, rounding after 2
decimal digits gives the wrong answer, but round after 10 digits and you get
the correct answer, or very close to it. So this shows how having more
precision helps.
+--+
| Jud McCranie [EMAIL PROTECTED] |
+--+
n I had numerical analysis that when we
ran it in single precision, we got no correct digits, when we ran it in double
precision we got 6 or so correct digits.
+-----+
| Jud McCranie [EMAIL PROTECTED] |
|
t on addition and subtraction.)
+------+
| Jud McCranie [EMAIL PROTECTED] or @camcat.com |
| |
| Where a calculator on the ENIAC is equipped with 19,000 |
| vacuum tubes and weighs 30 tons, computers in the future |
| may have only 1,000
7;s right - my error.
+------+
| Jud McCranie [EMAIL PROTECTED] |
+--+
At 12:53 PM 11/9/98 -0800, John R Pierce wrote:
>Note that prime95 periodically writes checkpoints to the disk, I have mine
set
>to 120 minutes, but I think the default is 30 minutes. If the disk spindown
>time is greater than the checkpoint time, the disk prime95 is using will
never
>go idle.
At 07:51 PM 11/13/98 -0800, William Stuart wrote:
>Another interesting thing about this conjecture...
>
>If it is correct, then there is no last prime.
>
And if Goldbach's conjecture is incorrect - then there is no last prime!
+----
t the L-L test is essentially as efficient as
possible. However, I think that there is room for improvement in the
algorithms for doing the arithmetic involved.
+-------+
| Jud McCranie [EMAIL
hese are the only exponents.
Actually n=2 is trivial too. You don't have to show that there are an infinite
number of solutions (in positive integers) for n=2, you only need to show one,
e.g. 3^2 + 4^2 = 5^2.
+-------+
| Jud McCranie
rd of Knuth, I'm impressed. If you see section 4.3.3 you'd know that
there are algorithms (for mult and div) that are faster than what are currently
used.
+----+
| Jud McC
d to my
surprise, the two programs took almost exactly the same amount of time to
run. Then I realized that what they were actually doing was essentially
the same (although the base conversion was a more complex program).
+------+
| Jud McCranie
At 09:36 AM 3/9/99 +0100, Henk Stokhorst wrote:
>
>With regards to the claim made by VME, Brian Beesley and I asked them to
>produce a factor of M(727). They did not come up with a factor.
It seems that he is claiming a primality test - not a factoring method.
>This endorsement was sent to y
At 10:45 AM 3/10/99 +0100, Peter Tichy wrote:
>I ran a search using Copernic, and this is what came out of it;
>
>http://www.aero.org/news/current/topAwards.html
The award came from the president of his COMPANY, not the president of his
COUNTRY, as was claimed. A big difference! Anyhow, there i
At 09:47 PM 3/9/99 -0800, John R Pierce wrote:
>Moeller Thomas L., Milstein Jaime, Generalized Algebraic Structures for the
>Representation of Discrete Systems, Linear Algebra And Its Applications
This is a journal, and doesn't seem to be a book coauthored by Moshe
Goldberg, as was claimed.
ivists would disagree.
+------+
| Jud McCranie [EMAIL PROTECTED] |
+--+
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
How does the current Celeron stack up against a P-II for this work?
+--+
| Jud McCranie [EMAIL PROTECTED] |
| |
| Where a calculator on the ENIAC is equipped with
At 01:52 PM 3/10/99 -0500, Joth Tupper wrote:
>Thanks for sharing the bib search results. There seems to be about a 10
>year gap between the
>2 sets of papers as well as some shift in field.
>
>The linear algebra papers
My guess is that they are from his PhD theses, and perhaps Moshe Goldberg
w
;multipliers that ran at a few terahertz it would take significantly less time
>than that.
The number of steps for the L-L test would bee too large my many, many
orders of magnitude.
+------+
| Jud M
At 09:37 AM 3/11/99 -0500, [EMAIL PROTECTED] wrote:
>In the early 1920's, two guys named Banach and Tarski were exploring a
This is getting off-topic, but the B-T theorem requires you to accept the
axiom of choice (which most mathematicians do). Here's some info:
http://www.cs.unb.ca/~alopez-o/
st one that fails to be prime is
M(8191) = M(M(13)).
+----+
| Jud McCranie [EMAIL PROTECTED] |
||
| 127*2^96744+1 is prime! (29,125 digits, Oct 20
7;t have enough time to test that. The
space required is a linear function of n whereas the time required is at
least a quadratic function of n, so the time requirement grows much more
rapidly than the space requirement.
+-----+
| Jud McCranie
counter example
is known and it has been conjectured that such a counter example must be
hundreds of digits long. "
So one strong PSP test and one Lucas test *seems* to work, but it hasn't
been proven to always work and no counterexamples are known.
+------
At 03:30 PM 3/25/99 -0500, [EMAIL PROTECTED] wrote:
>Mp is a Mersenne Prime with odd prime p "iff"
>3^((Mp-1)/2)=-1 (mod Mp) .
This looks like it is just based on Euler's criteria.
+------+
| Jud McCranie
At 09:42 AM 4/3/99 -0600, kilfoyle wrote:
>yep yep yep George... the search continues. It is not deterred by a small
>bug.
I'm not deterred either. In fact, I added a second machine since I found
out about the bug.
+---
ber of them.
http://www.astro.virginia.edu/~eww6n/math/MersennePrime.html
+------+
| Jud McCranie [EMAIL PROTECTED] |
+--+
ered? Or 120k+19? Why
>only those 16 reminders of
>~30 primes below 120?
Only primes of the form 2kn+1 can divide 2^n-1.
+-------+
| Jud McCranie [EMAIL PROTECTED] or @camcat.com |
|
At 02:35 AM 2/13/99 -0800, Scott Kurowski wrote:
>Has anyone seen the first link on Stanford Prof. Knuth's home page Recent
News?
>
I noticed recently that volume 4 is scheduled for publication 4/4/4. (Actually
volume 4A).
+----
With this setback, does it still make sense for machines slower than P-133
to default to double checking, or should some of them go back to initial LL
tests?
++
| Jud McCranie [EMAIL PROTECTED
rogram working on one number at a time.
+------+
| Jud McCranie [EMAIL PROTECTED] |
| |
| "317 is a prime, not because we think so, or because our |
| minds are shaped
I just got a 400 MHz Celeron, and it is working on 7,376,xxx. It is taking
0.250 seconds per iteration. How does this compare to a PII-400 and a
PIII-400? Is this about right for a Celeron-400?
+--+
| Jud McCranie [EMAIL PROTECTED
t it is reasonably well behaved.
+-------+
| Jud McCranie [EMAIL PROTECTED] |
| |
| I have m
ay that under the mean, reflect the other data with respect to the mean, and
calculate the standard deviation from that "massaged" data. Then a Normal
distribution should approximate it pretty well.
+-------+
| Jud McC
ng to do a Kolmogorov-Smirnov test to see if it was
close to a normal, but that is really designed for the raw data. Since the
data was in a histogram I used the Chi-squared test. The data posted was far
from a normal distribution (even just the right half of it was far from a
normal).
+---
not form one big team out of all of GIMPS and split the money, Honey?
+-------+
| Jud McCranie [EMAIL PROTECTED] |
| |
| I have macular star
At 10:49 AM 5/14/99 -0400, Rick Pali wrote:
>From: Jud McCranie
>
>> Why not form one big team out of all of GIMPS and split
>> the money, Honey?
>
>While I can't speak for others, I'm not in GIMPS for the money. While the
>awards are reasonably new, I'v
I publicly apologize to Mark Honey for misinterpreting his motives.
+---+
| Jud McCranie [EMAIL PROTECTED] |
| |
| I have macular stars in my eyes
At 01:20 AM 5/17/99 -0700, Jiho Kim wrote:
>When a machine is assigned "factoring" is that what it's
doing? Or are they
>trying to find as many factors for known composite as they can?
No, it is trying to find 1 small factor to avoid having to do the
Lucas-Lehmer test.
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 PROT
At 02:52 PM 5/18/99 -0600, Aaron Blosser wrote:
>So basically, it's just a poorly designed box. That's what you get for
>buying Dell, but that's just my opinion :-)
I've got 3 Dells, and I've run prime95 on at least two of them and I never had
the problem.
to find
a root, which immediately gave a factor. It worked great when the number was a
square. Otherwise it degenerated into a poor implementation of a brute force
search.
+---+
| Jud McCranie [EMAIL PROTECTED] |
|
>>Congratulations to everyone from GIMPS on the new *probable* prime,
Will the derails be announced when it is submitted to the journal, when it is
accepted by the journal, or when it appears in print?
+--+
| Jud McCranie [EMAIL PRO
I just noticed that the EFF is now offering $100,000 prize for the first
10,000,000 digit prime. I assume that this means that they consider the
1,000,000 digit prize essentially considered to have been claimed?
++
| Jud McCranie
ou'd have already received that much in interest. :-)
Yes. I hope I live long enough to see a billion-digit prime.
There's a good chance of it.
+----------+
| Jud
McCranie
|
|
|
| I have macular stars in my eyes. |
+--+
At 11:30 AM 6/6/99 -0600, Aaron Blosser wrote:
>I suppose it depends on whether Moore's Law can continue to hold
true. I'm
>not so sure that we can keep doubling speeds of processors every 18
months
>as predicted...
That's often stated, but it hasn't been holding true. We are a
factor of abou
At 04:51 PM 6/7/99 +0200, Steinar H. Gunderson wrote:
>Perhaps a gigadigit prime, but I think 10,000,000 should certainly be
within
>the limits.
I was thinking about it informally the other day, and I thought that I
expected to see 10,000,000-digit primes and 100,000,000-digit primes in
my lifet
The status page shows that for exponents in the range 3,310,000-3,960,000,
there are 225 exponents for which 2 L-L tests have been done, yet there are
40 exponents for which no factor is known, and no LL test has been done. I
have 2 questions:
1. Why have 2nd LL tests been done in many cases wh
At 09:22 PM 6/10/99 -0400, [EMAIL PROTECTED] wrote:
>I would venture to say that those 40 exponents are "out" at the moment,
>assigned to machines which have not yet turned in a result.
But I thought that the exponents were reassigned if no result was reported in 2
months. These were assigne
At 10:47 AM 6/11/99 -0500, JON STRAYER wrote:
>> As I said, unless there is an intervention or someone just
>> takes it upon themselves to double-check those exponents
>> with software other than George's (the very basis
>> of doublechecking), we won't get confirmation of
>> M37 until 2003
At 07:53 AM 6/11/99 -0600, Paul Derbyshire wrote:
>Those are probably just whichever 3M-area exponents got assigned to 286s and
>386s :-)
I wonder about that, however. A 286 can't run Prime95, and a 386 would require
a 387, right?
+--+
| Jud "progr
At 01:10 PM 6/11/99 -0600, Aaron Blosser wrote:
>
>If I see a test that will take well over a year, is it wrong of me to just
>do it myself with a manual assignment?
I think that is what should be done. A double check will have to be done
anyway, so let the year-long test serve as the double che
There seems to be a big discrepancy between what the status page at
merseme.org shows (updated 6-6-99) and what the PrimeNet status page
(updated hourly) shows as far as the exponents under 4,000,000. So maybe
these small exponents that the former page shows that I was concerned about
have actual
At 07:47 AM 6/12/99 +0200, Sturle Sunde wrote:
>Yes. I would get very pissed if someone snatched an exponent which I
>already spent a year of work on, and am still working on, without even
>telling me in advance.
We are all in some danger of this happening because of non-GIMPS people working
At 03:56 PM 6/12/99 +0100, Brian J. Beesley wrote:
>
>You might get even more "bangs per buck" by using Celeron 400
>processors, though these will be less quick than PII-400
On Prime95, my C400 is 28% faster than my PII-300, so a Celeron stacks up
pretty well. So if a PII-400 is 33% faster tha
At 12:41 PM 6/12/99 -0700, Terry S. Arnold wrote:
>You also have take into account the fact that the memory bus on C400 is
>running at 66 MHz white the same bus on the PII-400 is running at 100 MHz.
That's right, but the PII-300 I was comparing it to also has 66 MHz memory.
There are also diff
At 11:38 AM 6/13/99 +0200, Sturle Sunde wrote:
>
>And exactly how do you think that justifies that a GIMPS-participant does
>it knowingly?
I don't think it is justified, except for cases where they seem to have been
abandoned, or someone is purposefully holding up the project.
>This isn't a co
At 11:38 AM 6/13/99 +0200, Sturle Sunde wrote:
>And exactly how do you think that justifies that a GIMPS-participant does
>it knowingly?
I'd like to ask the following of readers of this list who have been working on
an exponent for more than 1 year, and have an expected completion date after
At 04:32 PM 6/13/99 +0200, Sturle Sunde wrote:
>
>Great. Next time Primenet tells me "Error, this exponent is already
>tested" on the exponent I reserved a few months ago, I should be very
>happy and tell myself: "Great! Someone have tested the exponent for me,
>and will get the credit if it
At 09:32 AM 6/13/99 -0600, Aaron Blosser wrote:
>Criteria I used were:
>
>1) Original *quite* long time to complete
>2) No check-ins for a period of at least 6 months.
I thought that if no check-in was done in 60 days, the number was put back in
the pool.
+--
At 11:46 AM 6/13/99 -0500, Mikus Grinbergs wrote:
>
>To those on this list who are pursuing why certain exponents are not
>being completed "sooner" -- think about it -- WHAT DIFFERENCE WILL
>IT MAKE in __your__ life when exponent so-and-so is completed ??
>
I write the exponents resulting in prime
At 04:32 PM 6/13/99 +0200, Sturle Sunde wrote:
>When a person tells the world which exponents he is testing, and
>continously reports his progress, people could at least complain to him
>before hijacking the exponents he has been testing for a year
Some people that are out of contact may be u
>From the FAQ:
"Be sure to report your results in a timely manner or your exponents may be
reassigned to someone else for testing."
+--+
| Jud "program first and think later" McCranie |
+--+
___
At 06:09 AM 6/14/99 -0400, [EMAIL PROTECTED] wrote:
>The reason it took so long is that it wasn't until now that ANYONE
>had Win9x run that long without rebooting.
I might have actually hit that problem and not realized it. Until recently,
for many months I had my old P-120 running in another
quot; every now and then.
>
>Aaron
>
>____
>Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
X-Sender: [EMAIL PROTECTED] (Unverified)
X-Mailer: QUALCOMM Windows Eudora Pro Version 4.1
Date: Mon, 14
There is a conjecture that the nth Mersenne exponent resulting in a prime
is approximately (3/2)^n. Consider Mersenne primes through M37. (I don't
know exactly what M38 is yet, and there may be other small ones. Also, the
double checks of the range through M37 haven't been completed.)
You can
If you take the following comma delimited file into a spreadsheet, and
graph it (say with a line chart) it shows the relationship of Mersenne
exponents to their index, for the first 37 Mersenne primes. The first
column is the log of (3/2)^n, the second column is the log of the exponent
of the nth
At 01:45 AM 6/24/99 -0700, Alan Simpson wrote:
>
>It is clearly not the case that the exponent of the n-th Mersenne prime is
>not (3/2)^P{n} or e^(gamma*n), but something like c^{n+o(n)), where "o(n)"
>is the usual "little-o of n" (lim_{n \rightarrow \infty} o(n)/n = zero (a
>severe abuse of n
Since Prime95 writes to the disk periodically, is it safe to do a disk
defragmentation while it is running?
+--+
| Jud "program first and think later" McCranie |
+--+
At 06:03 PM 6/24/99 -0400, lrwiman wrote:
>This would put the 38th mersenne at ~2.6million, the 39th at
~3.9million,
>and the 40th at 5.7million.
It doesn't work quite that way. It is a global property that doesn't say
anything about the individual Mersenne primes, just as the Prime Number Th
For those of us who don't have access to Wagstaff's 1983 paper "Divisors of
Mersenne Numbers", it is nicely summarized in "The New Book of Prime Number
Records", by Paulo Ribenboim, chapter 6, section V.A. (page 411-413 in this
edition). He gives 3 statements:
(a) The number of Mersenne primes <
At 03:58 PM 6/26/99 -0400, Allan Menezes wrote:
>According to Paulo Ribenboim's book quoted below by Jud Euler's Constant
>gamma=0.577215665... and working out the number of mersenne primes below
>p=700
>in Mathematica 4.0 gives 39.5572 primes, so we must be missing a prime if
>Wagstaffs' rig
At 12:14 PM 6/27/99 -0400, Geoffrey Faivre-Malloy wrote:
>How large will the exponent be for a 10,000,000 digit prime number?
digits x 3.32192 gives the approximate exponent.
+--+
| Jud "program first and think later" McCranie |
+-
The Status estimate of the chance that the number you are testing seems to
be off by a factor of e, based on Wagstaff's estimate.
+--+
| Jud "program first and think later" McCranie |
+--+
At 09:59 PM 6/28/99 +0100, Gordon Spence wrote:
>The GIMPS home page explains the following
>
>"Finally, if a factor is later found for a Mersenne number or the
>Lucas-Lehmer result is found to be incorrect, then you will "lose credit"
>for the time spent running the test."
>
>It is on always str
At 04:16 AM 6/29/99 -0400, Lucas Wiman wrote:
>All,
>Here is version 1.1 of the FAQ.
Here's a question that needs to be addressed: how to go from digits to
exponents, and exponent to digits.
+--+
| Jud "program first and think later" McCranie |
+--
At 04:16 AM 6/29/99 -0400, Lucas Wiman wrote:
>All,
>Here is version 1.1 of the FAQ.
Also. FAQs involve why do we think there are an infinite number of Mersenne
primes, how many are expected below a given limit, and what s the probability
of finding one.
+
At 09:04 PM 6/28/99 -0400, Peter Doherty wrote:
>>The Status estimate of the chance that the number you are testing seems to
>>be off by a factor of e, based on Wagstaff's estimate.
>>
>Yeah, I was wondering about that thing...
What I'm saying is that if p is prime, the best estimate that Mp is
At 11:17 PM 6/29/99 +0200, Steinar H. Gunderson wrote:
>Then what is the best fit? Exponential? :-)
It is slightly parabolic. The good news is that it is trending upward faster
than linearly.
+--+
| Jud "program first and think later" McCranie |
+---
At 03:05 AM 6/30/99 -0400, Lucas Wiman wrote:
>I realize this is probably a FAQ, (and I intend to put it there), why is
>the distribution of factors so non-linear?
Because small factors are more likely to divide a given number.
+--+
| Jud "program fir
At 10:47 AM 7/6/99 +0200, Benny.VanHoudt wrote:
>Now lets only focus on the set 2^p - 1 with p prime, i.e., the set
>of numbers that we are checking out at GIMPS. Has anyone proven that
>an infinite number these are NOT prime (this is VERY likely to be
>true)? If so, how can one prove this easily
At 01:05 PM 7/6/99 -0400, Lucas Wiman wrote:
>I'm not sure whether or not it has been proven whether or not there are
>an infinity of Sophie Germain primes of the form 4*n+3.
Whoops - it hasn't been proven.
+--+
| Jud "program first and think later"
At 06:55 PM 7/6/99 +0100, Brian J. Beesley wrote:
>
>Can you please supply a reference to this proof? Chris Caldwell's
>Prime Pages show this as a conjecture (with a strong heuristic
>argument).
No, I was wrong about it having been proven.
+--+
|
At 07:16 PM 7/6/99 +0200, [EMAIL PROTECTED] wrote:
> Please leave adequate white space in your right margin.
>Benny's twice-indented (indentified?) text twice still reads well, but
>three of Jud's indented lines wrap around on my 80-character screen.
I think I have mine set to wrap at 60 cha
At 06:19 AM 7/8/99 -0400, you wrote:
>All,
>In the book _Primes and Programming_ Head's method of multiplying
>two numbers mod n is mentioned. Is this actually more effiecient
>than simply multiplying the two numbers and taking the modulus?
>
Yes, because it keeps the numbers smaller. It was ori
At 11:52 AM 7/8/99 -0700, Rudy Ruiz wrote:
>I am not aware that anyone has yet proven the infinitude of Sophie
>Germain Primes. [Granted that, in itself, does not mean anything ;)
I was wrong. As far as I know, it hasn't been proven either (but it is
almost certainly true). I had seen a conj
At 08:11 PM 7/8/99 -0400, Pierre Abbat wrote:
>That is going to be a *lot* slower than FFT convolution, for numbers the size
>of the Mersenne numbers we're testing!
Head's algorithm is for getting x*y mod n when 0<=x,yM, where M is the largest integer you can store in a format
native to the com
At 10:16 AM 7/9/99 -0700, Kris Garrett wrote:
>Has it been proven that all mersenne numbers greater than one are
>square free?
As far as I know, it has not been proven (and no repeated factors are known
either).
+--+
| Jud "program first and think late
At 06:51 PM 7/9/99 +0100, Brian J. Beesley wrote:
>For reasonably small multi-precision numbers, Head's method is
>actually very good, if you're working on a true RISC processor with
>no integer multiply instruction.
I started using Head's algorithm in 1981 on my Apple II. It was better
than
1 - 100 of 208 matches
Mail list logo
