RE: Inane Stuff (Was: Mersenne: M38, SETI, and other random stuff )
On Thu, 10 Jun 1999, Colin Percival wrote: So we are about 7.5*10^10 P90 years away from our first billion digit prime. Following conservative estimates of cpu power and number of participants doubling every two years, I'd guess that we will have a our first billion digit prime in 2021, when we have 40 million participants and Pentium XV 1000GHz processors. Scott, do you have plans in place to ramp up the PrimeNet servers to handle these 40 million participants? :-) Kel Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: M38, SETI, and other random stuff
On Wed, 9 Jun 1999, Chris Nash wrote: Hi folks, As we all impatiently await verification of M38(?) a really stupid thought occurred to me, so apologies if it's a lot more ignorant than Chuck W.'s "definitive" post on the subject of GIMPS v SETI, or distributed computing in general. If the verification of M38 is making us impatient, how on earth would we feel if SETI did find E.T., and we had to wait thousands of years for our reply to get back? And, if we send M1, M2, M3 M38 as proof of our intelligence, what will *their* comparative results be by the time the message arrives? Talking about impatience, there is something I don't understand: are we waiting just for the doublecheck to be completed or does the EFF prize somehow require that M38 be kept secret until publication? I hope not, that would be very strange indeed... http://www.mat.puc-rio.br/~nicolau Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
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 assigned much more than 2 months ago. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
Jud McCranie [EMAIL PROTECTED] wrote: [Mysterious missing Mersenne exponents] But I thought that the exponents were reassigned if no result was reported in 2 months. These were assigned much more than 2 months ago. No, they're reassigned if no update is reported in 2 months. The update may be a keepalive or an expected completion date or almost anything. Some exponents take much longer than 2 months to LL test on slower machines. Those are probably just whichever 3M-area exponents got assigned to 286s and 386s :-) Get free e-mail and a permanent address at http://www.netaddress.com/?N=1 Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
At 07:53 AM 6/11/99 MDT, Paul Derbyshire wrote: Jud McCranie [EMAIL PROTECTED] wrote: [Mysterious missing Mersenne exponents] But I thought that the exponents were reassigned if no result was reported in 2 months. These were assigned much more than 2 months ago. No, they're reassigned if no update is reported in 2 months. The update may be a keepalive or an expected completion date or almost anything. The limit is 60 days after the completion date, and not since the last update. These ones never call back in since more than a year. Four of them will be still allocated a year from now. prime fact current days exponentbits iteration run / to go / exp date updated date assigned -- - - --- --- 4465127 60 470.2 313.8 373.8 26-Feb-98 09:23 4671439 * 60 369.8 149.2 209.2 06-Jun-98 20:31 4787599 61 373.9 664.1 724.1 02-Jun-98 16:42 4833901 61 401.9 407.1 467.1 05-May-98 16:35 4864591 61 373.0 34.0 94.0 03-Jun-98 13:18 4876111 61 411.3 51.7 111.7 26-Apr-98 07:59 4926563 61 436.6 105.4 165.4 31-Mar-98 23:58 5016679 61 385.5 383.5 443.5 22-May-98 02:09 5123693 61 369.6 -43.6 16.4 06-Jun-98 23:55 Yvan Dutil Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: personal account report
hello members, Recently I finished my first exponent testing, hoi hoi hoi, I send the result.txt manually to the prime server. In my personal report the exponent was registered, so far ok. But if I look into my personal report I see that the "LL P90 CPU yrs" and all the other numbers on the same line like "Exponents LL tested" are still all on zerro, why?? Did I do something wrong or what. Please clear this for me, I like to do it in the correct way. best wishes, Paul van Grieken Alcatel Telecom Nederland afd: T-TAC NE Postbus 3292 2280GG rijswijk Nederland Phone: + 31 70 307 9353 Fax: + 31 70 307 9476 Email: [EMAIL PROTECTED] Prive: Ruys de Beerenbrouckstraat 1 2613AS Delft Netherlands Marklin collector Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: status of exponents
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 sigh So? It's not like we are running out of work. -- There are only three reasonable numbers in software engineering: 0, 1 Infinity Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
Exponents are only re-assigned if the machine they are assigned to has not been heard from AT ALL over the past 60 days. So long as the machine checks in and tells PrimeNet that it is still working, it will let them take as long as they want to check the exponent. This was my complaint from a couple days ago -- one client in particular has four exponents checked out for double-checking, and is regularly checking in -- taking 11 months to check a single exponent. Even though those three "untouched" exponents won't even be LOOKED AT by the machine for up to three years, the will never expire because the machine checks in regularly (at least every 60 days) and reports that it did a few iterations. 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 sigh At 09:16 AM 6/11/99 -0400, you wrote: 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 assigned much more than 2 months ago. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Digest V1 #572
Mersenne Digest Friday, June 11 1999 Volume 01 : Number 572
--
Date: 09 Jun 1999 22:49:36 +0200
From: [EMAIL PROTECTED] (Rene H. Larsen)
Subject: Mersenne: Re: Self-test (was: Prime 95 Error Messages/ Misc)
"Pierre Abbat" [EMAIL PROTECTED] writes:
Most modern motherboards contain case and/or CPU temperature
sensors which can be read by software.
Is there a file in /proc that will tell me this?
It's not part of the standard kernel yet, but take a look at
http://www.lm-sensors.nu/.
HTH.
- --
/'"`\ zzzZ | My PGP Public Key is available at:
( - - ) | http://home1.inet.tele.dk/renehl/
- --oooO--(_)--Oooo--
Don't ya just hate it when there's not enough room to fin
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Date: Wed, 09 Jun 1999 21:55:27 -0500
From: kilfoyle [EMAIL PROTECTED]
Subject: Re: Mersenne: These go to 11 (WAS: blahblah...)
APL .. now that brings back memories!I was an APL wizard in the '70s
regards,
Michael...
Joth Tupper wrote:
Ground rules are critical, but how about
/.1
where "/" represents the APL-style monadic divide or multiplicative inverse.
1/.1
takes two.
- Original Message -
From: Ernst W. Mayer [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Tuesday, June 08, 1999 11:47 AM
Subject: Mersenne: These go to 11 (WAS: blahblah...)
Paul Leyland [EMAIL PROTECTED] wrote:
The radix is always 10.
{snip}
or, more concisely, (1+1+1)^(1+1) + 1.
Can anyone represent that number in fewer than (1+1+1)! ones?
How about
1 1,
where the shift is, of course, decimal.
Your shifty friend,
-Ernst
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Date: Wed, 09 Jun 1999 23:19:25 -0400
From: George Woltman [EMAIL PROTECTED]
Subject: Mersenne: Pentium Pro Optimization Help Needed
Hi all,
I'm trying to optimize prime95 for the Pentium Pro/PII/PIII
architecture. I'm fairly well versed in various execution units
and latencies, but some mysteries remain.
Are there any experts in this field - maybe even some Intel
employees - that could improve the code further? Even one clock
cycle in a macro that will be executed a few quintillion times is
a big help.
The new assemply macros are at ftp://entropia.com/gimps/lucas1p.mac
for you to look at.
Questions: Why is the code faster when I throw in some
no-ops (actually fxch st(0) instructions)? How can I force the
CPU to execute the floating point micro-ops in the optimal order?
Does reordering the fstp instructions have any effect? Are there
other issues I sould consider?
Regards
George - who is looking forward to IA-64 where I am in control of
the opcode scheduling once again. Not to mention lots of registers!
P.S.The clock timings were measured using the following loop. I can
provide more details upon request.
mov al, 0
mov ecx, 250; 1000 iterations
clp1: disp four_complex_cpm_fft_3 8, 16, 32 ;;; or some other macro
lea esi, [esi+64]
add al, 256/4
jnc clp1
lea esi, [esi-256]
dec ecx ; Check loop counter
jnz clp1; Loop if necessary
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Date: Thu, 10 Jun 1999 00:34:47 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Computer speeds factoring
I have two questions/comments:
Does anyone else remember something from a year or two back (actually may
still be a modern thing still)? This company was producing very fast
computers using ordinary chips and making the computer case into a type of
freezer, encasing the chip and keeping the chip very cold. This made the
computer run faster, I guess by increasing its conduction, and one result I
recall is getting a 600 MHz DEC Alpha chip to run at around 767 MHz? Has
anyone bought this kind of computer, or perhaps done some kind of home
modification (like all the overclocking)?
My second question, what is a good factoring program for Win98 on a PII
system that allows you to enter a very large number and attempt to factor it,
thereby proving it either composite or prime? Thanks for any help.
Re: Mersenne: Computer speeds factoring
Look at www.kryotech.com Gary Diehl [EMAIL PROTECTED] wrote: I have two questions/comments: Does anyone else remember something from a year or two back (actually may still be a modern thing still)? This company was producing very fast computers using ordinary chips and making the computer case into a type of freezer, encasing the chip and keeping the chip very cold. This made the computer run faster, I guess by increasing its conduction, and one result I recall is getting a 600 MHz DEC Alpha chip to run at around 767 MHz? Has anyone bought this kind of computer, or perhaps done some kind of home modification (like all the overclocking)? My second question, what is a good factoring program for Win98 on a PII system that allows you to enter a very large number and attempt to factor it, thereby proving it either composite or prime? Thanks for any help. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: status of exponents
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 sigh So? It's not like we are running out of work. But it seems that our work should be better prioritized. There are small exponents that were assigned at least 17 months ago that haven't been finished. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: Computer speeds factoring
If I'm not mistaken, 2 big problems keep showing up with these super-coolants. One is condensation which is really bad bad bad for your motherboard/CPU. The other (like with Peltier junction coolers) is that they often generate as much heat as they dissipate. Besides adding an active cooler, you often need to add even more case fans to get rid of the excess heat the Peltier devices generates. There's the nut who is working on total immersion of his system in oil, with an air-conditioner coil submersed as well. This would solve the problem of condensate, but there is concern that the mineral oil will break some of the components on the board. I like the idea, but instead of mineral oil, some inert water. Unfortunately, that's not easy to come by :-) otherwise you could just dunk the whole system into a refrigerated cooler of inert water and ramp up your clock speeds further than otherwise possible. But for all that effort, might as well spend more on a faster system. Aaron -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of Gary Diehl Sent: Thursday, June 10, 1999 5:23 PM To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Subject: Re: Mersenne: Computer speeds factoring Look at www.kryotech.com Gary Diehl [EMAIL PROTECTED] wrote: I have two questions/comments: Does anyone else remember something from a year or two back (actually may still be a modern thing still)? This company was producing very fast computers using ordinary chips and making the computer case into a type of freezer, encasing the chip and keeping the chip very cold. This made the computer run faster, I guess by increasing its conduction, and one result I recall is getting a 600 MHz DEC Alpha chip to run at around 767 MHz? Has anyone bought this kind of computer, or perhaps done some kind of home modification (like all the overclocking)? My second question, what is a good factoring program for Win98 on a PII system that allows you to enter a very large number and attempt to factor it, thereby proving it either composite or prime? Thanks for any help. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
I wonder about that, however. A 286 can't run Prime95, and a 386 would require a 387, right? ... or a 486 SX would require a 387 or 487 coprocessor. But since 387s cost buttons, the user might actually have one. The problem is, a 386+387 is still hopelessly slower than a Pentium, even at the same clock speed. Don't you think this discussion has gone on long enough yet? Regards Brian Beesley Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
On 11 Jun 99, at 10:32, Jeff Woods wrote: Exponents are only re-assigned if the machine they are assigned to has not been heard from AT ALL over the past 60 days. So long as the machine checks in and tells PrimeNet that it is still working, it will let them take as long as they want to check the exponent. So? There's plenty of work left for the rest of us 8-) This was my complaint from a couple days ago -- one client in particular has four exponents checked out for double-checking, and is regularly checking in -- taking 11 months to check a single exponent. Even though those three "untouched" exponents won't even be LOOKED AT by the machine for up to three years, the will never expire because the machine checks in regularly (at least every 60 days) and reports that it did a few iterations. Ah. Someone with a 386. We've had these before, it usually happens (eventually) that the user gets fed up or the machine gets upgraded, either way the problem "goes away". 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 sigh Well, they're not a serious problem, yet. When they _do_ become isolated instances preventing a landmark link confirmation of M(37) being achieved, then I'm sure someone will devote a few PII-400 CPU weeks to clearing them up. BTW note that PrimeNet does accept results for exponents not assigned to you, though it does mutter and won't credit you for the CPU time. Regards Brian Beesley Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: Computer speeds factoring
If I'm not mistaken, 2 big problems keep showing up with these super-coolants. One is condensation which is really bad bad bad for your motherboard/CPU. I worked on a system that keeped the temperature just above the dew point. But I don't know if I could afford to put one of those in my PC box. :-) Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
Will the Millenium Deities smite all GIMPS participants unless each and every exponent under 500 has been processed by 12/31/99 ? Assume uncompleted exponents were reserved in good faith. How does it make the world a better place to have others come along and say: "I see that splinter in your eye -- *you* have not finished yet !!"? WHY are these others so concerned about a few exponents not being finished soon? What possible difference does it make to them? mikus Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: 286's and 386's running Prime95
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? First off, a 286 in order to do floating point math needs a math coprocessor. The model of math coprocessor that goes along with a 80286 is the 80287 not a 387. But, Prime95 only runs on Windows95, and Windows95 only runs on 386s and higher so there are no 286s out there running Prime95. The lowest end 386 is the 80386SX-16 running at a whopping 16 Mhz. 386 SX's have a 32 bit internal bus (making them Intel's first 32 bit processor) and a 16 bit external bus. The 386DX is 32 bit inside and out, but most of the 80386DX-16s out there have a major bug in them that makes their external bus 16 bit just like the 386 SX. The CPUs that have this bug are from 1985 and have a double sigma mark on them, this distinguishes them from the working 386's. So, anything 386 or higher will run Prime95. Lennart Grebelius has a great benchmark page setup at: http://www2.tripnet.se/~nlg/mersenne/benchmk.htm Here he compares everything from a 386SX-16 to a P2-400 MHz (which is 540 times faster at running Prime95). Personally I will not run Prime95 on anything less then a P5-166, and I also will not run it on anything that does not have 32 MB or greater of RAM. Not that Prime95 is a resource hog, far from it, I just don't think it's worth my time to install it on anything slower then a 166, and I don't think it is fair to the user of the machine to run a program that requires 4 to 5 MB or RAM unless at least 32 MB is present. But far be it from me to judge how you run it, this is just my opinion. -Marc Marc Getty [EMAIL PROTECTED] Department of Dental Informatics, Temple University http://www.temple.edu/dentistry/di/215-204-7710 Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: status of exponents
What is the consensus on exponent "poaching"? 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? What would be the consequences of that? I know that if I test it and turn it in myself, the next time the slow machine does an update, it will get an "exponent already tested" message and remove it from the worktodo, and if it does finish up eventually and turn it in, would it count as a double-check (or even triple-check if it really takes a year)? Aaron -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of Yvan Dutil Sent: Friday, June 11, 1999 8:59 AM To: [EMAIL PROTECTED] Subject: Re: Mersenne: status of exponents At 07:53 AM 6/11/99 MDT, Paul Derbyshire wrote: Jud McCranie [EMAIL PROTECTED] wrote: [Mysterious missing Mersenne exponents] But I thought that the exponents were reassigned if no result was reported in 2 months. These were assigned much more than 2 months ago. No, they're reassigned if no update is reported in 2 months. The update may be a keepalive or an expected completion date or almost anything. The limit is 60 days after the completion date, and not since the last update. These ones never call back in since more than a year. Four of them will be still allocated a year from now. prime fact current days exponentbits iteration run / to go / exp date updated date assigned -- - - --- --- 4465127 60 470.2 313.8 373.8 26-Feb-98 09:23 4671439 * 60 369.8 149.2 209.2 06-Jun-98 20:31 4787599 61 373.9 664.1 724.1 02-Jun-98 16:42 4833901 61 401.9 407.1 467.1 05-May-98 16:35 4864591 61 373.0 34.0 94.0 03-Jun-98 13:18 4876111 61 411.3 51.7 111.7 26-Apr-98 07:59 4926563 61 436.6 105.4 165.4 31-Mar-98 23:58 5016679 61 385.5 383.5 443.5 22-May-98 02:09 5123693 61 369.6 -43.6 16.4 06-Jun-98 23:55 Yvan Dutil Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: Pentium Pro Optimization Help Needed
Or it could be a combination of decoding/code alignment problems (sub-optimal decode cycles) which cause goofy patterns in loops and such. I suggest running it thru VTUNE and see what comes up there... There's the good doc at: http://www.agner.org/assem/pentopt.htm which explains all this stuff better than I could ever hope to. -Original Message- From: Blosser, Jeremy [mailto:[EMAIL PROTECTED]] Sent: Friday, June 11, 1999 10:06 AM To: '[EMAIL PROTECTED]' Subject: RE: Mersenne: Pentium Pro Optimization Help Needed Umm... decoding optimization (4-1-1 rule) For example in four_complex_cpm_fft_3: ;;1-1-1 fld R6 ;; I2,I3,A2,r/i,A4,I1,R3,R1 fmulst(3), st ;; B2 = I2 * r/i ;23-27 fsubp st(2), st ;; A2 = A2 - I2 ;24-26 ;;1 (D1, D2 stall) fld R8 ;; I4,I3,A2,B2,A4,I1,R3,R1 ;;2-1 (D2 stall) fmulQWORD PTR [edi+24] ;; B4 = I4 * r/i ;25-29 fxchst(4) ;; A4,I3,A2,B2,B4,I1,R3,R1 ;;2-1 (D2 stall) fsubR8 ;; A4 = A4 - I4 ;26-28 fxchst(2) ;; A2,I3,A4,B2,B4,I1,R3,R1 Plus all the stores are decoded in separate cycles (2 uOps) I'm sure someone else will correct my mistakes ;) I'm sure you checked cache alignments... I can't think of anything else offhand... Also, I noticed that no attention was paid to as far as K6 optimization (ie tossing the fxch's) in the current code... Any effort to improve that or is it not worth it? -Original Message- From: George Woltman [mailto:[EMAIL PROTECTED]] Sent: Wednesday, June 09, 1999 10:19 PM To: [EMAIL PROTECTED] Subject: Mersenne: Pentium Pro Optimization Help Needed Hi all, I'm trying to optimize prime95 for the Pentium Pro/PII/PIII architecture. I'm fairly well versed in various execution units and latencies, but some mysteries remain. Are there any experts in this field - maybe even some Intel employees - that could improve the code further? Even one clock cycle in a macro that will be executed a few quintillion times is a big help. The new assemply macros are at ftp://entropia.com/gimps/lucas1p.mac for you to look at. Questions: Why is the code faster when I throw in some no-ops (actually fxch st(0) instructions)? How can I force the CPU to execute the floating point micro-ops in the optimal order? Does reordering the fstp instructions have any effect? Are there other issues I sould consider? Regards George - who is looking forward to IA-64 where I am in control of the opcode scheduling once again. Not to mention lots of registers! P.S.The clock timings were measured using the following loop. I can provide more details upon request. mov al, 0 mov ecx, 250; 1000 iterations clp1: disp four_complex_cpm_fft_3 8, 16, 32 ;;; or some other macro lea esi, [esi+64] add al, 256/4 jnc clp1 lea esi, [esi-256] dec ecx ; Check loop counter jnz clp1; Loop if necessary Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Re: Mersenne Digest V1 #572
On Fri, Jun 11, 1999 at 08:46:53AM -0700, Mersenne Digest wrote: This made the computer run faster, I guess by increasing its conduction, and one result I recall is getting a 600 MHz DEC Alpha chip to run at around 767 MHz? Has anyone bought this kind of computer, or perhaps done some kind of home modification (like all the overclocking)? I saw an article on Slashdot (http://slashdot.org -- try to pronounce that) some weeks ago. Try to make a search. Whoever wrote that article had made a dual-CPU cooler, so he could actually _double_ the CPU speed and still make it run. (It even had some info on _why_ cooling helped.) My second question, what is a good factoring program for Win98 on a PII system that allows you to enter a very large number and attempt to factor it, thereby proving it either composite or prime? Thanks for any help. As somebody pointed out, the giantint package does exactly that (well, actually, the numbers aren't 100% sure to be prime) for Linux/UNIX. Either find someone who's willing to port it, or get Linux. Example (previously shown on this list): --- steinar:~# echo 123123123123123123123123123123 | ./factor Sieving... 3 * 7 * 11 * 13 * 31 * 41 * 41 * 211 * 241 * 271 * 2161 * 9091 * 2906161 steinar:~# echo 1231231231231231231231231231231231 | time ./factor Sieving... Commencing Pollard rho... ... 111871 * Commencing Pollard (p-1)... .. Commencing ECM... Choosing curve 1, with s = 346492192, B = 1000, C = 5: .. Commencing second stage, curve 1... Choosing curve 2, with s = 2131939374, B = 1000, C = 5: .. Commencing second stage, curve 2... 18102915799 * 607957991560696039 1.92user 0.00system 0:02.12elapsed 90%CPU (0avgtext+0avgdata 0maxresident)k 0inputs+0outputs (100major+30minor)pagefaults 0swaps --- ---snip--- You must be thinking of KryoTech: http://www.kryotech.com/ Of course, Kryotech too. The article I was referring to showed a way to get an extra -10 or -20 degrees Celsius `on top of' Kryotech. (Totally built from scratch.) ---snip--- The optimization guide is packed full of tips. It's about 150 pages in total, although half of it is a reference guide. I've pointed George to this some time ago, and he told me there was a lot of errors in it. If you look in the source code, all three of these (usage of CMOVs/branch optimization, avoiding partial register stalls, and data alignment) are implemented in the code already. However, it tells very little about FPU optimization on the P6-family, which, I believe, is what George is after. Perhaps a posting on comp.lang.x86.asm (if I remember right) would be an idea? I posted a question there once, and got very much constructive information back. Thanks to David Willmore (not a turkey by any means), I've had a chance to try a soon- to-be-released update of my Mersenne code on a 500MHz Alpha 21264s, and it's extremely impressive - 0.18 seconds per iteration at FFT length 384K, fully three times faster than on my 400MHz 21164. Hmmm... I'm currently doing an exponent of 7398xxx on my PII/448 (bus-overclocked), which should be 384K FFT length. My best result is 0.197 secs/iteration (stable, but not across reboots) using mprime 18.1. This means the PII is about as fast as an Alpha (a little slower) on the same clock speeds. Is Alpha over-hyped, is something wrong, or is just George a terriffic x86 assembly coder? The performance on the 21264 is in line with the MIPS Which means Intel is also in line with the MIPS? (I just saw some benchmarks that promised K7 to be 40% faster than PII at FPU, looks like we have good times ahead of us!) ---snip--- 1. Why have 2nd LL tests been done in many cases when there are still exponents whose status is unknown? Probably because P133s (is this number right) or slower are now automatically assigned double-checking results, instead of full LL tests. (As a side note, an AMD K6/200 instantly began checking out double-checking assignments instead of factoring assignments when I set it to work 24 hours (instead of 8) a day. I consider this a bug, unless somebody has a good reason K6s shouldn't do integer arithmetics instead of FPU work.) ---snip--- My vote for "Most Inane" would be to the guy a year or two ago who claimed to know for an absolute certainty that there were only, (I think it was) 37 Mersenne primes. Whatever the number was, it was about one more than had been discovered at that point. `It is a scientific fact that your vision becomes worse if you shave off your beard.' (Or whatever whoever said.) I think much stupid has been said. Never say anything and claim 100% certainity :-) ---snip--- Even with a nice 550MHz PIII, a 33M exponent could be tested in maybe around 1/12 the time of a P90 (about 6 times faster, as well as being much more optimized...maybe more like 1/10). I think 80 years is a bit of an overestimate though...but I could be wrong on that. In fact, I think the 90
Re: Mersenne: Computer speeds factoring
Kryotech's FAQ reads: Q3: How do you prevent ice or condensation from forming around the very cold CPU? A3: We have a set of patents and extensive know-how for preventing condensation. This is the center of KryoTech's expertise arguably our most important value-add. We have been running -40C computer systems since December 1994 without condensation! I also remember reading an early press release on Kryotech a year or so ago that mentioned they surround the top of the CPU with a specially insulated cover that prevents the cold (which reaches the CPU top-cover) from being exposed to the outside air, thereby preventing condensation. Gary Diehl Aaron Blosser wrote: If I'm not mistaken, 2 big problems keep showing up with these super-coolants. One is condensation which is really bad bad bad for your motherboard/CPU. The other (like with Peltier junction coolers) is that they often generate as much heat as they dissipate. Besides adding an active cooler, you often need to add even more case fans to get rid of the excess heat the Peltier devices generates. There's the nut who is working on total immersion of his system in oil, with an air-conditioner coil submersed as well. This would solve the problem of condensate, but there is concern that the mineral oil will break some of the components on the board. I like the idea, but instead of mineral oil, some inert water. Unfortunately, that's not easy to come by :-) otherwise you could just dunk the whole system into a refrigerated cooler of inert water and ramp up your clock speeds further than otherwise possible. But for all that effort, might as well spend more on a faster system. Aaron -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of Gary Diehl Sent: Thursday, June 10, 1999 5:23 PM To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Subject: Re: Mersenne: Computer speeds factoring Look at www.kryotech.com Gary Diehl [EMAIL PROTECTED] wrote: I have two questions/comments: Does anyone else remember something from a year or two back (actually may still be a modern thing still)? This company was producing very fast computers using ordinary chips and making the computer case into a type of freezer, encasing the chip and keeping the chip very cold. This made the computer run faster, I guess by increasing its conduction, and one result I recall is getting a 600 MHz DEC Alpha chip to run at around 767 MHz? Has anyone bought this kind of computer, or perhaps done some kind of home modification (like all the overclocking)? My second question, what is a good factoring program for Win98 on a PII system that allows you to enter a very large number and attempt to factor it, thereby proving it either composite or prime? Thanks for any help. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: status of exponents
Okay then...like it or not, I took all those exponents that were posted to the list earlier and started them up. I had 3 quad-processor and 1 dual-processor PPro 200 machines not doing anything, so they're now working on those exponents. Aaron -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of Jud McCranie Sent: Friday, June 11, 1999 2:11 PM To: Aaron Blosser Cc: Mersenne@Base. Com Subject: RE: Mersenne: status of exponents 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 check. Anything less than a P=166 is defaulting to double check assignments. If it is taking a year, then it is running on something considerably slower. +--+ | Jud "program first and think later" McCranie | +--+ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Turkey season, already??? (Was: Whither goest thou, Alpha?)
Ernst W. Mayer wrote:
I seem to recall a long-buried thread on this list about how long
various processors take to cook a Turkey
The thread was about a (ahem) modest proposal for updating the standard
unit of GIMPS effort from the current CPU-model-dependent "P90-year" to
a unit that would be independent of CPU models and thus not subject to
obsolescence by advances in chip manufacture. Inspired by the
information-theoretic idea of measuring information in terms of entropy,
whose units are of energy, I propose that we use the energy used to
raise a standard mass (10-kg turkey) to a standard temperature
("done" according to _The Joy of Cooking_) by a GHz-class CPU
adapted for use of its waste radiation in a microwave oven.
...(screams of "Nooo! Not that again!" in the background :)
Of course not. It's much too early for turkey season, silly!
Richard ("Not a turkey either, but I know one when I see one") Woods
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Re: Mersenne: Re: Mersenne Digest V1 #572
My second question, what is a good factoring program for Win98 on a PII system that allows you to enter a very large number and attempt to factor it, thereby proving it either composite or prime? Thanks for any help. As somebody pointed out, the giantint package does exactly that (well, actually, the numbers aren't 100% sure to be prime) for Linux/UNIX. Either find someone who's willing to port it, or get Linux. Microsoft Visual C++ compiles it quite happily under Windoze. Or it is possible to get gcc to work in a "DOS box". Hmmm... I'm currently doing an exponent of 7398xxx on my PII/448 (bus-overclocked), which should be 384K FFT length. My best result is 0.197 secs/iteration (stable, but not across reboots) using mprime 18.1. This means the PII is about as fast as an Alpha (a little slower) on the same clock speeds. Is Alpha over-hyped, is something wrong, or is just George a terriffic x86 assembly coder? I have an Alpha 21164-533. For C code compiled using gcc run under linux, it's _at least_ 4x as fast as a PII-350. Considerably quicker than that, if the code can use 64-bit integers intelligently. George _is_ a teriffic x86 assembly coder. Ernst Mayer's program is written in a high-level language (Fortran-90); if anyone has the time the skill to do an Alpha assembly optimization of Ernst's code which is half as good as George's work on Intel, it would almost certainly run at least twice as fast. The performance on the 21264 is in line with the MIPS Which means Intel is also in line with the MIPS? (I just saw some benchmarks that promised K7 to be 40% faster than PII at FPU, looks like we have good times ahead of us!) Actually the K7 has pinched some ideas (like the 200 MHz 128-bit data bus) developed for the Alpha. I think Ernst was comparing the performance of the Alpha 21264 with the MIPS R12000 CPU running code from the same (Fortran-90) source. (As a side note, an AMD K6/200 instantly began checking out double-checking assignments instead of factoring assignments when I set it to work 24 hours (instead of 8) a day. I consider this a bug, unless somebody has a good reason K6s shouldn't do integer arithmetics instead of FPU work.) No. The effective CPU speed of a K6 at 200 MHz is _100_ MHz, the K6 FPU is less efficient than the Pentium FPU. Divide that figure by 3 if you're running 8 hrs/day and you end up with less than 50 MHz, so you get factoring assignments by default. Tell it you're running 24 hrs/day and you will get double-checking assignments. Well, most certainly 386s or 486s, my PII can run a 3M-exponent in a day or so. (286s can't run Prime95, of course, they would need a special version, and I'm not sure if George is keen on making one.) Waste of time. All the remaining operating 286's in the world put together probably don't amount to more than a dozen or so P90s. That depends on what you mean by `confirmation'. Since I'm totally lost in the number of Mersenne primes being found, I guess M38 is the unconfirmed, million-digit one, and M37 is the previous one. So, I guess what you're looking for, is confirmation that M37 really is the 37th Mersenne prime, not that it is prime. Is it really that important? It is, if you're going to denote them that way. If you're going to give them serial numbers in terms of discovery date rather than in terms of size, we're going to mightily confuse the inhabitants of the planet Zog when they get our list. In any case, the precedent has already been set. We can talk unambiguously about "the 37th Mersenne prime to be discovered" meaning "Clarkson's Number" or 2^3021377-1, but we should not talk about the "37th Mersenne prime" (unqualified) until we have double-checked all the exponents up to 3021377. I personally find it hard to think in terms of a 38th Mersenne prime discovery until it's verified. I know it's most unlikely (to put it mildly) that a "false positive result" would arise by chance, but, as they say, "If it looks like a duck and sounds like a duck, it probably _is_ a duck. But I won't be sure until I see it has webbed feet!" Sorry for being pedantic. Since the code is called (approx.) 500,000 times _per iteration_, and the FPU unit has latency of at least 2-3 cycles per instruction (correct me), I guess decoding stalls is only minor here, even though the function is inlined, so it has to be decoded many times. Latency is the time between the instruction entering the pipeline and the operation being complete. However the throughput is 1 floating- point add or multiply per cycle, so long as the code can keep the pipeline filled. If the processor stalls, the execution units empty and you _do_ lose (at least) the latency period before you start to get results out again. This is why avoiding stalls is important. Regards Brian Beesley Unsubscribe list info --
Re: Mersenne: Re: Optimisation
I believe this is the exact url: http://developer.intel.com/vtune/icl/demo.htm Otto George: If you goto this site there is a code profiler/optimiser available for free download for 14 day evaluation. It is about 40mb. http://developer.intel.com Sorry, I can't remember the exact area or page :-( regards G Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Re: Optimisation
If you goto this site there is a code profiler/optimiser available for free download for 14 day evaluation. It is about 40mb. http://developer.intel.com Sorry, I can't remember the exact area or page :-( try http://developer.intel.com/vtune/analyzer/demo2.htm -jrp Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Re: Mersenne Digest V1 #573
Please - if you can, avoid quoting anything that doesn't directly pertain to what you're responding to. Some people's posts have dozens of lines of unnecessary quoting attached. This is an annoyance to (probably the very few) those who use AOL and are forced to download an attachment when the digest exceeds a certain size. Anyways: 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 We can doublecheck with Prime95 now, that's a new feature. But different programs and systems are always a good idea. I propose (for maybe not the first time) two new systems: A) A doublechecking cleanup team of computers. A team of (say) five PIII-500s, 64MB SRAM and suitable motherboards, with cheap everything else (cases, etc, and probably only one old monitor to share among them all) should be sent to work on the smallest exponents not doublechecked. I know that we don't want to "poach" (good word) anyone's work, but exponents at the VERY bottom of the list really *do* need to be finished. If the "owners" of those exponents are annoyed, we can credit them for the CPU time they've invested, or give them another exponent, etc. But the last dregs need to be taken care of. The team of doublechecking cleanup computers should be pretty small (I picked five) so that we don't poach too many exponents but still get the work done. B) A first-LL-testing cleanup team of computers. This should be even smaller. One or two dedicated PIII-500s (and with the other characteristics I mentioned) should be sent to work on the smallest exponents not singlechecked. Again, we don't want to poach anyone's work, but oftentimes anomalies crop up (a person who's forgotten about GIMPS and hardly ever turns his computer on yet it occasionally reports from time to time, say) and again, we need to finish exponents at the bottom of the list. Of these two (probably not original) proposals, I consider the doublechecking one the most important because the slowest computers are usually there. Of course, these cleanup team(s) should be "offical" and given permission to do this. Ah, if only I could build a team of LASTLYs. (LASTLY: A PII-400 I built for the sole purpose of LL testing). S.T.L. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Poaching (was Mersenne Digest V1 #573)
A) A doublechecking cleanup team of computers. A team of (say) five PIII-500s, 64MB SRAM and suitable motherboards, with cheap everything else (cases, etc, and probably only one old monitor to share among them all) As a computer repairman, of two years, I agree with my father of (5 years computer repair experience, ~20 years electronics experience), and his co-worker (30 years of computer repair experience) that your *never ever* cheap out on power supplies. And crappy cases almost always come with crappy power supplies. This is expecially true for a team like that one that would have to have constant operation. Crappy power supplies can cause flaky performance in innumerable ways relating to CPU and motherboard operation, as well as drive operation. Just in case these things get built, what OS should they have, or does it matter significantly for speed? -Lucas Wiman Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Re: Mersenne Digest V1 #573
I propose (for maybe not the first time) two new systems: A) A double-checking cleanup team of computers. A team of (say) five PIII-500s, 64MB SRAM and suitable motherboards, with cheap everything else (cases, etc, and probably only one old monitor to share among them all) should be sent to work on the smallest exponents not doublechecked. I know that we don't want to "poach" (good word) anyone's work, but exponents at the VERY bottom of the list really *do* need to be finished. If the "owners" of those exponents are annoyed, we can credit them for the CPU time they've invested, or give them another exponent, etc. But the last dregs need to be taken care of. The team of doublechecking cleanup computers should be pretty small (I picked five) so that we don't poach too many exponents but still get the work done. 2 (since madpoo stopped) mersenne participant ( that I know of at the moment) are doing exactly what you are suggesting. Every night one of my computer ask for 7 days of double-checking work. Every morning I redistribute small exponnent to my other computers and release any exponent that are over a certain limit (2,025,000 at the moment). When my computer as not enough work queued I just raise my limit. That way I know that exponent are done in a timely manner and they won't be re-re-assign to someone who is going to "sit on it". of course it's alot of monitoring:) David Campeau P.S: Hope no one (akruppa, madpoo?) got mad because they could never get those realy small exponent :) __ Get Your Private, Free Email at http://www.hotmail.com Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
WHY are these others so concerned about a few exponents not being finished soon? What possible difference does it make to them? It doesn't affect me personally in the slightest, other than wanting to see that line item on the GIMPS home page under "Milestones", that we know M37 is truly M37 and not M38. Part of the reason many of us do this is to see the progress in material ways like that, and I don't want to have to wait until 2003 to see that milestone reached, when it is one computer holding up the chase. That's not the case today (one holdout stopping us) but it won't be too long before it is... Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Poaching (was Mersenne Digest V1 #573)
co-worker (30 years of computer repair experience) that your *never ever* cheap out on power supplies. And crappy cases almost always come with crappy power supplies. This is expecially true for a team like that one that would have to have constant operation. Crappy power supplies can cause flaky performance in innumerable ways relating to CPU and motherboard operation, as well as drive operation. I have to back Lucas up on this one, and can't stress it enough. In one form or another over the past few years I've been involved in mathematical computing 24 hours a day, seven days a week. Apart from one of the first Gateway P-120 motherboards (which apparently had a known tendency to overheat and Gateway were aware of it), an early US Robotics 28.8 modem (which was lousy design) and a modem which was struck by lightning (forgot to unplug the phone cord), the only hardware component to have failed has been power supplies. I'm currently on my fourth power supply in 2 years on my current machine. When the power supply fails, I have been fortunate and not had any permanent damage to other hardware components, mainly because voltage regulators tend to be quite robust components and, even in a failure, don't let much more than 3.3V or 5.0V hit the board. (Though exploding capacitors in the power supply *will* blank the CMOS). However a power supply is notoriously full of very poor, very cheap components. It is the 10c resistor, or 50c smoothing capacitor that fails - not very comforting when you may have thousands of dollars of hardware hanging off it. People who drive sports cars don't use the cheapest gasoline... It seems lately though that component quality is decreasing. AT power supplies seemed pretty indestructable, but ATX power supplies are much weaker. John Pierce is right, a $59 case isn't bad - I could have got the latest power supply without a case for $48. Resist the temptation though to go to a high street store and pick up a cheap power supply for $30... and believe me, a spare power supply you have hanging around, or a reconditioned one is *not* an option. It's not worth spoiling the ship for a ha-penny of tar... if you're building a decent system, don't try to save a few bucks on a power supply. A good brain is useless if the heart stops. I'm reminded of the Russian guy in "Armageddon" - "American components, Russian components... all made in Taiwan!". Chris Nash Lexington KY UNITED STATES === Co-discoverer of probably the 8th and 11th largest known primes. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Inane Stuff (Was: Mersenne: M38, SETI, and other random stuff )
Once again my apologies for lowering the tone, and many thanks for some sensible and thought-provoking responses! Following conservative estimates of cpu power and number of participants doubling every two years, I'd guess that we will have a our first billion digit prime in 2021, when we have 40 million participants and Pentium XV 1000GHz processors. 10^12Hz... wow! Can you imagine the technical innovation needed to get a machine where light only travels 0.3mm in a clock cycle? That's some densely packed, erm, stuff... probably not silicon, the sort of thing we probably can't conceive right now (electron obedience school?), but there's a good 22 years to go yet. Back in 1977, I seem to remember "VLSI" meant a digital watch was $100, now they're free with Happy Meals. As for 40 million participants, maybe they'll be giving away LL engines or Dubner crunchers with Happy Meals by then, maybe every electronic device in my house will be squaring and subtracting 2 in its idle time. I'm not counting on seeing either in my lifetime. Well, I still plan on seeing it in my lifetime. ;-) I'm with Spike on this one. If E.T. does make the call, there are going to be a lot of people dropping EVERYTHING. And even if we don't have "Microsoft SpaceBender V1.1a SR3" (courtesy of Bob Burrowes, thanks Bob) to make interstellar communication a possibility, there'll be a lot of people running for the cryogenic suspension chambers... Meanwhile, the potential M38 gets ever nearer... not long to wait now I shouldn't think. I hope Ernst or whoever is verifying will at least give us a yes or no answer, even if the EFF rules mean that the exponent won't be released to the world until it is in print... Chris Nash Lexington KY UNITED STATES === Co-discoverer of probably the 8th and 11th largest known primes. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
JON STRAYER [EMAIL PROTECTED] 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 sigh So? It's not like we are running out of work. No, nor will we ever, barring an ingenious mathematical proof that either a) There are finitely many Mersenne primes (with upper bound or maximum number of Mersenne primes) or b) All (or all but finitely many with an upper bound or maximum quantity for the sporadics) Mersenne primes follow some pattern. Imagine there turned out to be a link between primes patterns (or Mersenne prime patterns) and the Mandelbreot set? It's not out of the question. That thing has interesting additive combinatorics, also doubling patterns, Fibonacci sequences, and the like hidden in it. Get free e-mail and a permanent address at http://www.netaddress.com/?N=1 Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: CORRECTION about Microsoft software!
URGENT CORRECTION to the preceding Microsoft-related article. "Core breach" wouldn't begin to describe it. It would probably leave one of those subspace rifts that hangs around and swallows hapless ships long after the original disaster becomes last century's news... Get free e-mail and a permanent address at http://www.netaddress.com/?N=1 Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: [Re: Inane Stuff (Was: Mersenne: M38, SETI, and other random stuff )]
Chris Nash [EMAIL PROTECTED] wrote: 10^12Hz... wow! Can you imagine the technical innovation needed to get a machine where light only travels 0.3mm in a clock cycle? That's some densely packed, erm, stuff... probably not silicon, the sort of thing we probably can't conceive right now (electron obedience school?)... The technical term is "superconductor" and I can conceive it quite fine :-) (This will probably provoke more cryonics postings.) Room temp superconductors... or we can pull a star trek and use the warp drive to speed up the speed of light and thus the optical components inside the CPU. (This is how the computers on the NCC-1701-D supposedly work...if you don't believe me, read the technical manual, available at fine bookstores everywhere and on multimedia CD-ROM.) ...maybe every electronic device in my house will be squaring and subtracting 2 in its idle time. I'd rather compute a Mersenne LL test. Failing that, I'd devote the idle cycles to exploring the Mandelbrot set, not some Julia set. And the Julia set in question here is the world's least interesting...just a line segment. Square and add i and you get something a tad more interesting... like from a storm chaser's lucid dreams. I'm with Spike on this one. If E.T. does make the call, there are going to be a lot of people dropping EVERYTHING. And even if we don't have "Microsoft SpaceBender V1.1a SR3"... Now that would give a whole new meaning to "Internet Exploder". Can you spell "core breach"? Please, powers that be. DON'T TRUST *THAT* APP TO MICROSOFT! ANYONE BUT MICROSOFT! Get free e-mail and a permanent address at http://www.netaddress.com/?N=1 Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Connection with Mandelbrot? (was: status of exponents)
Me again, my wife's out of town so I'm surfing the net too much. Apologies if you're sick of me. b) All (or all but finitely many with an upper bound or maximum quantity for the sporadics) Mersenne primes follow some pattern. Imagine there turned out to be a link between primes patterns (or Mersenne prime patterns) and the Mandelbreot set? It's not out of the question. That thing has interesting additive combinatorics, also doubling patterns, Fibonacci sequences, and the like hidden in it. It's absolutely doubtless there is a link with the Mandelbrot set - and hopefully I won't fall in to the usual trap of trendy mumbo-jumbo and black magic that the subject usually yields. It might be doubtful that we could ever *use* this fact, but who knows, stranger things have happened, apparently the pretty colors can be generated by charging a metal plate in the shape of the set itself... As Paul says, the thing is oozing with combinatorics. Each of its components has an associated cycle length, in fact, each component has a root point which, if the iteration is applied n times, the point is mapped back to itself. Components (or "sprouts") are connected at single "attachment points", and the cycle length of a child component is a multiple of its parent. A lot of analysis has been done on the location of these points. But think of it like this. Suppose you wanted to know how many components were of each cycle length n. You'd have to find the root points, ie solve "n'th iterate of x=x", which is an equation of order (you guessed it) 2^(n-1). Factor out the root x=0 (the root of cycle length 1) and the equation has a Mersenne number degree. Of course, some of these roots are also roots for factors of n, but you can enumerate them - you'll also end up running for the Cunningham tables. The strange thing is, since the number of components of given cycle length grows exponentially, there are not enough "attachment points" for them all. Hence the familiar "mini-Mandelbrot" sets have to appear, seemingly in the middle of nowhere (though they are connected via some very convoluted infinite sequences - the set is, I think, proven to be a single connected piece). Hand-waving Prime cycle lengths are interesting, because of the connection points problem. A prime cycle length *should* produce more "island molecules" than a composite would. In theory then we could do a primality test; zoom very closely on a *very* tiny area of the Mandelbrot set (which we could compute by some iterative root-finding procedure) and have a look. If there's an "island molecule" there, N is prime, if not, N is composite. Obviously, mathematical accuracy - and rendering time - is quite an issue if you're staring so closely at the thing, but it's an intriguing thought experiment. Sounds radical? Not at all, we've all seen this process 38 times before... just not in the complex plane: The Mandelbrot set iteration z - z^2+c in C The Lucas test iteration x - x^2-2 in Z(N). It's just too much to be a coincidence. A Lucas test is nothing more than a very thin slice of the Mandelbrot set. Island molecules have a lot in common with Lucas pseudoprimes. /Hand-waving Chris Nash Lexington KY UNITED STATES === Co-discoverer of probably the 8th and 11th largest known primes. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Inane Stuff (Was: Mersenne: M38, SETI,and other random stuff )
I'm on a roll tonight. Here's another one from me. Sorry guys, but this one was just too plain freaky to be a coincidence. The technical term is "superconductor" and I can conceive it quite fine :-) (This will probably provoke more cryonics postings.) I can see it now, George will be asking all you hardware guys how to optimize version 118 for the 65536-bit Intel superconductor architecture. The hardware guys better start working on this stuff, software guys like these sort of gifts :) Room temp superconductors... or we can pull a star trek and use the warp drive to speed up the speed of light and thus the optical components inside the CPU. (This is how the computers on the NCC-1701-D supposedly work...if you don't believe me, read the technical manual, available at fine bookstores everywhere and on multimedia CD-ROM.) And darn fine it is too. And all true ya know. There's only one leap of faith required for it all to be possible (subspace), ok, maybe the transporter is something else, but E=mc^2 makes that already seem like fact. I had to stop myself going into Star Trek mode on my last post. Paul saved me the embarrassment because I would have made a mess of it. ...maybe every electronic device in my house will be squaring and subtracting 2 in its idle time. I'd rather compute a Mersenne LL test. Erm, Paul it *is* an LL test. I forgot the mod N, but there's no charge for that :) cycles to exploring the Mandelbrot set, not some Julia set. And the Julia set in question here is the world's least interesting...just a line segment. ... and it's "*the*" LL test as well. Freaky, eh? But surely not the world's least interesting? Let's go Star Trek with it, this uninteresting, line-segment Julia set is folded in subspace (ok, modulo N space, it's getting late and I really need a trek fix right now) into an LL test. I just posted that... how strange. Great minds think alike, and all that. Square and add i and you get something a tad more interesting... like from a storm chaser's lucid dreams. A very different LL test, but still an LL test. A lucid dream, most definitely, but perhaps a catalog of all the Lucas pseudoprimes discriminant -1 (so of the form 4n+3)? have "Microsoft SpaceBender V1.1a SR3"... Now that would give a whole new meaning to "Internet Exploder". Can you spell "core breach"? "Gimme an M, Gimme an I, Gimme a C.". URGENT CORRECTION to the preceding Microsoft-related article. I love the list server when the "preceding article" arrives afterwards. Some relativistic effect, obviously. "Core breach" wouldn't begin to describe it. It would probably leave one of those subspace rifts that hangs around and swallows hapless ships long after the original disaster becomes last century's news... Or maybe worse. One might board the hapless ship and find Bill Gates rather than Montgomery Scott suspended in the transporter pattern buffer... Enough already, I'm probably already in too many people's killfiles than is healthy. Chris Nash etc etc Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: status of exponents
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? 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. Hey, you coud have the P###-files, but tell me! As long as the people working on the exponent are actualy working of them, I think it is very little nice of you to hijack their exponents without even sending them an email in advance! At least: Stay away from my exponents! If you touch them, I will find you with the completed exponents report, track you down, tell the FBI that they don't have all your computer equipment and that you are searching for primes again, force you to to switch to SETI@home and factor the exponents you've tested to pieces, so that you'll loose credit for all the CPU time! Be afraid. B-) Also, most of my assignments, both double cheking and first time, are running on non-Intel Unix boxes. These are reserved directly form George, not from Primenet, so you won't find them. The Primenet software have flaws which makes it unuseable for other packages than Prime95/mprime. Primenet once hijacked 58 of the double cheking assignments I was working on due to a bug in the Primenet software. Unfortunately the next batch I got mostly contained exponents which wanted 256K FFT size instead of 128K. 256K FFT size means more than tvice the CPU-time, which means to slow to test on an Indy. Those 58 machines are therefore retired from GIMPS. 8-( -- Sturle URL: http://www.stud.ifi.uio.no/~sturles/ Er det m}ndag i dag? ~~ MMF: http://www.alladvantage.com/go.asp?refid=BUP399 - St. URLe Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
