Mersenne Digest Monday, August 2 1999 Volume 01 : Number 608 ---------------------------------------------------------------------- Date: Sat, 31 Jul 1999 14:31:40 -0700 From: Colin Percival <[EMAIL PROTECTED]> Subject: Re: Mersenne: Pepin's Test, etc. At 18:51:38 30/7/99 +0100, Brian J. Beesley wrote: >Given that x^2 mod 2^p-1 can be computed very efficiently using DWT >(getting the remaindering operation for free), it occurs to me that >it ought to be possible to compute x^2 mod 2^p+1 just as efficiently, >using different "magic numbers". In fact, it is possible to compute x^2 mod k*2^n+r efficiently, and I believe that it is possible in general to compute quickly (using the DWT) modulo a+b where gcd(a,b)=1 and the product of unique primes dividing a*b is small. Colin Percival _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 31 Jul 1999 18:07:00 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Mersenne: Re: A possible venue for a GIMPS meeting > "Good" number theory meetings are relatively common, but this > "Millennial Conference" looks like it will be exceptional. The list of > speakers is already very impressive and they will have "broadly accessible > survey lectures" (though that couuld mean many things...) Because of that, > it may be worth folks going to the expense to come. What do you think? > Should we try to organize something? I'm definitely in favor of it! Of course that could be because the U of I is about 45 minutes away from me by car, so I'm going whether or not you all are going. - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 31 Jul 1999 21:05:49 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: STOP BASHING PEOPLE WITH SLOWER MACHINES! > The problem I have with slow computers is that I cannot afford to run > them. A 40MHz 486 uses about 20 Watts, a 400MHz AMDK6 about 40 Watts. > However if you have your own hydroelectric power supply, or if someone > else is paying the electricity bill, the situation is different. If you are running the computers *anyway* then I doubt that Prime95 adds that much to your electric bill. Also, much of the power in computers is consumed in cooling and powering them. By using 1 power supply for multiple computers, you can save a bunch of power. I am working with a friend of mine to do just this. We have 2 HP mainframe PS's (500W), an older mainframe PS (circa 1980) that I got at a yard sale (300W), and several PS's from IBM microchannel servers (~200W each). With a fair amount of work :), we hope to have a number of 486/pentiums in a cabinet with central cooling. These computers will (if we ever get the thing built) be factoring Mersenne numbers in the DecMega range. This will (of course) still draw a massive amount of power, but it has the decided advantage of all the hardware being free! This is still an impractical watt/cycle, but we're doing this for the experience (TM). BTW, does anyone know of a DOS/Linux Mersenne factorer, written in assembler that can find 64 bit factors? (Other than Brian's factor95.c, I want to know what's out there) Thank you, - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 1 Aug 1999 01:42:07 -0400 (EDT) From: "Vincent J. Mooney Jr." <[EMAIL PROTECTED]> Subject: Mersenne: Wow ! Have you seen the Top Producer's List? 10,073 entries. Wow ! _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 1 Aug 1999 00:18:17 -0600 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: massive GIMPS cabinet > Also, much of the power in computers is consumed in cooling and powering > them. By using 1 power supply for multiple computers, you can save a > bunch of power. Power supplies only supply current for what's needed. Although they do indeed generate quite a bit of heat all the time, regardless of load, an overrated supply doesn't use more power than a matched supply would under the same stress. I can take a 500W power supply and it won't consume *much* more than a 180W supply would when hooked to the same motherboard. The 500W supply can power a lot more, but it's not being asked to do so in the above example, so besides a bit more heat on average, having 2 250W supplies or a single 500W supply is not a big difference. > I am working with a friend of mine to do just this. We have 2 HP > mainframe > PS's (500W), an older mainframe PS (circa 1980) that I got at a yard sale > (300W), and several PS's from IBM microchannel servers (~200W each). With > a fair amount of work :), we hope to have a number of 486/pentiums in a > cabinet with central cooling. These computers will (if we ever get the > thing built) be factoring Mersenne numbers in the DecMega range. Having one power supply per computer, besides the convenience of having it self contained, is the fact that the fan in a power supply is used not only to cool the supply itself, but to circulate air throughout the entire case. This is especially true for ATX spec cases and supplies, but is a general rule of thumb for all systems. You mention having central cooling for a cabinet, but I wonder if the added power that a central cooling unit (a 120V cabinet fan?) is offsetting any potential power savings by running less supplies total. Even though most power supplies come in ratings of at least 220W or so, the average motherboard uses only a fraction. More power savings can be had by finding less watt hungry hard drives. Laptop drives are 2.5" and generally consume far less power than your average 3.5" drive. There are adapters aplenty from electronics shops that let you plug your 2.5" drive into a normal IDE cable. CD ROM drives and floppies are big power hogs too, but they're not on all the time anyway, so that's not a problem. I'd just take a wild guess that the average computer (sans monitor) only uses about 100W on average, even with Prime95 running (maximum motherboard power usage: cpu, memory, etc. and hard drive spinning). Average power consumption is just that. But hard drives for instance will use more power when spinning up, so you do need to have a bit more "oomph" in your supply that what the normal running consumption is. For real fun, you can get power consumption figures for everything in a computer...add up the maximum values and tack on another 50% or so for a conservative margin, and that's really all you need. You could always maximize power transfer from the supply by finding a supply that isn't grossly overrated, but modern switching supplies, as I mentioned, don't tend to use much more power than the load is demanding, regardless of overrating. > This will (of course) still draw a massive amount of power, but it has the > decided advantage of all the hardware being free! This is still an > impractical watt/cycle, but we're doing this for the experience (TM). As long as you have fun, why not? :-) Of course, then if you have one supply go out, you lose all your computers. But there's always a tradeoff between cost and reliability. The servers I work with (even the storage units) all have N+1 power supplies...but the cost! Whew! Aaron _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 1 Aug 1999 03:51:51 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: RE: Mersenne: massive GIMPS cabinet > Having one power supply per computer, besides the convenience of having it > self contained, is the fact that the fan in a power supply is used not only > to cool the supply itself, but to circulate air throughout the entire case. > This is especially true for ATX spec cases and supplies, but is a general > rule of thumb for all systems. The main problem with running one supply/system is that I simply don't have that many supplies. These are mostly old ALR computers (486/66's) which I was able to save from the dumpster at the used computer store that I work at. We took the standard AT power supplies out of them, and sold them as used supplies. It certainly would not have been good for my job if I had said "Hey can I have these twenty $10 items, I thought you wouldn't mind." Images of the sarcastic comic book shop owner on the Simpsons "Please take my money *I don't want it*." Motherboard connectors are plentiful as people often bring in bad PS's, and I have been cutting off the connectors as of late. Though of course this involves bulk soldering :(, but that was the "fair amount of work" I mentioned. > You mention having central cooling for a cabinet, but I wonder if the added > power that a central cooling unit (a 120V cabinet fan?) is offsetting any > potential power savings by running less supplies total. Same problem as above, but when you add up the cost (in watts) of 20-30 12V fans, the gains become a bit more apparent (though still possibly not worth it). > Even though most power supplies come in ratings of at least 220W or so, the > average motherboard uses only a fraction. More power savings can be had by > finding less watt hungry hard drives. Laptop drives are 2.5" and generally > consume far less power than your average 3.5" drive. There are adapters > aplenty from electronics shops that let you plug your 2.5" drive into a > normal IDE cable. CD ROM drives and floppies are big power hogs too, but > they're not on all the time anyway, so that's not a problem. They will have only a floppy attached, which will run once (at boot up). > As long as you have fun, why not? :-) Of course, then if you have one > supply go out, you lose all your computers. But there's always a tradeoff > between cost and reliability. The servers I work with (even the storage > units) all have N+1 power supplies...but the cost! Whew! This shouldn't actually be a problem as the computers will only be running factoring assignments, and they should get these only a few at a time. The assignment server will be running on a UPS, and will keep track of which exponents are assigned. - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 1 Aug 1999 09:55:58 -0600 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: massive GIMPS cabinet > Motherboard connectors are plentiful as people often bring in bad PS's, > and I have been cutting off the connectors as of late. Though of course > this involves bulk soldering :(, but that was the "fair amount of work" I > mentioned. Why not just use the "lo-tech" wire nut? :-) > They will have only a floppy attached, which will run once (at boot up). Are these basically just "NC's", with a boot floppy and a network Windows 95 location? I went on vacation and when I got back, Christmas had come early. We got a shipment of 40 PC's in (mostly 166's). We only had to use about 10 of them, so the other 30 I get to setup however I want. My boss told me "Aaron, I want those computers looking for prime numbers", (I kid you not) so now I have to figure out the best way to do it. I can't hook these machines up to our network...they're on a completely different floor of our building with no network drops there. Otherwise, I'd do what I did with about 5 other machines and setup a mini network next to my desk with it's own hub. Not enough IP addresses for them all, so I used a private IP range and used a spare server with 2 NIC's and loaded a NAT program onto it. Beauty. But for these, I have enough hubs (I think) to get them all connected, but to assign work to them, I'm dreading having to check out exponents manually and distribute them manually to 30 machines. Ick. Is that copy of the older Primenet server still available? Could it be used to assign exponents to v18 clients for double checks? If so, that'd be nice. I could lug that machine up to my floor, plug it into the network, let it get exponents and send results every now and then, then lug it back down to the private network. Aaron _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 1 Aug 1999 16:37:43 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: RE: Mersenne: massive GIMPS cabinet >> They will have only a floppy attached, which will run once (at boot up). >Are these basically just "NC's", with a boot floppy and a network Windows 95 >location? You lousy Microsoft freaks! They will be linux boot disks that will run either Mprime v19, or Brian's factor95.c. We haven't decided whether to use Token Ring (has the advantage of being free), or ethernet (has the advantage of good development under Linux). The assignment server will probably be something very simple, maybe just using rlogin and perl. But the thing isn't built yet, so this is just a pipe dream. - -Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 1 Aug 1999 23:51:42 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Average Machines On Thu, Jul 29, 1999 at 02:36:00PM -0400, [EMAIL PROTECTED] wrote: >(more likely because their copy of Duke >Quakem 64 won't run on old computers, hee hee) Side note: When Pentium was new, Quake was coming out. Quake II didn't come out much after Pentium II (am I right here?), and it didn't take many months for Quake III (at least the test; being on vacation, I've got no clue at all if it's out or not...) to come out after the PIII. Does that mean we can predict Quake IV (or IIII, depending on what `system' you use), or even better, Pentium IV? (Yes, there _will_ be native x86 CPUs after Merced too, at least from what I've heard.) >S. "I want 2 million P1 processors!" L. Oh no... /* Steinar */ - -- Homepage: http://members.xoom.com/sneeze/ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 1 Aug 1999 23:57:12 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: STOP BASHING PEOPLE WITH SLOWER MACHINES! On Thu, Jul 29, 1999 at 01:31:13PM -0600, Aaron Blosser wrote: >Egads...I'm not telling *anyone* to NOT use slow computers...I'm >"suggesting" they use < p166 for double-checks or factoring. And do you have a good reason to suggest that? Honestly, what does a few months' (or even years') latency mean? Nothing. I run my P60 happily, and didn't switch to double-checking until recently. The fact that there are PIII-550s out doesn't degrade the performance of my P60, and bigger exponents don't, either. >>They can still outperform a couple of Pentiums. >This is an excellent illustration of my point. What? I don't think so :-) >I'd rather see computing power applied to a project with some thought given >to how that computing power can best be used. A 486, with it's rather >pitiful FP performance, should be given something to do that will stick with >integer ops, just for example. It makes little sense to have a 486 doing LL >testing when it would be flexing it's power best by doing factoring. In that case, every PPro, PII and PIII should be doing factoring only, because they really excel at factoring. (Benchmark for yourself and see.) >I hope I'm being clear that I don't consider slower computers useless >entirely...just useless for doing LL tests in the range of exponents >currently being assigned. Not useless, just slow. I still think it makes perfect sense. /* Steinar */ - -- Homepage: http://members.xoom.com/sneeze/ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 2 Aug 1999 21:06:19 +0100 From: Tony Forbes <[EMAIL PROTECTED]> Subject: Re: Mersenne: STOP BASHING PEOPLE WITH SLOWER MACHINES! "Steinar H. Gunderson" <[EMAIL PROTECTED]> writes >On Thu, Jul 29, 1999 at 01:31:13PM -0600, Aaron Blosser wrote: >>Egads...I'm not telling *anyone* to NOT use slow computers...I'm >>"suggesting" they use < p166 for double-checks or factoring. ... >>I hope I'm being clear that I don't consider slower computers useless >>entirely...just useless for doing LL tests in the range of exponents >>currently being assigned. >Not useless, just slow. I still think it makes perfect sense. I remember discussing a while back the problem of undetected errors. I came to the conclusion that, for example, the probability of getting a 6000000-ish exponent wrong is about 1/20. I assumed that the error rate is proportional to number of cycles in the LL test. Then someone suggested that it is more realistic for the error rate to be proportional to the duration of the run. It could be a serious problem for slow computers that take months and months to do a single LL test. An undetected bit error in the wrong place would invalidate the entire run. On the above assumption the chance of this happening is inversely proportional to the speed of the computer. For slow computers it could therfore be considerably worse than the 1/20 I estimated. On the other hand, factoring is relatively immune because there is not the long-range interdependence that exists with the LL test. Also the job of factoring is to find factors. There are no 'negative' results to collect. It is not a disaster if the occasional factor is missed. However, it was also pointed out that old processors and memory are more reliable. - -- Tony _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 2 Aug 1999 19:00:57 -0500 (CDT) From: Conrad Curry <[EMAIL PROTECTED]> Subject: Mersenne: F24 This is a forwarded message from Dr. Crandall in response to recent messages on the list. - ---------- Forwarded message ---------- Date: Mon, 2 Aug 99 15:57:32 -0700 From: Richard Crandall <[EMAIL PROTECTED]> This message is prompted by various queries Re: the 24th Fermat number. It is time to let the proverbial cat out of the proverbial bag. A group of us are currently resolving the character of F24, via the classical Pepin test, and will finish sometime in the Fall, using two separate float-based tests which will finish late summer, then integer-convolution-based verification into the Fall, these latter, integer tests bringing closure to a proof of whatever character. The group is: Richard Crandall, Ernst Mayer, Jason Papadopoulos, plus gracious volunteers such as Joe Buhler, Conrad Curry, Jason Klivington, Alex Kruppa, who have donated machine time or other support, plus the Number Theory Foundation and Apple Computer who have provided resources. - - R. E. Crandall Director, Center for Advanced Computation, Reed College Portland OR _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ End of Mersenne Digest V1 #608 ******************************
