Mersenne Digest Thursday, 4 March 1999 Volume 01 : Number 520 ---------------------------------------------------------------------- From: Jason Stratos Papadopoulos <[EMAIL PROTECTED]> Date: Wed, 3 Mar 1999 08:25:59 -0500 (EST) Subject: RE: Mersenne: Re: Mersennes for Martians On Wed, 3 Mar 1999, Brian J Beesley wrote: > > That is a remarkably bold claim. It's akin to saying that the only way of > > finding primes is by brute force testing of all candidates. > > How about a clever method of computing just the last few bits of > the residual - if we could work mod 2^64 instead of mod 2^p-1 then > that would give essentially a *huge* speed increase, even if the > algorithm was a great deal more complex. > Another thing that would work nicely (and not just for LL tests) would be if someone figured out a way to release the carries from a large multiplication while still in Fourier space. The you just perform an NTT, do a modular exponentiation for each digit of the transformed array, do whetever processing is needed to magically release the carries, and then do an inverse NTT to get the final answer. I've thought about something like this for a long time, but have no idea if it's even possible. jasonp ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Ryan McGarry <[EMAIL PROTECTED]> Date: Wed, 03 Mar 1999 08:55:33 -0600 Subject: Mersenne: Re: Mersenne Digest V1 #519 Actually, the 8088 ran at slightly over 8 MHz. The 8086, an earlier version, ran at 4.77. An 8088 was my first computer... Ah. Memories. Ryan McGarry 1977: 1Mhz 6502 or 4Mhz Z80 (also the Vax 11/780; Mhz?) 1981: 4.77Mhz 8088 in the IBM PC 1984: 6Mhz 80286 in the IBM AT 1986: 16Mhz 80386 in a Compaq 1990: 33Mhz 80386 (mine just turned 9 & still runs, with its third hard drive; the first drive cost about $10/MB) Mhz alone is not a direct measure of performance, even with equal word size. In 1983 I programmed a single-board PDP-11 clocked around 21Mhz in assembler, and since it had no multiply or divide instruction, it took about 480 microseconds to do a 16x16 unsigned integer multiply, which is far longer than the 30 microseconds or so that a 4.77Mhz 8088 would take. Ken ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: George Woltman <[EMAIL PROTECTED]> Date: Wed, 03 Mar 1999 09:48:14 -0500 Subject: Re: Mersenne: CAMP Hi, At 12:33 AM 3/3/99 -0500, Vincent J. Mooney Jr. wrote: >http://project.vobis.de/cgi-bin/mersenne.cgi >does not seem to work. What's up? It hasn't been operational for a few months. I'll delete the link soon. >Is there a substitute (I am not on primenet). Visit http://www.mersenne.org/top.htm and http://www.mersenne.org/top2.htm Best regards, George ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: George Woltman <[EMAIL PROTECTED]> Date: Wed, 03 Mar 1999 09:36:39 -0500 Subject: Mersenne: Printing M#37 (was ...Mathematica) Hi, At 11:46 AM 3/2/99 -0500, George Strohschein wrote: >I tried to get Mathematica 3.0 to calculate that 37th prime, but gave up on >my old 60 MHz P5 (Gateway) after about half a day. I then tried it on a 200 >Mhz CPU, but gave up again after about 6 hours. Can someone send me the >number so I can also print it out in 2 point font and see how big it really >is? Get Mikko Tommila's program from http://www.hut.fi/~mtommila/apfloat/ I'll bet your old P-60 can compute M#37 in less than a minute. Mikko proves once again the importance of using a good algorithm. Hope that helps, George ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: "John R Pierce" <[EMAIL PROTECTED]> Date: Wed, 3 Mar 1999 08:44:49 -0800 Subject: Re: MHZ (was re Mersenne: Fabs.) > 1977: 1Mhz 6502 or 4Mhz Z80 (also the Vax 11/780; Mhz?) Vax 11/780 ran on a 10MHz clock, but took 1uS to execute a 32 bit instruction, so lets call it 4MByte/sec. > 1981: 4.77Mhz 8088 in the IBM PC > 1984: 6Mhz 80286 in the IBM AT > 1986: 16Mhz 80386 in a Compaq > 1990: 33Mhz 80386 (mine just turned 9 & still runs, with its third hard drive; > the first drive cost about $10/MB) > > Mhz alone is not a direct measure of performance, even with equal word size. > In 1983 I programmed a single-board PDP-11 clocked around 21Mhz in assembler, > and since it had no multiply or divide instruction, it took > about 480 microseconds to do a 16x16 unsigned integer multiply, which is > far longer than the 30 microseconds or so that a 4.77Mhz 8088 would take. Indeed. Some examples I've worked with... IBM 1130 (designed in the 60s, I dealt with these in the early 70s), had a 2.2MHz clock but in fact took a minimum of 8 clock cycles to perform one 16 bit memory cycle, so was about 270kHz (3.6uS core cycle time), or 540kbyte/sec. intel 8080 (circa 1975). 2 MHz clock, minimum 4 clocks per 8 bit memory cycle, so 500kbyte/sec. Zilog Z80 (circa 1977). 4Mhz clock, 4 clocks/8bits, 1Mbyte/sec Intel 8088 in IBM PC: 5MHz clock, 5 clocks/8bits, 1Mbyte/sec Intel 286 in IBM PC/AX: 8MHz clock, 3 clocks/16 bits, 5.3Mbyte/sec Intel 386 in typical clone: 33MHz clock, 2 clocks/32 bits, 66Mbyte/sec burst, but far less than this sustainable. Intel 486DX2: 66Mhz clock, 2 clocks/32 bits, 132byte/sec internal, but 33Mhz bus clock gave 66MByte/sec peak burst Intel Pentium 90MHz, 90MHz core clock but 60MHz bus clock. life gets complex. CPU could execute 32 bits in 1 core clock, but memory bus typically had minimum of 3 clocks/64bit cycle for 160Mbyte/sec peak burst. Pentium-II 400MHz. memory bus is 1 clock burst at 100MHz/64 bits or 800Mbyte/sec peak. Core caches have multiple ports and dual execution units, way hard to peg a number on. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: [EMAIL PROTECTED] Date: Tue, 2 Mar 1999 21:13:46 +0100 Subject: Mersenne: if a discovery? This question goes out to those of you who have written your names in the pages mathematical history as explorers of new primes. What did your computers say or do when you discovered that new big prime number? Ring a bell? Play "God save the Queen"? Draw a picture of Mersenne with his hand out-streatched to shake your hand? or did it just show you a picture of the gimp himself (in full 'uniform') with something out-stretched for you to shake?? :) ___________________________________________________________________ You don't need to buy Internet access to use free Internet e-mail. Get completely free e-mail from Juno at http://www.juno.com/getjuno.html or call Juno at (800) 654-JUNO [654-5866] ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Jud McCranie <[EMAIL PROTECTED]> Date: Wed, 03 Mar 1999 14:05:29 -0500 Subject: Mersenne: [ Mersenne] Re: Mersennes for Martians At 09:20 AM 3/3/99 +0000, Brian J Beesley wrote: >How about a clever method of computing just the last few bits of >the residual - if we could work mod 2^64 instead of mod 2^p-1 then >that would give essentially a *huge* speed increase, even if the >algorithm was a great deal more complex. It is conceivable, but I doubt such a thing is possible. It could be though. >Also, if you can find quicker arithmetic algorithms, then *please* >get in touch with Donald Knuth! There may be some (fairly small) >scope for improvement in the implementation - You've heard 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 McCranie [EMAIL PROTECTED] | | | | ... algorithms are concepts that have existence apart | | from any programming language. The word "algorithm" | | denotes an abstract method of computing some output | | from some input ... -- Donald Knuth, CACM, 1966 | +--------------------------------------------------------+ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: "brian j. peterson" <[EMAIL PROTECTED]> Date: Wed, 3 Mar 1999 15:16:04 -0700 (MST) Subject: Re: Mersenne: RE: Mersenne Digest V1 #517, Mathematica On Tue, 2 Mar 1999, George Strohschein wrote: # Hi, # I tried to get Mathematica 3.0 to calculate that 37th prime, but gave up on # my old 60 MHz P5 (Gateway) after about half a day. I then tried it on a 200 # Mhz CPU, but gave up again after about 6 hours. Can someone send me the # number so I can also print it out in 2 point font and see how big it really # is? # # thanks, # George the number is at http://www.mersenne.org/files/prime3.txt, but has line breaks. if you want to, you can run this command to get rid of the line breaks: perl -e "while (<>) { chop; print; }" < input_file_here > output_file_here i'd send you my copy, but 909526 bytes is a lot over a modem. - -bjp ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: [EMAIL PROTECTED] Date: Wed, 3 Mar 1999 19:09:41 EST Subject: Re: Mersenne: Re: Mersennes for Martians In a message dated 2/27/99 12:54:05 AM Eastern Standard Time, [EMAIL PROTECTED] writes: > Earlier I posted the notion that Mersenne primes might be used to > impress extraterrestrial civilizations. After thinking it thru, I think we > can make a stronger arguement than that: Mersenne primes might > be the *best* yardstick to *prove* a certain level of technological > achievement, perhaps the most logical yardstick. > > Consider: Interstellar messages may be in the form of binary messages > where the number of bits is the product of two large primes (call them > M and N). Any mathematically oriented receiver would place the bits > into an MxN array and color in the 0s (or 1s) and get a black and white > picture. These pictures cannot be used to *prove* ones level of technology > level for they could easily be faked. We could create a picture of a > more advanced city that we currently have, for instance, from a model. > > But, the primes *cannot* be faked. You either have the computational > ability to find them or not. We could send out a list of all known > primes as a proof of computational prowess, but I would suggest > sending only the Mersennes would prove our technology to any possible > exocivilizations with far less power wasted sending all known primes. > > Can anyone think of any way to *prove* the level of sophistication > of our current society, better than a list of Mersenne primes? spike > Anyone out there who has the radio to receive our message is smart enough to talk to -- why rule them out if they're a bit mathematically behind? If you just want to tag your message in an obvious way that says "NOT A NATURAL PHENOMENON, A REAL MESSAGE" you don't have to send anything LIKE all primes, just a few dozen will be plenty. A picture formed by a MxN matrix of dots, where M and N are Mersenne primes, is gonna be REALLY REALLY big...... ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: [EMAIL PROTECTED] Date: Wed, 3 Mar 1999 17:28:21 -0800 (PST) Subject: Re: Mersenne: if a discovery? MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. MY GOD, IT'S FULL OF STARS. On Tue, 2 Mar 1999 [EMAIL PROTECTED] wrote: > This question goes out to those of you who have written your names in the > pages mathematical history as explorers of new primes. What did your > computers say or do when you discovered that new big prime number? Ring a > bell? Play "God save the Queen"? Draw a picture of Mersenne with his hand > out-streatched to shake your hand? or did it just show you a picture of > the gimp himself (in full 'uniform') with something out-stretched for you > to shake?? :) > > ___________________________________________________________________ > You don't need to buy Internet access to use free Internet e-mail. > Get completely free e-mail from Juno at http://www.juno.com/getjuno.html > or call Juno at (800) 654-JUNO [654-5866] > ________________________________________________________________ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : WWW: http://www.silverlink.net/poke : Boycott Microsot : : E-Mail: [EMAIL PROTECTED] : http://www.vcnet.com/bms : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Gary Untermeyer <[EMAIL PROTECTED]> Date: Wed, 03 Mar 1999 20:38:28 -0700 Subject: Re: Mersenne: if a discovery? Greetings everyone, [EMAIL PROTECTED] wrote: > MY GOD, IT'S FULL OF STARS. Best laugh I've had on this list in a long time! :-) Thanx, poke Gary Untermeyer ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Spike Jones <[EMAIL PROTECTED]> Date: Wed, 03 Mar 1999 20:05:40 -0800 Subject: Re: Mersenne: Category 1,2 or 3 ? Gordon Spence wrote: > Nowadays I still have the trusty P100 that found the prime... Gordon, that machine will make a great museum piece some day. Is it for sale? I suspect such a thing would be quite valuable. spike ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ From: Spike Jones <[EMAIL PROTECTED]> Date: Wed, 03 Mar 1999 20:50:02 -0800 Subject: Re: Mersenne: RE: Mersenne Digest V1 #517, Mathematica brian j. peterson wrote: > On Tue, 2 Mar 1999, George Strohschein wrote: ...Can someone send me the > number so I can also print it out in 2 point font and see how big it really is? > > the number is at http://www.mersenne.org/files/prime3.txt, but has line > breaks. if you want to, you can run this command to get rid of the line > breaks: > perl -e "while (<>) { chop; print; }" < input_file_here > output_file_here Or, you can paste it into Microsloth Word and use your find/replace feature. Find [paragraph mark] replace with []. Then you can set font to Geneva 2 point and it should all fit on 6 pages. spike ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ End of Mersenne Digest V1 #520 ******************************
