Mersenne Digest Tuesday, January 11 2000 Volume 01 : Number 678 ---------------------------------------------------------------------- Date: Mon, 10 Jan 2000 12:36:27 +1100 From: Simon Burge <[EMAIL PROTECTED]> Subject: Re: Mersenne: Prime95 makes Java slow? Jud McCranie wrote: > I've got an application that uses Java for its interface. When Prime95 is > running, the Java app is extremely slow at times. When prime95 isn't > running, it always seems to be OK. Could it be that prime95 doesn't > realize that the Java app needs some CPU time? The only thing that comes to mind is the java memory garbage collector runs at idle priority, so it would compete with prime95 for idle CPU. Take this with a grain of salt because I know almost 0 about java, and have never used it :-) Simon. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 09 Jan 2000 20:34:36 -0500 From: George Woltman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: cpu years/day vs GFlops/sec Hi, At 06:50 PM 1/6/00 EST, [EMAIL PROTECTED] wrote: >Spike Jones wrote: > >>Processor gurus, please: using the equivalence that is suggested >>by the primenet status page [86.6 P90 CPU yr/day = 1042 GFlops] >>I calculate that a floating point operation must be about 3 CPU cycles. > >Indeed, I calculate ~0.4 FLOP/cycle, which at first glance seems about a >factor of 2 too slow, even on the humble P90 (which should, assuming no >cache misses, be able to dispatch one FADD per cycle and (I believe - x86 >experts, please correct me if I'm wrong) one FMUL every other cycle, for >a peak throughput of 1.5 FLOP/cycle. The humble P90 can only do one FADD *OR* FMUL per cycle. Thus, maximum throughput is 1.0 FLOP/cycle. Worse yet a floating point load takes one clock and a store takes two clocks. With only 8 registers there are a lot of loads and stores. The PPro, P-II, P-III, and Celeron have a better architecture that allows loads and stores to run in parallel with the FADDs and FMULs. This makes it easier to approach the 1.0 FLOP/cycle theoretical maximum. Regards, George _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 8 Jan 2000 20:05:02 EST From: [EMAIL PROTECTED] Subject: Mersenne: Mlucas on SGI After a several-month hiatus, I again have some decent CPU time on a colleague's pair of SGIs. On a 195MHz R10000 with 4MB L2 cache, Mlucas 2.7z is getting .27 seconds per iteration at FFT length 384K. Compared to George's posted timing of .211 sec on a 400MHz PII, that's a relative performance of 160%, which is the highest I've ever seen - it's even a little better than on an Alpha 21264 with same-size L2 cache, although the latter runs at a much higher clock rate. (On a 250MHz R10000 with a smaller 1MB L2 cache, Mlucas needs .29 sec, for an RPI of 116%.) I think SGI's problem is that although the R10K and R12K can do about the same amount of work per cycle as the Alpha 21264, SGI can't seem to jack up the MHz anywhere near the 21264, nor can they sell them as cheaply (one can get a 500MHz PC-style 21264 for around $3000 nowadays.) But for those of you who have access to them, the SGIs are nice Mersenne engines. - -Ernst _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 09 Jan 2000 17:52:59 -0800 From: Colin Percival <[EMAIL PROTECTED]> Subject: Mersenne: Re: cpu years/day vs GFlops/sec On Thu, 6 Jan 2000 18:50:41 EST, [EMAIL PROTECTED] wrote: >Indeed, I calculate ~0.4 FLOP/cycle, which at first glance seems about a >factor of 2 too slow, even on the humble P90 (which should, assuming no >cache misses, be able to dispatch one FADD per cycle and (I believe - x86 >experts, please correct me if I'm wrong) one FMUL every other cycle, for >a peak throughput of 1.5 FLOP/cycle. Almost. Although the FADD unit can start an instruction every cycle and the FMUL unit every second cycle, they share some overhead (eg, decode and control logic), such that only one of the two can be started in any given cycle. This is true of both P5 and P6 architectures. Colin Percival _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 10 Jan 2000 03:13:41 EST From: [EMAIL PROTECTED] Subject: Mersenne: Re: Mersenne Digest V1 #677 In a message dated 10/01/00 01:24:32 GMT Standard Time, [EMAIL PROTECTED] writes: << ------------------------------ Date: Thu, 06 Jan 2000 18:34:09 -0800 From: Stefan Struiker <[EMAIL PROTECTED]> Subject: Mersenne: The Second Mersennium Behind Us, How Now For Myriad The Third? Quiet Flows The List, so here is a Y10K query: Does the "official" Y2K retrofit cover rollover from 9999 to 10000? Tick, tick, Stefan S. >> The CMOS RAM has a century byte which should now be storing 20. Assuming that it can go up to 255, current systems should be capable of storing dates up to 25599 before there is a problem. George S. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 10 Jan 2000 16:27:19 -0000 From: "McMac" <[EMAIL PROTECTED]> Subject: Mersenne: The Second Mersennium Behind Us, How Now For Myriad The Third? > Date: Thu, 06 Jan 2000 18:34:09 -0800 > From: Stefan Struiker <[EMAIL PROTECTED]> > Subject: Mersenne: The Second Mersennium Behind Us, How Now For Myriad The Third? > > Quiet Flows The List, so here is a Y10K query: > > Does the "official" Y2K retrofit cover rollover from 9999 to 10000? There is no "official" retrofit as such - but I would guess that it's a mix of yes and no - Anything just converting a number to a string will get the right date (the problem with Y2K being that 19 was presumed as a prefix, and this should no longer be the case). Anything with a 4 byte string will fall over at this stage and stick us back at the year 0. (Technically, the year "0000"). Hopefully, by then, we really *won't* be using software written in this day and age. Chances are we won't be using AD anymore, either. The next date-related problem, IIRC, is in 2034 - something to do with C/C++'s common date function overflowing. And following that, maybe some software peeps will make the same mistake of presuming "20", and 2100 will be a problem. McMac I used up all my sick days, so I'm calling in dead. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 10 Jan 2000 19:01:14 +0000 From: Tom Goulet <[EMAIL PROTECTED]> Subject: Re: Mersenne: The Second Mersennium Behind Us, How Now For Myriad The Third? - --3MwIy2ne0vdjdPXF Content-Type: text/plain; charset=us-ascii 2038, and it's more a Unix problem than a C problem. Unix states the date as the number of seconds since the beginning of 1970. Simply, after some time in 2038, a 32 bit variable can not hold that many seconds. 64 bit machines will have the year 20 quadrillion problem or something. :-) TomG >The next date-related problem, IIRC, is in 2034 - something to do with >C/C++'s common date function overflowing. And following that, maybe some >software peeps will make the same mistake of presuming "20", and 2100 >will be a problem. > >McMac >I used up all my sick days, so I'm calling in dead. > >_________________________________________________________________ >Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm >Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers - --3MwIy2ne0vdjdPXF Content-Type: application/pgp-signature - -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.0.1 (GNU/Linux) Comment: For info see http://www.gnupg.org iD8DBQE4eix6eft5KNi607wRAvmmAKDAUnbnjpHRfiSIbfsTPiszv31EfwCfRlJB W6Ubb3FpxgVDWOoGEAtacjE= =C7l7 - -----END PGP SIGNATURE----- - --3MwIy2ne0vdjdPXF-- _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 12:09:37 +0100 (CET) From: Henrik Olsen <[EMAIL PROTECTED]> Subject: Re: Mersenne: The Second Mersennium Behind Us, How Now For Myriad The Third? On Mon, 10 Jan 2000, Tom Goulet wrote: > 2038, and it's more a Unix problem than a C problem. > Unix states the date as the number of seconds since the beginning of 1970. > Simply, after some time in 2038, a 32 bit variable can not hold that > many seconds. 64 bit machines will have the year 20 quadrillion problem > or something. :-) Actually, in '38 the problem is that if the 32 bit integer is signed, it becomes negative, it's good for another 68 years if it's used unsigned. > > TomG > > >The next date-related problem, IIRC, is in 2034 - something to do with > >C/C++'s common date function overflowing. And following that, maybe some > >software peeps will make the same mistake of presuming "20", and 2100 > >will be a problem. > > > >McMac > >I used up all my sick days, so I'm calling in dead. > > > >_________________________________________________________________ > >Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > >Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers > - -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ Leonardo DiCaprio: Your social class is stuffy. Let's dance with the ship's rats and have fun. Kate Winslet: You have captured my heart. Let's run around the ship and giggle. (The ship SINKS.) Leonardo DiCaprio: Never let go. Kate Winslet: I promise. (lets go) Titanic, the Movie-A-Minute version _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 13:16:40 +0100 From: "Grieken, Paul van" <[EMAIL PROTECTED]> Subject: Mersenne: Status last discoverd prime Dear members, Last year there was a email about the new found prime. I could read there was a second check to see if it was really a prime. After that I did not see any result. Can someone tell me what the status is of the last found mersenne prime. just because I am curious about it. best prime hunting, Paul van Grieken Alcatel telecom Nederland Afd: TTAC Netwerk Elementen Tel: 070-3079353 email: [EMAIL PROTECTED] marklin collector _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 13:39:10 +0100 From: "Grieken, Paul van" <[EMAIL PROTECTED]> Subject: Mersenne: V18.1.1 to V19.1 of prime Dear members, Currently I am running with Prime V18.1.1 Can someone tell me what the advantage is to go to V19.1 Is it faster or what. I use a Pentium III with 450MHz. Can I just download and install the V19.1 Do I have to reinatall the automatic internet situation to get and upload information to the internet prime server. Please inform. Best wishes, Paul van Grieken Alcatel telecom Nederland Afd: TTAC Netwerk Elementen Tel: 070-3079353 email: [EMAIL PROTECTED] marklin collector _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 13:39:10 +0100 From: "Grieken, Paul van" <[EMAIL PROTECTED]> Subject: Mersenne: V18.1.1 to V19.1 of prime Dear members, Currently I am running with Prime V18.1.1 Can someone tell me what the advantage is to go to V19.1 Is it faster or what. I use a Pentium III with 450MHz. Can I just download and install the V19.1 Do I have to reinatall the automatic internet situation to get and upload information to the internet prime server. Please inform. Best wishes, Paul van Grieken Alcatel telecom Nederland Afd: TTAC Netwerk Elementen Tel: 070-3079353 email: [EMAIL PROTECTED] marklin collector _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 14:50:52 +0000 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: V18.1.1 to V19.1 of prime On Tue, Jan 11, 2000 at 01:39:10PM +0100, Grieken, Paul van wrote: >Currently I am running with Prime V18.1.1 >Can someone tell me what the advantage is to go to V19.1 >Is it faster or what. It is faster, and has some new functions (like P-1 factoring). Also, it can test large numbers -- larger than v18 can. See the WHATSNEW.TXT file included for more information. >Can I just download and install the V19.1 >Do I have to reinatall the automatic internet situation to get and upload >information to the internet prime server. Prime95 v19 can be installed over Prime95 v18 without problems. Just quit v18, install, and restart prime95.exe. /* Steinar */ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 14:53:12 +0000 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Mersenne: Duplicated mail -- please ignore All, I hit a wrong key, and sent another copy of Paul van Griekens help mail. It is my fault, not his -- please just ignore the duplicate. /* Steinar */ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 09:46:09 -0700 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: The Second Mersennium Behind Us, How Now For MyriadThe Third? > On Mon, 10 Jan 2000, Tom Goulet wrote: > > 2038, and it's more a Unix problem than a C problem. > > Unix states the date as the number of seconds since the > beginning of 1970. > > Simply, after some time in 2038, a 32 bit variable can not hold that > > many seconds. 64 bit machines will have the year 20 quadrillion problem > > or something. :-) > Actually, in '38 the problem is that if the 32 bit integer is signed, it > becomes negative, it's good for another 68 years if it's used unsigned. Dunno 'bout all that, but another problem was that in order to do a "quick and dirty" fix of the Y2K problem, a good number of people implemented windowing. Some used a window of 1930-2029 (which most Microsoft software uses to interpret 2 digit years), some used 1940-2039, etc. That gives those idiots another 29 years to fix the software the right way. I'd say "Oh, we won't still be using the same programs 29 years from now", but I'm sure that's what all those programmers said back in 1971 when they were writing their software with 2 digit years. Actually, MS software allows you to modify the window, so you could slide it to a different date. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 21:54:49 +0000 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Mersenne: Re: The Second Mersennium Behind Us, How Now For MyriadThe Third? On Tue, Jan 11, 2000 at 09:46:09AM -0700, Aaron Blosser wrote: >Dunno 'bout all that, but another problem was that in order to do a "quick >and dirty" fix of the Y2K problem, a good number of people implemented >windowing. The funny thing is, somebody has actually been granted a patent on this. Now. I saw that in DataEase, running on MS-DOS 3.21. Something like 10 years ago. I've heard some rumours that they're reconsidering that patent, though... /* 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: Tue, 11 Jan 2000 23:02:32 +0000 From: Tony Forbes <[EMAIL PROTECTED]> Subject: Re: Mersenne: The Second Mersennium Behind Us, How Now For MyriadThe Third? Aaron Blosser <[EMAIL PROTECTED]> writes >Dunno 'bout all that, but another problem was that in order to do a "quick >and dirty" fix of the Y2K problem, a good number of people implemented >windowing. Some used a window of 1930-2029 (which most Microsoft software >uses to interpret 2 digit years), some used 1940-2039, etc. > >That gives those idiots another 29 years to fix the software the right way. One software company I know of is using a window of 1948-2047. So they could have a date problem in 2048. Surely this is the real 'Y2K bug'. - -- Tony _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 12 Jan 2000 02:31:00 +0300 (MSK) From: "Andrew L. Neporada" <[EMAIL PROTECTED]> Subject: Re: Mersenne: mprime andr STOP signal On Tue, 11 Jan 2000, Brian J. Beesley wrote: > On 6 Jan 00, at 21:08, Andrew L. Neporada wrote: > > > I am running mprime v 19.1 for FreeBSD, and sometimes I stop it using STOP > > signal ( especially when I want to see some films or so -- my computer is > > not fast enough ). Could this practice cause errors in LL test? I > > understand, that I maybe should just interrupt mprime and then launch it > > again, but I don't like this solution. > > Should be totally safe. > > Why not use "nice" to run mprime at a lower priority, in which case > you should be able to leave it running in the background without > making foreground applications run slowly? mprime will still get all > the free CPU cycles available, so it won't slow down except when you > give the system something "more important" to do. > > Regards > Brian Beesley > Yes, I'am using "nice" at maximum level (20 for FreeBSD), but I think this is not enough, especially when I run programs that eat a lot of CPU and memory (for example X,netscape, and compiling something big at the same time). Another example: there is a significant amount of UNIX (FreeBSD) boxes in our institute. This boxes are used mainly as workstations, but sometimes people run some CPU intensive calculations (C or Mathematica) that takes hours of CPU time. When mprime runs at nice=20 and another CPU intensive program runs at nice=0, mprime eats about 30% of CPU. This is not acceptable, I suppose. So, I write a small daemon that monitors system load and stops mprime when average (average period 5 min) system load become more then 1.8 and run it again when this value become less than 0.4. It's a very simple program. Maybe this feature should present at mprime? What is your opinion? P.S. Sorry for my English. Andrew. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 16:47:52 -0700 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Re: The Second Mersennium Behind Us, How Now For MyriadThe Third? > On Tue, Jan 11, 2000 at 09:46:09AM -0700, Aaron Blosser wrote: > >Dunno 'bout all that, but another problem was that in order to > do a "quick > >and dirty" fix of the Y2K problem, a good number of people implemented > >windowing. > > The funny thing is, somebody has actually been granted a patent > on this. Now. > I saw that in DataEase, running on MS-DOS 3.21. Something like 10 > years ago. > I've heard some rumours that they're reconsidering that patent, though... 'Tis true. It doesn't surprise me that many companies are teaming up to fight the patent. Windowing was *the* best way to quickly fix all that software, and a good number of software vendors used it. If I recall right, the guy who owns the patent wasn't asking for much in the way of royalties from each company (but amounts to a lot when totalled), but I think the fight revolves around whether this guy really invented the idea, or whether it's just one of those common sense things that can't be patented, or something like that. MSNBC online probably has a story on it in their tech section. Ah...sure enough: http://www.msnbc.com/news/333372.asp _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 19:03:58 -0500 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: The Second Mersennium Behind Us, How Now For MyriadThe Third? At 09:54 PM 1/11/00 +0000, Steinar H. Gunderson wrote: >Dunno 'bout all that, but another problem was that in order to do a "quick > >and dirty" fix of the Y2K problem, a good number of people implemented > >windowing. > >The funny thing is, somebody has actually been granted a patent on this. Whoops! I'm violating someone's patent! (Don't tell anyone.) +--------------------------------------------------------+ | Jud McCranie | | | | 137*2^197783+1 is prime! (59,541 digits, 11/11/99) | +--------------------------------------------------------+ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 19:22:02 -0500 From: Jud McCranie <[EMAIL PROTECTED]> Subject: RE: Mersenne: Re: The Second Mersennium Behind Us, How Now For MyriadThe Third? At 04:47 PM 1/11/00 -0700, Aaron Blosser wrote: 'Tis true. It doesn't surprise me that many companies are teaming up to >fight the patent. Windowing was *the* best way to quickly fix all that >software, and a good number of software vendors used it. >If I recall right, the guy who owns the patent wasn't asking for much in the >way of royalties from each company (but amounts to a lot when totalled), but >I think the fight revolves around whether this guy really invented the idea, >or whether it's just one of those common sense things that can't be >patented, or something like that. This is getting off topic, but: The criteria for something to be patentable is that the average practitioner in the field wouldn't think of it. So it boils down to whether the average programmer would think of windowing, given the problem. +--------------------------------------------------------+ | Jud McCranie | | | | 137*2^197783+1 is prime! (59,541 digits, 11/11/99) | +--------------------------------------------------------+ _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 11 Jan 2000 21:33:05 -0500 From: Jud McCranie <[EMAIL PROTECTED]> Subject: RE: Mersenne: Re: The Second Mersennium Behind Us, How Now For MyriadThe Third? At 04:47 PM 1/11/00 -0700, Aaron Blosser wrote: Off topic, but: > If I recall right, the guy who owns the patent wasn't asking for much in the >way of royalties from each company (but amounts to a lot when totalled), but >I think the fight revolves around whether this guy really invented the idea, >or whether it's just one of those common sense things that can't be >patented, or something like that. MSNBC online probably has a story on it >in their tech section. Ah...sure enough: >http://www.msnbc.com/news/333372.asp . " Dickens applied for the patent in October 1996 " I was using windowing in 1987, so his patent is invalid (prior invention). +--------------------------------------------------------+ | Jud McCranie | | | | 137*2^197783+1 is prime! (59,541 digits, 11/11/99) | +--------------------------------------------------------+ _________________________________________________________________ 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 #678 ******************************
