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Old 2008-10-10, 22:02   #1
philmoore
 
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Default The probable primes

All primes up to 216389+67607 have been certified as definitely prime, either with Dario Alpern's Java applet or with Marcel Martin's Primo. The larger ones are only known to be probable primes. They were discovered in an effort to which David Broadhurst, Lars Dausch, Jim Fougeron, Richard Heylen, Sander Hoogendoorn, Marcin Lipinski, Phil Moore, Michael Porter, Mark Rodenkirch, Payam Samidoost, and Martin Schroeder all contributed. (My apologies if I have left anyone out.) The five largest were discovered by our project.

The probable primes, in order of size, are:

221954+77899 now proven prime by engracio
222464+63691 now proven prime by engracio
224910+62029 now proven prime by gd barnes
225563+22193 now proven prime by engracio
226795+57083 now proven prime by ET
226827+77783 now proven prime by engracio
228978+34429 now proven prime by Cybertronic
229727+20273 now proven prime by Cybertronic
231544+19081 now proven prime by engracio
233548+ 4471 now proven prime by Cybertronic
238090+47269 now proven prime by Cybertronic
256366+39079 now proven prime by Puzzle-Peter
261792+21661 now proven prime by Puzzle-Peter
273360+10711 now proven prime by Puzzle-Peter
273845+14717 now proven prime by Puzzle-Peter
2103766+17659
2104095+7013
2105789+48527
2139964+35461
2148227+60443
2176177+60947
2304015+64133
2308809+37967
2551542+19249
2983620+60451
21191375+8543
21518191+75353
22249255+28433
24583176+2131
25146295+41693
29092392+40291

(The following was in the original version of this posting, October 2008.)
The first nine numbers on this list have between 6600 and 9500 digits, and could probably be proven prime using either Primo or a distributed version of ECPP. Although it is not one of the main purposes of this project, any such proof does put us a tiny step closer toward proving the dual Sierpinski conjecture. (Of course, we have no idea how to prove any of the largest numbers prime given current theory and technology.) I estimate that it would take a single processor on my 3000 MHz Pentium D system about 2 months to generate a primality certificate for either of the two smallest numbers using Primo version 2.3.2. If anyone would like to try one of these, post a reservation for a particular number below. Note that version 3.0.7 of Primo is now the preferred version, and is considerably faster than version 2.3. (It also does not need the override of the 10000 bit limit of version 3.0.6)

Last fiddled with by philmoore on 2014-09-29 at 18:03 Reason: Added the most recent proven prime!
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Old 2008-10-21, 20:45   #2
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You might want to include a link to the older version of Primo. All I could come up with through google was a link to the Primo homepage, and they only have version 3.0.6 available for download.
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Old 2008-10-21, 20:48   #3
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Quote:
Originally Posted by Kevin View Post
You might want to include a link to the older version of Primo. All I could come up with through google was a link to the Primo homepage, and they only have version 3.0.6 available for download.
Yes, I second this--my friend Gary also tried to find an older version of Primo through Google and instead got a nasty virus. We definitely don't want other users picking up similar infections unnecessarily.

Last fiddled with by mdettweiler on 2008-10-21 at 20:49
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Old 2008-10-21, 21:03   #4
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Quote:
Originally Posted by Kevin View Post
You might want to include a link to the older version of Primo. All I could come up with through google was a link to the Primo homepage, and they only have version 3.0.6 available for download.
Is there something wrong with the current version of Primo? I've got version 2.3.2. It is ~4MB zip. Not sure if this forum allows files that large, but I will try to post it here if you need it.
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Old 2008-10-21, 21:10   #5
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Quote:
Originally Posted by retina View Post
Is there something wrong with the current version of Primo? I've got version 2.3.2. It is ~4MB zip. Not sure if this forum allows files that large, but I will try to post it here if you need it.
First of all, the current version has a limit of (I think) 10,000 digits--from what I hear (never actually used it myself), it will simply refuse to prove anything bigger than that. The earlier versions (including 2.3.2) don't have that limitation.

Yes, if you could please post the file, that would be great--though, unfortunately the limit for forum attachments is way less than 4MB. If you'd like, I'd be glad to host it on the web with a Google Pages account I have--just email it to me (bugmesticky at gmail dot com) and I'll get it put up.

Max

Last fiddled with by philmoore on 2008-12-01 at 02:23 Reason: The current version limit is 10,000 bits, not digits.
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Old 2008-10-21, 21:27   #6
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Default you can use either version of primo

Here's a cross-post about a feature that I didn't know about until yesterday - http://www.mersenneforum.org/showpos...5&postcount=13
So, you can use either version (up to the hard-coded limit of 50000 bits).

I am not sure if Marcel is happy about this, but the cat is out of the sack now.
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Old 2008-10-21, 22:05   #7
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Thanks for the note - Norman Luhn says that 3.0.6 is quite a bit faster than 2.3.2, you just have to edit the configuration file to override the 10000 bit limit:

Change [Setup] to [Setup+], and add:
MBS=25000

The maximum possible limit is 50000 bits, about 15000 digits, but Norman is currently having trouble with the program at around 10000 digits.

I am able to begin testing 2^21954+77899 after making the changes. You need to create an input file for the number you want to test. Look in the work folder in Primo to see formats.

My estimates of the time needed to create the certificates may be too large, being based on an earlier version of Primo.
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Old 2008-10-21, 22:10   #8
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The largest I ever certified was 4845-digit and that was too long for my wits. Something like three weeks.
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Old 2008-10-22, 05:41   #9
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How does one come up with a time estimate? I might be interested in running 2^{22464}+63691 if I had a better idea of how long it would take. I'd probably be running it on a Q6600 at stock settings (2.4ghz).
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Old 2009-01-21, 01:46   #10
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I'm trying the top number on a Q6600 at 3 something ghz. Its been running for 28 hrs. It says phase 1 test 5 run 2 bits 21835/21955. How close to done is it?
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Old 2009-01-21, 02:01   #11
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A month or two.

Serious. If the computer crashes or needs a reboot, it's ok - there are recovery files saved at certain reasonable time points and you will not lose much time. All you need is commitment, and the computer will do the rest.
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