The probable primes

[philmoore]

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
2^1191375+8543
2^1518191+75353
2^2249255+28433
2^4583176+2131
2^5146295+41693
2^9092392+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)

[Kevin]

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.

[mdettweiler]

Originally Posted by Kevin

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.

[retina]

Originally Posted by Kevin

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.

[mdettweiler]

Originally Posted by retina

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

[Batalov]

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.

[philmoore]

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.

[Batalov]

The largest I ever certified was 4845-digit and that was too long for my wits. Something like three weeks.

[Kevin]

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).

[Joshua2]

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?

[Batalov]

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.