The probable primes

[jrk]

Originally Posted by gd_barnes

Can anyone tell me what "Wine" is, other than something you drink?

It's a program for running Windows binaries on Linux.

http://winehq.org/

[philmoore]

Originally Posted by gd_barnes

Question: For the next unreserved test, what is the chance that it is composite? I'm speculating 1 in 10^20.

More like 1 in 10^85, see Crandall and Pomerance, section 3.4.

Originally Posted by gd_barnes

This is a very interesting project. I was floored in the presentation that the dual Riesel problem had been completely tested to n=282K. Phil, did you do that on your own? That's quite a bit of work! If I wasn't coordinating 2 projects already, I'd be interested in starting the dual Riesel project. I hope that someone does that in the foreseeable future.

I tested up to n=262144 on my own after my friend Rob helped me narrow down to 327 k values. I will open a thread in this subforum and make my sieve file and list of (k,n) values available so if anyone wants to go further, they can.

Originally Posted by gd_barnes

One more thing, what do you mean by "validating" the certificate. What do you do? Just rerun the test and match them up?...kind of just like we'd match up residues on double-checks with the -1 and +1 forms.
Gary

I validated the certificate for 2^16389+67607 twice, once with Primo, and the second time using a program called CertVal written by Jim Fougeron. If I remember correctly, Primo took about half a day while CertVal took a little over a day. Primo generates a list of prime numbers:
P1 > P2 > P3 > ... > Pn
plus a set of elliptic curves for each consecutive pair. P1 can be proven prime if P2 can be proven prime, P2 can be proven prime if P3 can be proven prime, and so on. The elliptic curve provides the proof. The original run discovers the primes and and curves, but doing the calculations to verify that the chain provides a proof of primality of P1 is much faster than the original run.

[mdettweiler]

Originally Posted by gd_barnes

I'm pretty fuzzy on Linux. I just run programs on it. Can anyone tell me what "Wine" is, other than something you drink? Max, if you read this...you're the Linux guru. Are you familiar with it?

As jrk said...a program for running Windows binaries on Linux. It's still somewhat of a work in progress, so there are quite a number of programs on which it will crash or otherwise not behave properly. I've used it myself and have found that it does work pretty well with many prime-search programs. I've never tried it with Primo (in fact I've never even used Primo at all! ), though I'll see if I can get the chance to take a whack at it next time my computer's booted into Linux. If it works, I'll see about getting Wine and Primo loaded up on one of your quads--which one would you be wanting to run it on?

[TimSorbet]

Originally Posted by gd_barnes

That's too bad that 2 backups aren't made from Primo. That's rotten to lose that much work. I know that Newpgen has that option but to my knowledge, none of the other primality proving and sieving software does that, although I'm guessing that Prime95 probably does for the huge Mersenne tests.

Yeah, by default (it's an option) Prime95 saves two backup files and goes through a fairly complicated process to resave them so that any single random failure will still result in at least one good save file.

[engracio]

So Phil once I completed the certification, you would be able to recertify the prime based on the result? Also when the certification completes what exactly am I looking for? What does Primo output to say it certified the prime?

[philmoore]

Originally Posted by engracio

So Phil once I completed the certification, you would be able to recertify the prime based on the result? Also when the certification completes what exactly am I looking for? What does Primo output to say it certified the prime?

Primo produces three files during the certification process, a Task Report (TR file), a Certification Report (CR file), and the Primality Certificate which is the OUT file. I would need the OUT file to verify that it does indeed prove that your number is prime. However, the brief Task Report does at least assert that Primo proved the number was prime.

[gd_barnes]

Thanks Max. Except for "Crunchford", it doesn't matter which AMD machine Wine and Primo are loaded on. I don't want to take a core of my Intels and since Crunchford has your servers and stuff on it, it'd be better to avoid it. Also, as I recall, Primo runs faster on AMD's then Intel's.

Phil, can you give me a link to Primo version 3.0.6? I'm going to play around with that newer version on my Window's laptop or desktop.

I've run one of the older versions previously to prove the PRP's for my top-5 prime quadruplates so unless there has been some big change in the interface, I should be familiar with how to run it.


Gary

[kar_bon]

Primo 3.0.6 download:

http://www.ellipsa.net/public/misc/downloads.html

[mdettweiler]

Originally Posted by gd_barnes

Thanks Max. Except for "Crunchford", it doesn't matter which AMD machine Wine and Primo are loaded on. I don't want to take a core of my Intels and since Crunchford has your servers and stuff on it, it'd be better to avoid it. Also, as I recall, Primo runs faster on AMD's then Intel's.

Okay, sounds good. I just finished downloading Primo 3.0.6 right now, and will give it a try under Wine shortly on my computer.

[gd_barnes]

Max tested Primo 3.0.6 under Wine in Linux and it worked well. I messed around with it on my Window's laptop and I could get it to handle anything up to 50,000 bits (~15,000 digits), which means that it should be able to test the first 12 PRP's here. He said he'd get it loaded on one of my machines by the weekend. Therefore, I'd like to reserve:

2^24910+62029

I'll start on it Monday or Tuesday after the NPLB rally.


Gary

[philmoore]

See post 7. Primo has successfully certified numbers up to 7993 digits, but Norman Luhn has run into trouble around 10000 digits. So it will be interesting to see how far we can go with it.