Okdoke Thanks Norman, will try it when I am ready to run phase 2.:smile:

Ole ole ole ojeeeeeeeee , we are the loooooooooooosers :no:

status of 2^28978+34429:
Ph1 Test 179 23705 bits left
Ph2 Test 1-125 done

[QUOTE=Cybertronic;219133]Ole ole ole ojeeeeeeeee , we are the loooooooooooosers :no:
[/QUOTE]

"It ain't over till the fat lady sings." or [url=http://www.zitate-online.de/sprueche/sportler/18325/der-ball-ist-rund-und-das-spiel-dauert-90-minuten.html]Sepp Herberger[/url]

Not the first time the group plays were bad for GER!

Any plans to do the next one on the list Cybertronic? How long would it take?

The same plane, but not I. Maybe a team. It takes 18 months on a P II 965

Are there plans to "modify" Primo and make it distributed-ready?

Luigi

[quote=ET_;219268]Are there plans to "modify" Primo and make it distributed-ready?

Luigi[/quote]

Only manual via admin.
The admin distributed the tasks.
17000 digits are alluring. 2nd place in the TOP-20 page.

Justin (enderak) has recently run a double check on the sequence for 2[SUP]1191375[/SUP]+8543, verifying that it is the smallest prp of its sequence. I have just finished checking that all the residues match the residues I found with pfgw a couple of years ago. It took me awhile to find the residues from the range 1.00-1.05M, or I would have posted this a few days ago! Some of the residues were matched to 62-bit residues from an older version of pfgw.

I also have a similar double check running on the sequence 2[SUP]983620[/SUP]+60451 on a slow computer. After this one, only the five sequences of Five or Bust will remain to be double checked.

Status:

Ph1: 17494 bits left
Ph2: TEST 1-324 done.

Time left : 7 days

Hello members !

2^28978+34429 is now proven prime.

Elapsed time : 1030 h

All the best,

Norman

:groupwave:

Luigi

:bow wave::bow wave::bow wave:

Awesome, down to 20 probable primes left, and one undiscovered prp! I don't know what we'll do for excitement around here once Engracio finishes his Primo run. Hopefully, we'll find that last prp soon, as this is the longest period we have gone without a new prp discovery.

Thanks, Norman, for a significant contribution to a nice sub-project, as well as an important extension of Primo's capabilities.

Thank you Phil and all !:smile:

You can get the certificate here:

[FONT=&quot]
[url]http://www.sendspace.com/file/xm62yc[/url]
[/FONT]

Congrats Norman, I promise I will finish soon.:unsure: Or later:smile:

Top-20 page was updated :smile:

[url]http://www.ellipsa.eu/public/primo/top20.html[/url]

Good luck , Engracio !

[quote=Cybertronic;221132]Top-20 page was updated :smile:

[URL]http://www.ellipsa.eu/public/primo/top20.html[/URL]

Good luck , Engracio ![/quote]

Thank you Norman. I am now running Phase 2 on the first 500 test and did what you instructed and sf= and pm= are not there anymore.:smile: w00t

The test runs are finally picking now. Hope to be done soon.

I would like to thank Norman for all his help and finding out where I messed up on my prime hunting. Without him I feel I would have wasted months of continues work. Thank you again Norman.:smile:

I have certified 2^31544+19081 as a prime and in the process of checking and signing the certificate by Primo. The process will probably take all weekend. Unless I ran into problem and not followed/verified Norman's process.

Here is hoping I can post again with success.

e

all done.

e

:bow wave::bow wave:
Awesome! I received your certificate, and everything appears to be in good shape.
:wacky::maybeso::wacky::maybeso::wacky:

So what do we do for entertainment now? :unsure:

[quote=philmoore;223633]:bow wave::bow wave:
Awesome! I received your certificate, and everything appears to be in good shape.
:wacky::maybeso::wacky::maybeso::wacky:

So what do we do for entertainment now? :unsure:[/quote]


Find the last prime.:mellow:

:tu:

Congrats engracio!

Congrats Engracio :tu: !

That was your first multicore certificate.

A 9500 digit number in 6 months :smile:

---
Norman

:groupwave:

So who is giving 256366+39079 a spin?

[quote=henryzz;223670]So who is giving 256366+39079 a spin?[/quote]

You could.

Thanks Norman for the help. I wonder how long before we all get knocked off the top-20 list.:blush:

[URL]http://www.ellipsa.eu/public/primo/top20.html[/URL]

Like Norman I think I will take a break from Primo for a while. It is a long slog this last one. Until we get better technology I will just have to try to find the last prime for FOB and hopefully another k with SOB.

Thanks to Justin (enderak) who has now double-checked the sequences for 75353 and 28433, and helped me finish double-checking the sequence for 60451. Matching residues now proves that 2[SUP]983620[/SUP]+60451, 2[SUP]1518191[/SUP]+75353, and 2[SUP]2249255[/SUP]+28433 are the smallest probable primes of their respective sequences. Only the three sequences for 2131, 41693, and of course, 40291 are not completely double-checked now. We found a couple of missing residues, but only two actual errors in the first time prp tests, both for the 28433 sequence at exponents greater than 2 million. I am hoping that in a couple of years, GPU processing may help speed up the double-checking for these last three sequences, but the results so far do tend to confirm a low error rate in general for Five or Bust work. Good work, everyone, and thanks again, Justin!

PFGW
 

Hello, can anyone send me a [URL="http://www.sendspace.com"]www.sendspace.com[/URL] link for downloading the latest version of windows-pfgw 3.4.1 ?

[URL]http://openpfgw.svn.sourceforge.net/viewvc/openpfgw/pfgw_win_3.4.1_20100927.zip?view=log[/URL]

I have ever trouble with "sourceforge.net".

Thanks !

This thread is enough.

[QUOTE=Cybertronic;233329]Hello, can anyone send me a [URL="http://www.sendspace.com"]www.sendspace.com[/URL] link for downloading the latest version of windows-pfgw 3.4.1 ?

[URL]http://openpfgw.svn.sourceforge.net/viewvc/openpfgw/pfgw_win_3.4.1_20100927.zip?view=log[/URL]

I have ever trouble with "sourceforge.net".

Thanks !

This thread is enough.[/QUOTE]
Here you go: [URL]http://www.sendspace.com/file/1dmq5y[/URL]

I believe the original zip-file have bugs ,or ?

-------------

@mdettweiler

Thank you :smile:!

LLR now has the option of the BPSW primality test as well as the Frobenius test: [URL="http://www.mersenneforum.org/showthread.php?t=15332"]http://www.mersenneforum.org/showthread.php?t=15332[/URL]

[URL="http://www.trnicely.net/misc/bpsw.html"]http://www.trnicely.net/misc/bpsw.html[/URL]
[URL="http://mathworld.wolfram.com/Baillie-PSWPrimalityTest.html"]http://mathworld.wolfram.com/Baillie-PSWPrimalityTest.html[/URL]

[CODE]2^56366+39079 is base 2-Strong Fermat PRP! Time : 5.705 sec.
2^56366+39079 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -3, D = 13) Time : 20.933 sec.
2^61792+21661 is base 2-Strong Fermat PRP! Time : 5.952 sec.
2^61792+21661 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 21.883 sec.
2^73360+10711 is base 2-Strong Fermat PRP! Time : 7.675 sec.
2^73360+10711 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 29.307 sec.
2^73845+14717 is base 2-Strong Fermat PRP! Time : 7.968 sec.
2^73845+14717 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -3, D = 13) Time : 31.113 sec.
2^103766+17659 is base 2-Strong Fermat PRP! Time : 16.176 sec.
2^103766+17659 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11) Time : 60.245 sec.
2^104095+7013 is base 2-Strong Fermat PRP! Time : 17.081 sec.
2^104095+7013 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -7, D = 29) Time : 64.099 sec.
2^105789+48527 is base 2-Strong Fermat PRP! Time : 16.764 sec.
2^105789+48527 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -4, D = 17) Time : 61.494 sec.
2^139964+35461 is base 2-Strong Fermat PRP! Time : 33.342 sec.
2^139964+35461 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 129.441 sec.
2^148227+60443 is base 2-Strong Fermat PRP! Time : 33.912 sec.
2^148227+60443 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 130.399 sec.
2^176177+60947 is base 2-Strong Fermat PRP! Time : 56.482 sec.
2^176177+60947 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 5, D = -19) Time : 221.824 sec.
2^304015+64133 is base 2-Strong Fermat PRP! Time : 148.693 sec.
2^304015+64133 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11) Time : 622.268 sec.
2^308809+37967 is base 2-Strong Fermat PRP! Time : 147.017 sec.
2^308809+37967 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -7, D = 29) Time : 618.084 sec.
2^551542+19249 is base 2-Strong Fermat PRP! Time : 541.642 sec.
2^551542+19249 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -3, D = 13) Time : 2477.977 sec.[/CODE]

I'm working on the last 7 prps.

2^983620+60451 is base 2-Strong Fermat PRP! Time : 1765.694 sec.
2^983620+60451 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11) Time : 9495.456 sec.
2^1191375+8543 is base 2-Strong Fermat PRP! Time : 2585.068 sec.
2^1191375+8543 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11) Time : 12651.006 sec.
2^1518191+75353 is base 2-Strong Fermat PRP! Time : 4108.723 sec.
2^1518191+75353 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 6, D = -23) Time : 21756.783 sec.

2^2249255+28433 is base 2-Strong Fermat PRP! Time : 9788.623 sec.
2^2249255+28433 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 41861.086 sec.
2^4583176+2131 is base 2-Strong Fermat PRP! Time : 45341.497 sec.
2^4583176+2131 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 263278.015 sec.
2^5146295+41693 is base 2-Strong Fermat PRP! Time : 62297.273 sec.
2^5146295+41693 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 327043.150 sec.

Jeff Gilchrist is doing 2^9092392+40291
[URL]http://www.mersenneforum.org/showthread.php?t=15242[/URL]

2^9092392+40291 is base 2-Strong Fermat PRP! Time : 190718.322 sec.
2^9092392+40291 is strong-Fermat and BPSW PRP, Starting Frobenius test sequence
2^9092392+40291 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11) Time : 953429.151 sec.

How long it takes to test whether 2^56366+39079 is a prime?

And how 2^5146295+41693?

For 2[SUP]56366[/SUP]+39079, Norman estimated 18 months on a 3.4 GHz Phenom II X4 965. Perhaps with the newer version of Primo and a faster computer, maybe a little less, but who knows? More cores would be better, of course.

On the other hand, I estimated 225 billion years for 2[SUP]5146295[/SUP]+41693 via ECPP, maybe only 60 billion years (on a single processor) if we could prove the generalized Riemann hypothesis:
[url]http://www.mersenneforum.org/showthread.php?t=12784[/url]

There's a new Primo version, 4.0.0 which is not only 64-bit but uses multiple cores (up to 16). Looks like it runs on Linux only, and is still an alpha version.

I don't have a spare computer with decent specs to install Linux on and test it out, but it looks like it might open the door to proving a few more of the PRP's.

Link: [URL]http://www.ellipsa.eu/public/primo/primo.html[/URL]

OK, I'll bite and try to prove the next two candidates in the list.

I'm taking a 3 week break now. Both tests have eliminated ~3500 bits so far. The smaller one is taking less time per step but the gains per step are smaller and there is more backtracking. So they are nearly equally fast atm.

Status update:

[FONT=&quot]Test 196 Bit 49147/56367[/FONT][FONT=&quot]
[/FONT][FONT=&quot]Test 153 Bit 55754/61793[/FONT][FONT=&quot]

[/FONT]The smaller one is noticeably picking up speed.

[QUOTE=philmoore;169315] 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.[/QUOTE]

If I understand this correctly, each Primo run not only proves the candidate, but also all the intermediate numbers P1...Pn. Would it be worth the work to collect these so if another run happens to stumble across one of them the rest of the proof could be "recycled"? Don't know about the chances of something like this happening though...

[QUOTE=Puzzle-Peter;307633]If I understand this correctly, each Primo run not only proves the candidate, but also all the intermediate numbers P1...Pn. Would it be worth the work to collect these so if another run happens to stumble across one of them the rest of the proof could be "recycled"? Don't know about the chances of something like this happening though...[/QUOTE]
The chances of this happening is so small. The chance of hitting each number at size ~2^n is around 1 in 2^n. n is > 50000 so the chance is very small indeed. 2^50000 is much larger than the number of numbers in the factordb even. By the time the numbers get small enough that it could happen it would be faster to regenerate it.

That would be any random number. As all our numbers need to be primes the probability would be much greater. Still too small though.

The larger of the two runs crashed without writing a .tmp file. The screenshot shows the latest files. I sent this to M. Martin and I hope he can tell me how to resume this.

I was able to reconstruct a .tmp file so only one day of work was lost.

Status update:
[FONT=&quot]Test 401, Bit 41779 / 56367[/FONT][FONT=&quot]
[/FONT][FONT=&quot]Test 264, Bit 51633 / 61793[/FONT][FONT=&quot]

[/FONT]

Who should be credited when submitting to the TOP5000 list? These numbers are small but they still make the TOP20 ECPP list.

Never mind. I just copied what Cybertronic used.

The certificate for 2^56366 + 39079 can be found here:

[URL]http://www.sendspace.com/file/y8jrn1[/URL]


The other test is down to 44000 bits. I hope I can finish it this year.

Congratulations!

I'll run a validation.

Did you try to submit it to factordb? It will do a linux-based validation, too (unless you will hit a limit that Markus may have set). I've submitted it on your behalf. The link to factordb is going to be better than sendspace (when it is processed).

Thanks!

Factordb? I think I've read this before but honestly I don't even really know what it is. I can guess from the name though. But this numbers does not have any factors. I am confused. I think I need to do some reading...

It could be a factor for some other number, and as such its character has to be known. Here's [URL="http://factordb.com/index.php?query=2%5E56366%2B39079"]where it sits[/URL]. It is an extremely useful data warehouse. Their internal validation is different from Primo, an open-source script (there was a discussion some place in the factordb thread).

Here's some fun that you can have with this now proven number P=2^56366+39079:
If you construct a PRP of a form a*(P^3+b*P^2+c*P)+-1 (that's only for example; you can use some other forms), then you can immediately prove it prime by N+-1 method based on P being a proven prime.

Wow Peter , congratulations !

[QUOTE=Puzzle-Peter;315532]Thanks!

Factordb? I think I've read this before but honestly I don't even really know what it is. I can guess from the name though. But this numbers does not have any factors. I am confused. I think I need to do some reading...[/QUOTE]

[QUOTE=Batalov;315543]It could be a factor for some other number, and as such its character has to be known. Here's [URL="http://factordb.com/index.php?query=2%5E56366%2B39079"]where it sits[/URL]. It is an extremely useful data warehouse. Their internal validation is different from Primo, an open-source script (there was a discussion some place in the factordb thread).

Here's some fun that you can have with this now proven number P=2^56366+39079:
If you construct a PRP of a form a*(P^3+b*P^2+c*P)+-1 (that's only for example; you can use some other forms), then you can immediately prove it prime by N+-1 method based on P being a proven prime.[/QUOTE]

Nominally after a certificate has been uploaded the status changes from PRP to P, but c.f. [URL="http://www.mersenneforum.org/showthread.php?p=313123#post313123"]here[/URL], that's broken at the moment. Pretend it's a P. :smile:

[QUOTE=Dubslow;315549]Nominally after a certificate has been uploaded the status changes from PRP to P, but c.f. [URL="http://www.mersenneforum.org/showthread.php?p=313123#post313123"]here[/URL], that's broken at the moment. Pretend it's a P. :smile:[/QUOTE]
Nothing is broken. You've never dealt with primes large enough. There's always a delay for the validation step. It is surely infinitesimal for PRPs of the aliquot run-of-the mill size.

I had submitted sizeable certificates before. For them, the delay is significant. Now, here, this particular number is a monster. Nothing will be "usual" here. Not only FactorDB, but the [URL="http://primes.utm.edu/primes/page.php?id=109914"]UTM pipeline[/URL] will be quite possibly manually shunted. (UTM makes special notes for offsite validations that they cannot reproduce but that had come from trusted sources.)


P.S. Ho-ho-ho. Look at out old "friend" Liquid N[sub]2[/sub]. Submitted [URL="http://primes.utm.edu/primes/page.php?id=109912"]a PRP[/URL] to them instead of Lifchitz&Lifchitz. It will be removed - look at it now before too late.

Congratulations! At 16968 digits, it is the fourth largest prime proven by ECPP, and the largest proven by Marcel Martin's Primo.

[QUOTE=Batalov;315552]Nothing is broken. You've never dealt with primes large enough. There's always a delay for the validation step. It is surely infinitesimal for PRPs of the aliquot run-of-the mill size.

I had submitted sizeable certificates before. For them, the delay is significant. Now, here, this particular number is a monster.[/QUOTE]

Is validating the same as re-running Phase2 in PRIMO? That took one week with 16 threads on 12 physical cores.

No, it is much faster. It verifies that all relations are valid. (There's also a very fast signature checking, that's almost instantaneous, but only checks that the file is not damaged in transfer or not manually edited.)

It should be done today. (Running on a slow 4-cpu box.) [COLOR=green]...Done. The certificate is valid.[/COLOR]

I see a user comment has been added on Chris Caldwells pages. Thanks! Could anybody tell me how to do this in the future? I can edit the existing comment now which is great because the sendspace link will expire and I hope to see the certificate an Marcel Martins page at some point (no answer to my email to him yet). But how can I make a new comment? I seem to be unable to find out :blush:

David is your co-author; I guess that is an authentication worth enough.
Log in with the credentials you created (PrimeGrid for example could create an account for you that you won't be able to log in to, but here, this is not the case), and look around.

I've never had an occasion to post a comment. Standard official comments had been posted on my behalf, e.g. a [URL="http://primes.utm.edu/primes/page.php?id=95243"]Generalized Fermat[/URL] note. If I will happen to find a Proth prime that will be a Generalized Fermat Factor, PrimeGrid will compute that and also post it on my behalf.

[QUOTE=Batalov;316008]David is your co-author; I guess that is an authentication worth enough.
[/QUOTE]

Does that give me a non-infinite Erdős number? :missingteeth: certainly the closest I'll ever get.

However, here's a little pre-christmas present:

2^61792+21661 is now a certified prime.

[URL]http://www.sendspace.com/file/0tt6t5[/URL]

Only german.

Hallo Peter, herzlichen Glückwunsch ! Das nenne ich mal eine Hausnummer ... dagegen erscheint mein Rekord von 2010 ein Witz zu sein.


Gruß

Norman

Hi Norman,

thanks! It is the nature of records that they will be broken some day. Let's see who will take primo to the next level.

Congratulations, Peter and Marcel! Thanks also to Norman, whose previous work helped Marcel update Primo to the current multi-core version. Only 18 more probable primes to certify to prove the dual Sierpinski conjecture as a theorem!

I tried the next candidate, 2^73360+10711 but it wouldn't get past test1. It seems we reached the end of primo's useful range.

Might be worth waiting until [URL]http://mersenneforum.org/showthread.php?t=17554[/URL] is a viable option.

The method needs to be checked and a program needs to be made public. If ecpp ran in O(x) then this runs in O(x^(3/4)). In other words a lot faster once overhead is insignificant.

[QUOTE=Puzzle-Peter;324922]I tried the next candidate, 2^73360+10711 but it wouldn't get past test1. It seems we reached the end of primo's useful range.[/QUOTE]

Thanks for trying this. I had hoped that maybe the next two, 2^73360+10711 and 2^73845+14717, might yield to primo. I wonder if your log file would be of use to Marcel Martin in case he might be interested in extending the capabilities of the program.

[QUOTE=philmoore;325046]Thanks for trying this. I had hoped that maybe the next two, 2^73360+10711 and 2^73845+14717, might yield to primo. I wonder if your log file would be of use to Marcel Martin in case he might be interested in extending the capabilities of the program.[/QUOTE]

So did I hope but Marcel Martin did not sound very interested in making major changes to primo. I am afraid this is the end of that path.

[QUOTE=Puzzle-Peter;325064]So did I hope but Marcel Martin did not sound very interested in making major changes to primo. I am afraid this is the end of that path.[/QUOTE]
It might be worth trying 2^73845+14717. You were unlucky with the smaller one that there was nowhere to backtrack to since it was the first iteration. Maybe that will be more lucky.

...and Peter, you probably already cranked the factoring limits to the top (2^32), right?
_______________

P.S. I started an 8-thread test on 2^73845+14717 (no intent to finish!)
and the .cr file says that it moved on to the 2nd test... but look at that gain! ;-)
[FONT=Arial Narrow][1][/FONT]
[FONT=Arial Narrow]Type=4[/FONT]
[FONT=Arial Narrow]Gain=3[/FONT]
[FONT=Arial Narrow]Index=1.10120[/FONT]
[FONT=Arial Narrow]D=-335755[/FONT]
[FONT=Arial Narrow]H/G=96/8:12[/FONT]

[QUOTE=henryzz;325065]It might be worth trying 2^73845+14717. You were unlucky with the smaller one that there was nowhere to backtrack to since it was the first iteration. Maybe that will be more lucky.[/QUOTE]

The problem is it might well do several iterations, followed by a lot of backtracking and finally give up. This might easily waste several CPU months, even years and I'm still debating with myself about taking the risk.

[QUOTE=Batalov;325069]...and Peter, you probably already cranked the factoring limits to the top (2^32), right?
_______________

P.S. I started an 8-thread test on 2^73845+14717 (no intent to finish!)
and the .cr file says that it moved on to the 2nd test... but look at that gain! ;-)
[FONT=Arial Narrow][1][/FONT]
[FONT=Arial Narrow]Type=4[/FONT]
[FONT=Arial Narrow]Gain=3[/FONT]
[FONT=Arial Narrow]Index=1.10120[/FONT]
[FONT=Arial Narrow]D=-335755[/FONT]
[FONT=Arial Narrow]H/G=96/8:12[/FONT][/QUOTE]

2^32, yes.

Gain=3 woohoo ;-) I'll have to think about this. I'd love to do some real biggies but the risk of losing lots of time is considerable...

Actually, as I now look at the primo GUI window (I didn't have access to the terminal before, so I simply read the .CR file) -- the gain is not just 3 bits. The progress is show as "Test 2 | Bits [B]73784/73846[/B]", so I don't have a good grasp of the semantic of the "Gain" line. But of course the stalling scenario like you described would be impossible to predict just yet.

If it gets to say Test 10, I can forward you the package?

Another way in the old "Luhnization" routine would be to deliberately start from the very beginning many times in parallel, avoiding the paths already taken by other "threads".

I kept a close eye on my primo runs and so far the "Gain=" value always equalled the bit difference from one test to the next. I have no idea what to think of your numbers.

OK I see you're trying every trick in the book to get me enticed. Right. You win. Take it to test 10 and I'll take over ;)

EDIT: What does the .cr file say now? There might have been a backtrack. First path gave a gain of 3 bits which means the next step will give up and backtrack rather early (backtracking is dependent from various factors, one of them being the gain that is sacrificed by going back one step), then a better Step1 with a larger gain was found.

You are right - I should have looked in the .cr file again. :-)
It is indeed a backtrack.
[CODE][Setup]
MaxConcurrentTasks=8
SieveUpperBound=2^32

[Backtrack]
Count=1

[1, backtrack:1]
Type=4
Gain=3
Index=1.10120
D=-335755
H/G=96/8:12

[1]
Type=4
Gain=62
Index=1.30522
D=-1904820
H/G=320/16:20
[/CODE]
It all makes sense now. I've always trusted that Gain meant literally a gain in bits.

[QUOTE=Batalov;325140]
If it gets to say Test 10, I can forward you the package?
.[/QUOTE]

I guess you never got to Test 10? Doesn't matter, I started it...

No, indeed, I got lucky with 1-2-3 and then backtracked. I don't think I got to 10. I can search for that folder...

The newer and newer Primo version are probably increasingly better trained for larger and larger sizes; so the later you start, the better chances are to arrive earlier.

Never mind searching for the folder. I won't get near that box for several days now, so it will just run its course anyway.

Backtracking can be manipulated via the primo.ini file so I might have to do that and start once again. We'll see.

Who feels motivated to run a verification?

[URL]http://www.sendspace.com/file/hxjfvg[/URL]

EDIT: Marcel Martin has added new/more/better discriminants to one of his latest releases, so maybe 2^73360+10711 is doable now. I'll leave that to others though.

Congrats for the [URL="http://www.ellipsa.eu/public/primo/top20.html"]top Primo proof[/URL] of [URL="http://primes.utm.edu/primes/page.php?id=116522"]2^73845 + 14717[/URL] :bow:

Pray tell us, what are the specs of the hardware used?

[QUOTE=paulunderwood;361036]Congrats for the [URL="http://www.ellipsa.eu/public/primo/top20.html"]top Primo proof[/URL] of [URL="http://primes.utm.edu/primes/page.php?id=116522"]2^73845 + 14717[/URL] :bow:

Pray tell us, what are the specs of the hardware used?[/QUOTE]

Not just top Primo proof, but the third largest ECPP ever completed (at least on this planet.) Maybe we should rename this project "Seventeen or Bust" since we have exactly seventeen prps left to prove.

Congratulations, Peter, it looks like you started in May? How many cores?

Most of the proof was done on a dual Xeon machine with 16 threads on 16 physical cores. I found a 1:1 ratio to be the fastest.

Just for fun I tried 2^73360+10711 once again with PRIMO 4.10. This version was successful in test1 thanks to the new discriminant tables. It will be an on-and-off job, but I will continue this run unless somebody else would rather do it.

[QUOTE=Puzzle-Peter;373565]Just for fun I tried 2^73360+10711 once again with PRIMO 4.10. This version was successful in test1 thanks to the new discriminant tables. It will be an on-and-off job, but I will continue this run unless somebody else would rather do it.[/QUOTE]

How long does it take to prove these numbers prime? :huh:

[QUOTE=Trilo;374685]How long does it take to prove these numbers prime? :huh:[/QUOTE]

Using good hardware (16 physical cores in a dual-XEON box) it's about 3 to 4 months going 24/7. Runtime depends heavily on how much backtracking is needed, especially in the beginning when one backtrack can easily cost 2 days, so it's hard to give a precise estimate.

Done. I'll upload the certificate to factordb.

[URL]http://primes.utm.edu/primes/page.php?id=118567[/URL]

Very nice, congratulations, Peter! Congratulations as well to Marcel for some very impressive improvements to Primo. This number is now the eighth largest ECPP, Peter's result from last December which was then the third largest is now the seventh, and Primo has now proven 6 out of the 8 top ECPP results, including the second largest, which is also the largest proven Wagstaff prime.

The next three probable primes on the list (see post #1 in this thread) have 31237, 31336, and 31846 digits respectively, and are considerably larger than the current ECPP record of 26643 digits. Probably too soon to tackle these yet, but I expect they will be proven in a few years. If anyone checks to see how the current version of Primo does on any of these, a report would be welcome.

[QUOTE=philmoore;384088]If anyone checks to see how the current version of Primo does on any of these, a report would be welcome.[/QUOTE]

According to Marcel Martin, the theoretical limit that PRIMO can handle is a little bit less than 100,000 bits, so no chance of doing these plus he told me he does not plan on extending PRIMOs limit.

EDIT: found his mail, the limit is [FONT=&quot]99648 bits [/FONT]

Congrats!

When I started my P18689 in Sep 2013, it would have been the largest Primo result. It took 3 months with Primo 4.0.1 + 4.0.4 on a 3930K (12 threads, which is faster on that machine than 6 -- perhaps faster memory), and ended up 2nd behind Peter when it finished, and is now 11th. That's my main dev machine so ran lots of xterms plus a few other programs at the same time though nothing very long running. I also had a fun scare a couple months in when another process filled the disk and Primo crashed, losing all the data. Daily backups to the rescue.

LOL I know that feeling! Had the "no space left on device" problem after about 1500 tests. PRIMO crunched on, but the files had 0 bytes. Then, in phase 2, the next shock. Every test needs 3 steps in phase 2 "building polynomial", "factoring polynomial" and "computing curve and point". I never noticed the first one, because it takes so little time. But one test spent more than 10 hours on "building polynomial". I thought it had crashed or maybe the intermediate file was corrupt. But on the next morning it had moved on...

This is most probably the end of my XXL PRIMO test series. Let's wait for Paul to finish his monster and then let's see what will happen.

Is there a particular reason why the latest versions of fastecpp are not available?

[QUOTE=Puzzle-Peter;384108]According to Marcel Martin, the theoretical limit that PRIMO can handle is a little bit less than 100,000 bits, so no chance of doing these plus he told me he does not plan on extending PRIMOs limit.

EDIT: found his mail, the limit is [FONT=&quot]99648 bits [/FONT][/QUOTE]

Now that Primo has proven a new ECPP record at 29271 digits, our next three numbers (31237 to 31846 digits) don't seem that far from possible. It will be interesting to see how long the new record stands. The current Primo limit is 29998 digits, so the program has now worked successfully close to this limit.

[QUOTE=philmoore;391307]Now that Primo has proven a new ECPP record at 29271 digits, our next three numbers (31237 to 31846 digits) don't seem that far from possible. It will be interesting to see how long the new record stands. The current Primo limit is 29998 digits, so the program has now worked successfully close to this limit.[/QUOTE]

AFAIK the next release (due in Jan.) will be able to do up to ~35000 digits.

Any reservations for ECPP?

[QUOTE=bbb120;509659]You can use mathematica ,function PrimeQ[2^73360+10711]

[CODE]MillerRabin[n0_,a0_]:=Module[{n=n0,a=a0,s,m,t1,k},
s=0;m=n-1;While[Mod[m,2]==0,m=m/2;s=s+1];
t1=PowerMod[a,m,n];
If[t1==1,Return[True]];
k=0;While[k<s-1&&t1!=n-1,k=k+1;t1=Mod[t1^2,n]];
If[t1==n-1,Return[True],Return[False]]
]
[/CODE]
Miller Rabin code by using mathematica,

MillerRabin[2^73360+10711, #] & /@ {17, 257, 65537, 10^200 + 267}
{True, True, True, True}
this is too fast,ECPP is too slow,

miller rabin is simple and realible![/QUOTE]

Miller-Rabin does not certificate a prime, it shows PRPs.

[QUOTE=ET_;509667]Miller-Rabin does not certificate a prime, it shows PRPs.[/QUOTE]

miller rabin really does not give any certificate a prime ,
but several miller rabin test with one lucas test is very fast and very very Reliable!

[QUOTE=bbb120;509721]...with one lucas test...[/QUOTE]
Which Lucas test? [URL="https://en.wikipedia.org/wiki/Lucas%27_reagent#Lucas_test"]This[/URL]?

There is no such thing as a very very very very very very very very very very very very probable prime. No. Either it is a prime - or just a PRP.

[QUOTE=bbb120;509721]miller rabin really does not give any certificate a prime ,
but several miller rabin test with one lucas test is very fast and very very Reliable![/QUOTE]

It maybe very reliable for "industrial use". It is certainly quicker than ECPP, but not quite as fast as, for example, Proth's Theorem's test. PFGW will run combined Fermat+Lucas test with its "-tc" switch, and will attempt to prove a number (100%) prime -- no question, no doubt, no 1/10^10000000000000000 chance of not being prime. :smile:

[QUOTE=Batalov;509723]Which Lucas test? [URL="https://en.wikipedia.org/wiki/Lucas%27_reagent#Lucas_test"]This[/URL]?

There is no such thing as a very very very very very very very very very very very very probable prime. No. Either it is a prime - or just a PRP.[/QUOTE]

[url]https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test[/url]
[url]https://en.wikipedia.org/wiki/Lucas_pseudoprime#Strong_Lucas_pseudoprimes[/url]

you can read this for lucas test!