[quote=Cybertronic;199399]BTW , I'm now at TEST 16..37802/38091.

When you work correct, you should be done with Phase 1 at 31th december 09:smile:[/quote]

I hope so.:smile: test 304/19006bit as we speak. Might be a few days later since When I am not by the computer I prp for FOB on this computer.

I wonder, only TEST 22 of Phase 2.
What is the CPU- type of your multicore PC ?

[quote=Cybertronic;199407]I wonder, only TEST 22 of Phase 2.
What is the CPU- type of your multicore PC ?[/quote]
Actually it is on test 32 now but phase 2 cores are being done on older Pentium 4 and soon AMD X2 4600+. I see no rush on it unless I am close to test 900 on phase 1. Phase 1 cores are on Q6600.

My plan Norman is when this *.tmp completes Phase 2 test 50, I will stop it. Save the *.tmp file to the Pre-certificate folder. This *.tmp was with the test completed up to test 229.

Copy the newest *.tmp which is done up to test 303 and break it down to 50 test each and run 2 cores each on the Intel P4 and AMD X2. Hopefully I will catch up enough to Phase 1 test so that I can merge it as soon as possible. There should be no problem as long as I am using the same *.tmp files correct??

[quote=engracio;199434]There should be no problem as long as I am using the same *.tmp files correct??[/quote]

Yes, it is correct.

[quote=Cybertronic;199399]BTW , I'm now at TEST 16..37802/38091.

When you work correct, you should be done with Phase 1 at 31th december 09:smile:[/quote]

Well Norman, I think I might have done something that is not correct. For the last 30 test, I seem to move forward several test and primo would go back track several test and move forward some more. Or worse one test would move forward but two run would come up with different bits. I normally took the lowest bit but eventually it would back track or become dead end and primo would back track until it can find another track to move forward. Last night I only ran 1 core on test 376 run1, this morning it was on test 378 and has backtracked again to test 377 with the same bit number.

Is this normal. Happy new year to you already.:smile:

[quote=engracio;200458]Well Norman, I think I might have done something that is not correct. For the last 30 test, I seem to move forward several test and primo would go back track several test and move forward some more. Or worse one test would move forward but two run would come up with different bits. I normally took the lowest bit but eventually it would back track or become dead end and primo would back track until it can find another track to move forward. Last night I only ran 1 core on test 376 run1, this morning it was on test 378 and has backtracked again to test 377 with the same bit number.

Is this normal. Happy new year to you already.:smile:[/quote]

Pity Engracio !
Maybe, you don't have the same strategy in detail. (Or I misunderstand you) I believe , you have now 18500 bits ( a tiny number :smile: )

My number is out of any power laws ( for running times ).
At this time I have any TEST of 28 and 29. (37476 bits)

Also happy new year to you ! Only 3.5 hours than we have 2010 :smile:

P.S. I have now a Phenom II X4 965 (3.4 GHz). 10^700+7 takes 2min 40s

I have no doubt that your calculation is correct, it is just that I seem to be going back and forth on the test. It would go forward a few test then back track one or two test. Redoing the same test seems to take longer. That is why I have not made more progress in the last two weeks. Good thing is I have almost done 250 test on Phase two.:smile:

Norman I have finally finished 2^26827+77783 and running the verification on it.:smile: After 24hrs it is on test 360/1076. w00t:toot:

I know that after test 675 Primo was just crunching right thru it, on both phase 1 and phase 2. What should I expect when Primo complete the verification? Thanks.

Congratulations, Engracio. You should be finished within another day. I'll update post #1. I see that the prime is just barely too small to make Chris Caldwell's top 20 ECPP list, but we should send the certificate to Marcel Martin, as it is still one of the largest numbers ever to be certified by PRIMO.

Congrats Engracio! A great effort!

Thanks guys, Primo verified the prime as proven in 33hrs. Phil pls check your email to see if we need anything else.:smile:

Congrats also from me !

I'm now on TEST 54 ...it works , but very slow. I use not the complete time.

[QUOTE=engracio;202361]Thanks guys, Primo verified the prime as proven in 33hrs. Phil pls check your email to see if we need anything else.:smile:[/QUOTE]

Congratulations! :smile:

Luigi

2^31544+19081 engracio

[quote=engracio;204301]2^31544+19081 engracio[/quote]


Good luck !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Don't forget to set MSC=26

I'm on TEST 93. 10758 digits left :sick:

I missing the last one on the PRIMO TOP-20 page.

Thanks Norman, I wasted 10 days going back and forth on the first 8 test. Got tired of it and re initialized the same test. I am now on test 8 after only 1 day and have not backtracked yet. I guess the first initialization was corrupted or bad. I should have dumped the first one sooner but I did not.:sad:

Well having Phenom x4 965 is way better than a Q6600. With a small oc it did 10^700+7 in 2min 20s.

2^31544+19081 is 9496 digits only. I am using Primo3.0.9, is it different than 3.0.7?

[quote=Cybertronic;204333]Good luck !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Don't forget to set MSC=26

I'm on TEST 93. 10758 digits left :sick:

I missing the last one on the PRIMO TOP-20 page.[/quote]

[QUOTE=engracio;204355]I am using Primo3.0.9, is it different than 3.0.7?[/QUOTE]

From the changelog:

[quote]
v3.0.9
The [Comments] sections of input files are reported in the [Comments] sections of output files.
v3.0.8
Added a Double file management option. It might be useful when dealing with very big numbers.
[/quote]

[quote=paleseptember;204369]From the changelog:[/quote]

Thanks Ben, I've read that too. If I am not mistaken the double file management option came about after I and either Gary or Luigi had a corrupted *.tmp. I had to restart my test after almost halfway done, now I hope this will prevent this from happening.:smile:

I was asking Norman more as far as how we save certain files on the process he developed.

[quote=engracio;204355]Thanks Norman, I wasted 10 days going back and forth on the first 8 test. Got tired of it and re initialized the same test. I am now on test 8 after only 1 day and have not backtracked yet. I guess the first initialization was corrupted or bad. I should have dumped the first one sooner but I did not.:sad:

Well having Phenom x4 965 is way better than a Q6600. With a small oc it did 10^700+7 in 2min 20s.

2^31544+19081 is 9496 digits only. I am using Primo3.0.9, is it different than 3.0.7?[/quote]


8 TEST only one day is very good ! 2-3 is normal. V 3.0.9 is the same like 3.0.7. No speed ups.

OC's make no sence, because the temperature is ever critical (>60°)...
and we have winter ! In summer , my roomtemperature is 30° or more

The black edition works stabil with Vcore=1,265 V ( default=1,4V ) so the temp go down from 60° to 50°. Every core works with 100%.

BTW , the Phenom 965 with MSC=20 can TEST 10^700+7 in 2min 00s

Norman

[quote=Cybertronic;204384]8 TEST only one day is very good ! 2-3 is normal. V 3.0.9 is the same like 3.0.7. No speed ups.


Norman[/quote]

Yea it is good that most except for one test was run 1 and the early part of run 1 at that, meaning the index are at least less than 25,000.

I thought that since it is a bigger prime, the slowness of the first test was normal. But when I backtracked twice on the same 4 test, looking like it was going in a loop, I stopped the test and started again. It was early enough for a restart.

Thanks for the info.

[quote=engracio;204424]

I thought that since it is a bigger prime, the slowness of the first test was normal. But when I backtracked twice on the same 4 test, looking like it was going in a loop, I stopped the test and started again. It was early enough for a restart.

Thanks for the info.[/quote]

That is typical for PRIMO. When you found another TEST n [ Example 10 with 31089 bits and later 10 with 31095 bits ] then you have to do delete the old *.s10 file. I had have also this problem. Normally PRIMO delete *.s file automatic and then PRIMO make a backtrack....found another TEST n and create a new *.sxxx -file.

Do you remember ?

"Originally Posted by [B]engracio[/B] [URL="http://www.mersenneforum.org/showthread.php?p=191699#post191699"][IMG]http://www.mersenneforum.org/images/buttons/viewpost.gif[/IMG][/URL]
[I] Do you know how many test is on 2^26827+77783. Thanks."

I said :"Between 1065-1075. "

Really exact 1076 TEST, 1076:Type=0

That just about the limit !!!

[U]

[/U] [/I]

Technically the prime consisted a total of 1075 test, test 1076 is like the end of file. So yes Norman, you hit on the head.:smile:

[quote=Cybertronic;204583]Do you remember ?

"Originally Posted by [B]engracio[/B] [URL="http://www.mersenneforum.org/showthread.php?p=191699#post191699"][IMG]http://www.mersenneforum.org/images/buttons/viewpost.gif[/IMG][/URL]
[I] Do you know how many test is on 2^26827+77783. Thanks."

I said :"Between 1065-1075. "

Really exact 1076 TEST, 1076:Type=0

That just about the limit !!!

[/I][/quote]

Engracio, PRIMO page was updated.:smile:

[quote=Cybertronic;204618]Engracio, PRIMO page was updated.:smile:[/quote]

Thank you SIR!!!:tu:

Status report of 2^38090+47269:

TEST 122 35022/38091 bits , RUN 1,2,3,4,5 simultaneous.

Well I am glad your wu is moving along. Mine after 10 days is back to test 10 again. It has been back and forth all the way up to test 16. So far backtrack count=20.

I'll give it another week, if I don't make any decent progress no mas.

20 backtracks ? Wow!
Do you run on 4 cores ?

Progress!
 

I just received a remarkable email from Professor Wilfrid Keller in Hamburg:

[QUOTE] February 17, 2010
Dear Phil Moore,

With reference to your list of PRPs at

[url]http://www.mersenneforum.org/showpost.php?p=145066&postcount=1[/url]

I wanted to report that 2^31483+29333 (9478 digits) and
2^56363+26213 (16967 digits) might be removed from the list,
as I found the smaller primes 2^1891+29333 (570 digits) and
2^1271+26213 (383 digits). Primality was established using
Marcel Martin's Primo and kindly verified by David Broadhurst:

> I confirm your findings, completely.
> Here are APR-CL proofs by Pari-GP:
>
> parisize = 400000000, primelimit = 20000000
> ? isprime(2^1271 + 26213)
> %1 = 1
> ? isprime(2^1891 + 29333)
> %2 = 1

Luckily, none of the above-mentioned PRPs had previously been
attacked with Primo!

Let me tell you the background of this. At the suggestion of John
Blazek from PrimeGrid, I recently reworked my web page

[url]http://www.prothsearch.net/sierp.html[/url]

on Sierpinski's problem, which had been "frozen" in November 2002.
The desire was to "see all data in one central location", as John
put it.

In that context, David Broadhurst pointed me to your current work
on the "dual" Problem. I have to admit that I wasn't aware, at
that point, of the impressive four PRPs discovered within the
frame of "Five or Bust" (truly remarkable!). I only knew of the
two record Primo "certifications" by Norman Luhn, but probably
didn't relate them to the "dual problem".

Also, I hadn't looked at Payam Samidoost's page

[url]http://sierpinski.insider.com/dual[/url]

for a long time.

Revisiting Payam's page, and after having "practised" with the
"prime Sierpinski problem", I was curious to compute the
frequencies similar to the f(m) for the original Sierpinski problem,
to get some insight into the different "elimination behaviour". For
instance, it was interesting to see that in the range in question
there are 6714 cases where k + 2^2 = (k + 2^1) + 2^1 = p (a prime)
with k + 2^1 composite, so that two consecutive odd k's are
eliminated at once in each case.

Continuing with my "reproduction of known results", I finally
discovered the two primes which in fact should have appeared on
the "list of all k < 78557 such that the first probable prime
k + 2^n found" has n within 1000 < n < 10000.

Everything else seems to have been verified (as far as PRPs were
concerned) up to n < 2^12 = 4096.

May I finally mention that I greatly enjoyed your paper on the
"mixed problem", and also your delightful talk on "Perfect, Prime,
and Sierpinski Numbers".

With kind regards,

Wilfrid Keller
[/QUOTE]

We are so lucky that neither of the two probable primes in our list had been subjected to the torture test via Primo! I have now deleted them from post #1 in this thread. When I took up this project in 2007, I verified that all of the odd k values < 78557 [B]not[/B] listed in Payam Samidoost's webpage had a prime k+2^n with n < 1000. But I assumed that the data up to n < 20,000, apparently discovered by Mark Rodenkirch and verified by David Broadhurst, was essentially accurate. Mark and David are very careful people, so I suspect a software problem with an old version of pfgw. But Professor Keller has only verified this data up to n = 4096, so it may be worthwhile to verify the rest of it. I currently have verification data in progress for the 7 sequences 37967, 60451, 75353, 28433, 8543, 2131, and 41693. If you care to verify that any of the remaining sequences in post #1 of this thread have no probable prime less than that listed, post below.

I checked over that 2^ 38090 +47269 is the first prime of 2^n+47269.
So my work is not waste.

In addition to the sequences represented by the 30 primes/probable primes now listed in post #1 of this thread, plus the 40291 sequence, there are an additional 16 sequences for which we should verify that the proven primes below are indeed the smallest in each sequence. I am reasonably certain about the eight sequences I started with in 2007, including the five of Five or Bust, as I started my search at n = 1, and double-checking has so far confirmed that at least the early tests were accurate. Wilfrid Keller has checked all of these sequences up to n = 4096.

2[SUP]4870[/SUP]+20209
2[SUP]5335[/SUP]+41453
2[SUP]5759[/SUP]+64643
2[SUP]5760[/SUP]+5101
2[SUP]5883[/SUP]+24953
2[SUP]6022[/SUP]+48859
2[SUP]6144[/SUP]+26491
2[SUP]6262[/SUP]+49279
2[SUP]6477[/SUP]+56717
2[SUP]6496[/SUP]+31111
2[SUP]6649[/SUP]+6887
2[SUP]9696[/SUP]+48091
2[SUP]11152[/SUP]+23971
2[SUP]12075[/SUP]+14033
2[SUP]12715[/SUP]+14573
2[SUP]16389[/SUP]+67607

(Note that 2[SUP]6022[/SUP]+48859 has two digits transposed on Payam Samidoost's page.)

If no one else does it first, I will check as many as I can the weekend of 27 February. Of course, double-checking the last few sequences is an ongoing concern, but I should be able to confirm the rest, and at least verify whether there are any more errors on Samidoost's page.

[quote=philmoore;205981]Wilfrid Keller has checked all of these sequences up to n = 4096.

2[sup]4870[/sup]+20209
2[sup]5335[/sup]+41453
2[sup]5759[/sup]+64643
2[sup]5760[/sup]+5101
2[sup]5883[/sup]+24953
2[sup]6022[/sup]+48859
2[sup]6144[/sup]+26491
2[sup]6262[/sup]+49279
2[sup]6477[/sup]+56717
2[sup]6496[/sup]+31111
2[sup]6649[/sup]+6887
2[sup]9696[/sup]+48091
2[sup]11152[/sup]+23971
2[sup]12075[/sup]+14033
2[sup]12715[/sup]+14573
2[sup]16389[/sup]+67607[/quote]
I have just verified these from n=4000 and found the first PRPs at the numbers listed on all of them (i.e. assuming Wilfrid Keller and I did not make any big mistakes, the n's listed are indeed the lowest PRPs for those k's).

[QUOTE=Mini-Geek;205983]I have just verified these from n=4000 and found the first PRPs at the numbers listed on all of them (i.e. assuming Wilfrid Keller and I did not make any big mistakes, the n's listed are indeed the lowest PRPs for those k's).[/QUOTE]

Thanks, Tim. What software did you use for the verification?

We still have the primes/probable primes listed in post #1:

2[SUP]21954[/SUP]+77899
2[SUP]22464[/SUP]+63691
2[SUP]24910[/SUP]+62029
2[SUP]25563[/SUP]+22193
2[SUP]26795[/SUP]+57083
2[SUP]26827[/SUP]+77783
2[SUP]28978[/SUP]+34429
2[SUP]29727[/SUP]+20273
2[SUP]31544[/SUP]+19081
2[SUP]33548[/SUP]+4471
2[SUP]38090[/SUP]+47269 (checked by Cybertronic)
2[SUP]56366[/SUP]+39079
2[SUP]61792[/SUP]+21661
2[SUP]73360[/SUP]+10711
2[SUP]73845[/SUP]+14717
2[SUP]103766[/SUP]+17659
2[SUP]104095[/SUP]+7013
2[SUP]105789[/SUP]+48527
2[SUP]139964[/SUP]+35461
2[SUP]148227[/SUP]+60443
2[SUP]176177[/SUP]+60947
2[SUP]304015[/SUP]+64133
2[SUP]308809[/SUP]+37967
2[SUP]551542[/SUP]+19249
2[SUP]983620[/SUP]+60451
2[SUP]1191375[/SUP]+8543
2[SUP]1518191[/SUP]+75353
2[SUP]2249255[/SUP]+28433
2[SUP]4583176[/SUP]+2131
2[SUP]5146295[/SUP]+41693

It might be especially helpful to do 2[SUP]31544[/SUP]+19081, as Engracio is not too far into the ECCP proof yet, and also 2[SUP]28978[/SUP]+34429, as it is probably the next one on the list to prove.

[quote=philmoore;205995]Thanks, Tim. What software did you use for the verification?[/quote]
PFGW with the -f option and an ABC2 file (not a pre-sieved sort of file). Was pretty fast, but I wouldn't want to check all the larger ones that way. Pre-sieving a file would definitely help for that.

I presieved the sequence 2[SUP]n[/SUP]+19081 with srsieve, and got down to 130 tests or so, then confirmed that Engracio's number 2[SUP]31544[/SUP]+19081 was indeed the smallest in that sequence. I will do the rest soon, but I just didn't want him to continue running Primo on it if it was not the smallest.

How is it going, Engracio? Any progress?

[quote=philmoore;206086]I presieved the sequence 2[sup]n[/sup]+19081 with srsieve, and got down to 130 tests or so, then confirmed that Engracio's number 2[sup]31544[/sup]+19081 was indeed the smallest in that sequence. I will do the rest soon, but I just didn't want him to continue running Primo on it if it was not the smallest.

How is it going, Engracio? Any progress?[/quote]

Thanks Phil. It is very slow. I have not given up yet but if I backtracked more than moving forward. I might consider prp'ng more productive.:sad:

[quote=engracio;206090]I have not given up yet but if I backtracked more than moving forward. I might consider prp'ng more productive.:sad:[/quote]

Indeed Engracio, I can sing a song about this....:smile:..and now add
2000 decimal digits to your number :surprised

I believe 11467 digtis with PRIMO is the highest of emotions.

[quote=Cybertronic;206093]Indeed Engracio, I can sing a song about this....:smile:..and now add
2000 decimal digits to your number :surprised

I believe 11467 digtis with PRIMO is the highest of emotions.[/quote]

I know, I know. You have done more difficult primes than I and it is also different to you than the other primes.:huh:

When I run all 5 runs on a test overnight, when I wake up I see 4 different digit bit next test. Which one do you pick with better chance of not backtracking?

The excel file is more important than ever now due to more backtracking of tests.

[quote=engracio;206095]
When I run all 5 runs on a test overnight, when I wake up I see 4 different digit bit next test. Which one do you pick with better chance of not backtracking?
[/quote]

When you have 4 different ways than you have luck. Ever way is important.
You start the TEST x with the lowest bit and test RUN 1,2,3,4 ... if not TEXT x+1 then you start another TEST x
Example:
You will save all 4 ways of TEST 10.
copy *.tmp to *.10_30901
copy *.tmp to *.10_30893
copy *.tmp to *.10_30907
copy *.tmp to *.10_30899

4 ways is good, you have enough margin to get no backtrack...
or you start this 4 ways similtaneous. Start with RUN 1

[quote=Cybertronic;206096]
4 ways is good, you have enough margin to get no backtrack...
or you start this 4 ways similtaneous. Start with RUN 1[/quote]

Next time I will try it. Just hate picking the wrong one and going back again.:down:

Good news - I have just finished verifying that all of the primes in our list less than Norman's 2[SUP]38090[/SUP]+47269 are indeed the smallest in their respective sequences, so we haven't wasted any Primo cycles! I expect to get most of the larger ones verified next week, but I don't expect anyone to reserve 2[SUP]56366[/SUP]+39079 before then. (It is doubtful whether Primo can even certify such a huge number, 16968 digits!)

[quote=engracio;206098]Next time I will try it. Just hate picking the wrong one and going back again.:down:[/quote]

...then it is better you start 4 ways at the same TEST. There is ever a good chance to get the next TEST. My experience.

The good news is, when you overcome the backtracks then you have "free drive" for the next 20 TESTs and the number of bits fall down to bits-500


Cheer up !


Ahhh , addition to RUN 5 . The process for larger index numbers will be slower and slower.... so the maximum I test is index=110000. (138000 is the maximum and take a lot of time for nothing)

[quote=philmoore;206099]Good news - I have just finished verifying that all of the primes in our list less than Norman's 2[sup]38090[/sup]+47269 are indeed the smallest in their respective sequences, so we haven't wasted any Primo cycles! I expect to get most of the larger ones verified next week, but I don't expect anyone to reserve 2[sup]56366[/sup]+39079 before then. (It is doubtful whether Primo can even certify such a huge number, 16968 digits!)[/quote]


Nice ,Phil ! You call the numbers as PRIME :smile:.
BTW, a 16968 digit number takes 700 days (on a Phenom 965,using 4 cores) , if PRIMO can handle this.
2250 TESTs total. Note, the energy costs are (500 EUR,700 dollars)

status report: TEST 152 34096/38091 , done maybe end of May 2010
I will report a new status every 50 TESTs.

Well after two restart because of all the backtracking, the third I guess is the charm:smile:. I have finally broke the 30 test level and moving along until I hit the next 20 test brick wall. This iteration sure feels a whole lot better than the first two. I do not know why the first two was problematic but it was.:sad:

Hello everyone.

On February 21st 2010, I did a discovery, that will maybe benefit this project greatly. In simple terms, I concluded, that any number can be proven prime using WinPFGW even if the number is of the form i.e. 2^28978+34429. So how to do it?... you may ask. "Simple"... i may not say, however it is duabel, without the use of Primo or other "bruteforce" non mathematical model prime search programs or scripts.

I concluded on February 21st 2010, that ALL numbers (at least ALL positive, and maybe even 0) but at least all numbers>0 can be converted to the proveable form of: k*b^n-1 (but not k*b^n+1) or in most cases k*(prime)b^n-1. So now I'm just awaiting to hear news from Geoff on weather or not he can make a program that can search and find a solution of the form k*b^n-1 for any number >0 and have it printed to an input file which can be used for Mprime, WinPFGW, LLR or whatever program one prefers to use as proofing program.

I'm not sure if this is of any use at the moment, but if Geoff declines to make such a program that can search for any possible solution of the form k*b^n-1 that makes a total convertion for any positive number >0, then does anyone here knows of someone else who will or would be willing to make such a program? Remember if such a program is made properly, it will very fast find a solution with an exact Log(PRPnumber)=Log(k*b^n-1 solution) match.

It is possible to find a match using a spreadsheet, but due to the limitations of only comparing the Log number to the 15th decimal, it means that it is hard to rule out many of the false solutions, wich will either be a little to big or a little too small, presented by the spreadsheet.

Sorry for this long posting, but in short terms, spare your resources currently spend on running proofs using Primo, since I think they are better spend on trying to find the remaining PRP and withhold proving the remaining PRPs untill some sort of conversion program is created.

Well this was just my 2 cents on this one, but I know for a fact that now in stead of talking trillions and trillions of years on prooving a megaPRP, it will and should actually be possible to do it (dependent on how long the solution takes to find) in a matter of days or weeks (at most) :smile:

Hope this all made sence. Else feel free to ask any questions and I'll try to give you my thoughts and answers as best as I can.

Regards

KEP

[QUOTE=KEP;206774]
I concluded on February 21st 2010, that ALL numbers (at least ALL positive, and maybe even 0) but at least all numbers>0 can be converted to the proveable form of: k*b^n-1 (but not k*b^n+1) or in most cases k*(prime)b^n-1.[/QUOTE]

I am extremely skeptical. You are saying that for for any positive q, it is possible to write q as k*b^n-1 for some k and b such that pfgw can then run a deterministic primality test. This requires a factorization of q+1 as k*b^n, and most people believe factoring q+1 is in general a MUCH more difficult problem than proving whether q is prime. Recall that even proving numbers of the form k*2^n-1 prime requires k < 2^n, which rules out most possible numbers q. So even if we don't need to factor k itself, finding a base b seems most unlikely.

If you still think you are on to something, try presenting a small example to show us how your method works.

[QUOTE=KEP;206774]
I concluded on February 21st 2010, that ALL numbers (at least ALL positive, and maybe even 0) but at least all numbers>0 can be converted to the proveable form of: k*b^n-1 (but not k*b^n+1) or in most cases k*(prime)b^n-1. [/QUOTE]

What do you mean with [COLOR="Red"]k*(prime)b^n-1[/COLOR] ?

Luigi

[QUOTE=philmoore;206782]I am extremely skeptical. You are saying that for for any positive q, it is possible to write q as k*b^n-1 for some k and b such that pfgw can then run a deterministic primality test. This requires a factorization of q+1 as k*b^n, and most people believe factoring q+1 is in general a MUCH more difficult problem than proving whether q is prime. Recall that even proving numbers of the form k*2^n-1 prime requires k < 2^n, which rules out most possible numbers q. So even if we don't need to factor k itself, finding a base b seems most unlikely.

If you still think you are on to something, try presenting a small example to show us how your method works.[/QUOTE]

Well I don't have an example, but I know, that for a fact running a 10000 digit test and prove if composit or prime can be done for the form k*b^n-1 in most cases (unless you have a several million digit base) in less than 10 seconds, while today you are using several months maybe even years on proving a q=2^n+p, which gives a lot of time to find the exact log(q)=log(k*b^n-1) solution.

Finding a solution with the proper software, should be done rather quickly, since it can be done this way:

using 2^28978+34429=q

q=8724 digits and log(q)=8723,2472143508470749037256913264

Now we have to find a k*b^n-1 solution where log(k*b^n-1)-log(q)=0

Since we are interested in finding the smallest k and the lowest base, our starting base should be 2. Now we have to do as follows:

log(q)/log(b)=log(8723,2472143508)/log(0,3010299956)=28978
Our starting n is then n=28978
Since we know that we can not exceed or go below log(q), then we now have to find the first k, for which k*2^28978-1 equals log(q). In my case I found using my spread sheet a strong candidate, which of course didn't match the full log(q), but for 1*2^28978-1 only the last 5 decimal digits in the decimal expansion varied from 2^28978+34429 (most likely the difference is 34430 since my strong solution is 2^28978-1).

It is obvious that non of your numbers can be transformed into a k*2^n-1 number, but the system is the same, no matter what base is used. I have manually checked up to n=24 and all prime bases <100, but no solutions was found. But the system is that one keep shooting for the lowest possible k and starts out with the lowest possible base. According to my experiences, it should also be enough to only test for solutions looking like this: k*primebase^n-1, since it should cover all positive numbers possible to write in the world.

I hope you got the idea, but to sum up, it is faster to prove a k*b^n-1 number and it is possible to write all q as k*b^n-1. And according to my system, it comes down to searching for a log(q)-log(k*b^n-1)=0 solution, starting out with the lowest possible base and searching the highest possible n, simply to get the lowest possible k in the solution.

Regards

KEP

[QUOTE=ET_;206784]What do you mean with [COLOR="Red"]k*(prime)b^n-1[/COLOR] ?

Luigi[/QUOTE]

Short and easy answered: k*primebase^n-1

I mean by that, that all numbers in the world should be possible to write in the form of k*primebase^n-1. Actually it appears to be much the same as factoring is only nescessary to do for p=prime, since all other p's is factoring the same numbers as p=prime. So in this case all k*primebase^n-1 covers the same numbers as k*b^n-1 would do.

Hope this covers your question.

Regards

KEP

You mean, some (every) number q , we can transform into q=k*p^n +/-1 ?

I think , that is not possible.

"using 2^28978+34429=q"

The factors of 2^28978+34428 or 2^28978+34430 are very rare. So it is not
sure to find (all of thinks) another relevant p^n what divided q-1 or q+1. Not in numbers with more than 10000 digits.

Maybe "pfgw" look for such forms.

both

"34201516571902560263*6^ 458 +1"
and the full length
"84589808111699289076243980310211398247526850801960339840075034~
984937005024785098788429830885818943087114229827966521865223571~
519264113061169061153911278676167484505717761550245627075220022~
027484879544154295256581059294887566388370992159484228535984032~
144355515243922299730621242005526658978769754968619183432465407~
98095726043089650831743692750635100484349589165217838171947009
"

we get with -tc option "is prime!"

Yes every number q is possible to transform into the form of:

q=k*b^n-1 or q=k*(p)b^n-1

If we are searching for only odd q, which any prime q above 2 is, then we will be covered by searching only the primebases. But regarding the transformation of q into k*b^n-1, then it is all a matter of having the right software, which does a search for a solution according to my previous post. If the numbers are very small, then it can be done manually, however with big numbers, it is nescessary with some sort of software to do the search among the primebases for a k*primebase^n-1 solution wich meets the demand of having log(q)-log(k*b^n-1)=0! With huge numbers, there is too many k/n solutions to search, before the right one is found, to even making it remotely possible to do by hand.

I'm not sure if I quite understood everything you wrote mr. Cybertronic, however in short terms, all q=k*b^n-1 it is just a matter of finding the right base and the right k.

However, I'll try to build a list, showing all q<=1M and wich k*primebase^n-1 they transform to. I'll construct the list such as k<b^n

Hope I got it right and got it all.

Regards

KEP

[QUOTE=KEP;206828]
I'll try to build a list, showing all q<=1M and wich k*primebase^n-1 they transform to. I'll construct the list such as k<b^n

Hope I got it right and got it all.

Regards

KEP[/QUOTE]

Mind that pfgw has another limitation, IIRC: k<2[sup]63[/sup].

Luigi

[QUOTE=ET_;206831]Mind that pfgw has another limitation, IIRC: k<2[sup]63[/sup].

Luigi[/QUOTE]

Okay I didn't know that, but that could potentially cause a problem since some of the PRPs here, might convert to a solution where k>2^63 even though the k's will start out low. Do you happen to know about any limitations in the base?

If I recall correctly, the limitation in n is maybe 12 million digits or maybe n=12M, this may however have changed since it was in a 2 year old version of PFGW that I read that.

However no matter what limitations there is to the software currently, it doesn't change anything regarding the fact that all q=k*b^n-1 :smile: (and maybe it is enough to search only k*(p)b^n-1 even though a further study should clear up that theory).

On another note, the limit in k, will eventually cause a problem for CRUS, unless another solution is found in the future once they eventually exceed the k limit on the really big conjectures :smile:

Regards

KEP

[QUOTE=philmoore;206782]I am extremely skeptical. You are saying that for for any positive q, it is possible to write q as k*b^n-1 for some k and b such that pfgw can then run a deterministic primality test. This requires a factorization of q+1 as k*b^n, and most people believe factoring q+1 is in general a MUCH more difficult problem than proving whether q is prime. Recall that even proving numbers of the form k*2^n-1 prime requires k < 2^n, which rules out most possible numbers q. So even if we don't need to factor k itself, finding a base b seems most unlikely.[/QUOTE]

Phil was being polite. Let me be blunt. Your idea can NOT, does NOT, will NOT work. Please stop extrapolating from tiny examples.

You are factoring q-1 or q+1 into k*b^n.
[U][COLOR=#810081][URL="http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic"]Fundamental_theorem_of_arithmetic[/URL].[/COLOR][/U]
n can only be as high as the highest degree of the consituent prime factors which will be very small (single digits), and k will be the rest.
No use.

Axn and Batalov, its obvious none of you are getting what I'm saying, so please talk nice to me. But since you don't care, then I really will not spend any more time on this very productive idea. Just remember for future references, that just because there is something one doesn't get, it doesn't mean that it is impossible or that you can allow yourself to blunt. But it's all up to yourself, but a fact is that if your project isn't open to new ideas, then nothing usefull is ever going to be produced.

Apparently this project is just a waiste of time, so I'm just glad that nothing much of resources has been waisted on trying to figure a way to help you.

TAKE CARE!

KEP

EDIT: Just took a look at the wiki link, it just emphasize that none of you are getting what I'm stating or trying to explain. But as previously mentioned it's your waist of resources and gladly not mine!

Hey KEP, keep cool !

I'm sure it is easy to show that one of our numbers we can't transform into k*p^n+1 (or -1). Is there generally an example then it is a huge of luck.
My opinion.

"EDIT: Just took a look at the wiki link, it just emphasize that none of you are getting what I'm stating or trying to explain. But as previously mentioned it's your waist of resources and gladly not mine!"

This is not fair.

Otherwise you have right. Every prime is of form k*2^n+1 :smile:

23=11*2^1+1
29=14*2^1+1
31=15*2^1+1
...

[quote=KEP;206828]However, I'll try to build a list, showing all q<=1M and wich k*primebase^n-1 they transform to. I'll construct the list such as k<b^n[/quote]
Do that for q=419. Take care. -Serge

(due to length limitations, instead of having the giant number here, I'm just going to link to its page at the FactorDB, and replace it throughout with 'm')

m is chosen as the odd number such that 2^21954+77899=m*2^n-1.
m=[URL="http://factordb.com/search.php?id=153093338"](2^21954+77900)/4[/URL]
[code]2^21954+77899=m*2^2-1[/code]This has already been proven prime by conventional means, and is just being used as an example.
Here's what PFGW does with it, with this command: "-qm*2^2-1 -tp"
[code]PFGW Version 3.3.1.20100111.Win_Dev [GWNUM 25.13]

Primality testing m*2^2-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FFT length 2048 on 2^21954+77899
Calling Brillhart-Lehmer-Selfridge with factored part 0.28%
m*2^2-1 is Lucas PRP! (9.3029s+0.0805s)

Done.
[/code]Why did it revert to a PRP test instead of being able to do a N+1 primality test? Read this from pfgwdoc.txt: (bold mine for emphasis)
[quote]A.3. More details/methods used

Pfgw can work with numbers from 2 up to almost 2^79700000 (about 24000000
digits). It can find probable primes with Fermat's method, with bases
from 2 to 256.
To be more precise: The largest FFT is 4 million elements long, with 19
bits per element. GFN's can be tested upto 24M digits, and generic numbers
upto 12M digits.
To prove a number prime, other methods need to be used.
[B]Only a small percentage of all numbers can be easily proven prime.
Name a number N, then you must be able to factor N-1 or N+1 to 33.33% to
find a proof using PFGW.[/B]
If N-1 is factored deep enough, then Pocklington's test can be applied.
If N+1 is factored deep enough, then Morrison's test can be applied.
If N^2-1 is factored deep enough, a combined method can be used.

A.3.1 Fermat's method
Fermat's method is NOT a proof, but more like a quick indicator that a
number might be prime.

A.3.2 Pocklington's test
This test can be used whenever N-1 can be factored to 33.33% of the size
of N. (Actually, the factored part must be greater than the cube root of
N/1000000). This test is conclusive.

A.3.3 Morrison's test
[B]This test can be used whenever N+1 can be factored to 33.33% of the size
of N.[/B] (Actually, the factored part must be greater than the cube root of
N/1000000). This test is conclusive.

A.3.4 F-Strong test
This test is used when you use the -t option, and your factors don't reach
the magic 33.33%. It is a strong-primality test, and gives more certainty
than a Fermat test, but still is NOT a proof!
[/quote]So unless N+1 can be factored to 33.33% of the size of N, you can't do the conclusive N+1 test. (and same thing with N-1) It is, of course, possible to turn any number into k*b^n-1, and (I think) possible to use an N+1 test on any number, but unless the k is smaller than b^n, you probably won't meet that magic 33.33% size limit without factoring N+1.
So you can trade a difficult primality test for an easy one in addition to a difficult factoring. It is MUCH easier to do a primality test on a number with thousands of digits than to try to factor a number with thousands of digits. With current hardware and methods, and without extraordinary luck, it's basically impossible to factor m.

Kenneth-

In addition to what Tim wrote, I can add that for some special forms we can use the "helper" primes. One of the larger examples that I found last summer was a 9016-digit PRP
[FONT=Fixedsys]N = (52*10^9015-43)/9 = 57777...77773[/FONT] (many sevens in the middle).

Why is that? That's because N-1 factors to slightly more than 33.33%.
The rich collection of repunits is studied fairly well, and it turns out that
[FONT=Fixedsys]N-1 = (52*10^9015-43)/9 -1 = [/FONT]
[FONT=Fixedsys]= (52*10^9015-52)/9 =[/FONT]
[FONT=Fixedsys]= 2^2*13*(10^9015-1)/9 =[/FONT]
[FONT=Fixedsys]= 2^2*13*(10^3005-1)/9 * c6011[/FONT]
But (10^3005-1)/9 happens to be [URL="http://hpcgi2.nifty.com/m_kamada/f/tm.cgi?p=31"]fully factored[/URL] (which is lucky! because this is 33.33% of the N-1).

After proving primality of the 2379-digit cofactor with Primo, I provided these and a few small prime factors from the 6011-digit cofactor in a helper file, and voila - a proof by PFGW with 33.62% factored part. All less than in a day (including Primo).

[FONT=Arial Narrow]Primality testing (52*10^9015-43)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file ../h9015
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 5+sqrt(5)
Calling N-1 BLS with factored part 33.62% and helper 0.05% (100.92% proof)
[B](52*10^9015-43)/9 is prime![/B] (27.5956s+0.0014s)[/FONT]

There are much more elegant examples (see [URL="http://tech.groups.yahoo.com/group/openpfgw/"]openpfgw yahoo group[/URL]), but this is one is very simple to tell in one paragraph. (not bragging; this is not a very large number)

See PFGW's manual about the helper file.

-Serge

A followup on the notice from Wilfrid Keller:

He has now confirmed that all primes (or prps) up to 2[SUP]61792[/SUP]+21661 are indeed the smallest in their respective sequences, and has tested the remaining sequences out to n = 42000. I have independently confirmed all of his findings, and continued up to 2[SUP]551542[/SUP]+19249. This leaves only the six largest probable primes not confirmed to be the smallest in their sequences, so I will slowly continue this project. We did find one more error on Payam Samidoost's webpage, the prime 2[SUP]1622[/SUP]+32449 was apparently missed, as the prime listed for that sequence was 2[SUP]1814[/SUP]+32449. Given that 2[SUP]1885[/SUP]+29777 was also missed, but later discovered, I suspect some errors in early versions of pfgw. Mark assures me that error checking is much more robust in the current version. Samidoost's webpage has disappeared, but I replaced the link with the cached version of Neil Sloane's:
[url]http://www.research.att.com/~njas/sequences/a076336c.html[/url]

I intend to prepare a file of Sloane sequence A067760 as far as (78557-1)/2soon and upload it to the Forum.

Status:
Phase 1:TEST 200 (9879 digits left, 70 days to go)
Phase 2:TEST 1-159 done.

Status:
Phase 1:TEST 250 (9365 digits left, 60 days to go)
Phase 2:TEST 1-209 done.

Happy easter !

Now I'm below 30000 bits ! :smile: 60% done.

Status:
Phase 1 TEST 300, 8895 digits left, 46 days left
Phase 2 252 TESTs done

Next report at TEST 400 in 14 days

Status:
Phase 1 TEST 400, 8032 digits left, 32 days left
Phase 2 345 TESTs done

Next report at TEST 600 at May, 7th

So people , new status.. not 600, but 566 :smile:

Phase 1 at TEST 566 (6699 digits left)
Phase 2 TESTs 1-499 done.

May, 25th was calculated ... then the certificate is available.

Status:
Phase 1 at TEST 800, 4916 digits left
Phase 2 1-720 done
Signing points 1-684 complete

In PRIMO , I like this number :smile:!
[url]http://www.sendspace.com/file/1un0wn[/url]

Very nice, test 1000! Looking forward to an announcement later this week...

[quote=philmoore;215769] Looking forward to an announcement later this week...[/quote]

later this week ? :smile:

I'm shure , the certificate is done today :banana:

Ph1 : TEST 1156 , 2200 digits left
Ph2 : TEST 1119
Signing points 1-1039 done

I did it ! New record proven prime by PRIMO
 

Hello primfans, you read correct !

The 11467 digit number " 2^38090+47269 " is now PROVEN PRIME by PRIMO !!!

:fusion::bounce wave:

Running time was full 5 months of uninterrupted computation on a 3,4 GHz Phenom II X4 965 processor. ... or >> 150000 hours on a Athlon 1 GHz system.

More details in Logbook.xls and ecpp11467.out file.

Certificate available here:
[FONT=&quot][URL]http://www.sendspace.com/file/wanpui[/URL][/FONT]

So, after one year of PRIMOing , I make a break here.

A well-deserved break! Congratulations on the incredible achievement! :bow:

:party::party::party:

:maybeso::banana::maybeso::banana::maybeso:

:bow wave::bow wave:

[QUOTE=philmoore;215871]:party::party::party:

:maybeso::banana::maybeso::banana::maybeso:

:bow wave::bow wave:[/QUOTE]

Yeah, what Phil said. Awesome work!

Thank you !! :smile:

[QUOTE=Cybertronic;215881]Thank you !! :smile:[/QUOTE]

Congratulations Norman! :smile:

[quote=philmoore;215871]:party::party::party:

:maybeso::banana::maybeso::banana::maybeso:

:bow wave::bow wave:[/quote]

Good job Norman!!! Congratulations. I am getting there, slow, but getting there.

I take "2^28978+34429". 45 days are acceptable. So the list will be complete what we can do with PRIMO. :smile:

What would it take to test the next few numbers in the list, besides lots of CPU time? A new version of Primo, whole new software, something more?

My understanding is that we are only limited by two things - time and the 50K bit limit of Primo. Software that is threaded (i.e. software that automatically does the same thing that Cybertronic does manually) and didn't have the bit limit should enable us to test at least the next few numbers in a semi-reasonable amount of time, especially if it could be multi-threaded across 4, 6, 8, or even more cores.

First of all , the latest version is not limited ... I mean , you can test more than 100000 bits. It is enough for a world record.

The power law is d^3,75 and that is very stable.

The next number takes about 18 months on a 3,4 GHz quadcore and have near 17000 digits. The chance is marginal to prove this large numbers.
It was a luck for me. Maybe one point I had have to finished TEST 1, only one ! My gigantic triplet with 10047 digits from 2008 , I can't certified with PRIMO.


More cores than 4 are better. You can TEST more possible ways simultan, also you can calculate Phase 2 parallel.

I don't believe that exist a multicore version of PRIMO...for Marcel is it to
expansiv to rewrite. He told it me one year ago.

"You to be crackers" to beat the actual record..it was very hard for my nerves. You need near 120 days a full time visual contact to the display.
I doubt that PRIMO can certified the actual record alone. Is it so, it takes near 3 years on a Phenom 965.


So, the first 100 bit are done ( at TEST 4 )

Thank you for the information. I thought the latest version was still limited to 50K bits. Also, I did not know there was luck involved with proving the large numbers, just time.

My memory may be fallible here, but I do remember Marcel Martin expanding his table of discriminants in one release of Primo. He said that it would increase the size of numbers that could be proven with the program, but that at some point, the program would run in to numbers that it could not certify. My guess is that Francois Morain's FastECCP program plus access to a sizeable cluster of processors could probably do the next four numbers, but I don't believe that his program is publicly available. The record Mills' prime with 20562 digits was proven on a cluster in 2007 after 9 months of work! Of course, computers are faster now...

Too bad that Marcel does not have the time or inclination to write a multi-processor version, but Norman has definitely proven that the concept is a good one. Sooner or later, some programmer will take up the challenge.

[quote=philmoore;216131]My memory may be fallible here, but I do remember Marcel Martin expanding his table of discriminants in one release of Primo. He said that it would increase the size of numbers that could be proven with the program, but that at some point, the program would run in to numbers that it could not certify. My guess is that Francois Morain's FastECCP program plus access to a sizeable cluster of processors could probably do the next four numbers, but I don't believe that his program is publicly available. The record Mills' prime with 20562 digits was proven on a cluster in 2007 after 9 months of work! Of course, computers are faster now...

Too bad that Marcel does not have the time or inclination to write a multi-processor version, but Norman has definitely proven that the concept is a good one. Sooner or later, some programmer will take up the challenge.[/quote]
Following links on the Prime Pages' [url=http://primes.utm.edu/bios/page.php?id=689]FastECPP entry[/url], I was able to find what appears to be a downloadable FastECPP version [url=http://www.lix.polytechnique.fr/~morain/Prgms/ecpp.english.html]here[/url]. Might this be what you're looking for?

Also, a quick question since I'm not very familiar with how ECPP works: just how parallelizable can it get? That is, with FastECPP, can it be massively distributed (i.e., split up into work chunks and reserved by a disparate group a la PRP testing or sieving), or does it have to be done within a somewhat-directly-connected cluster?

That version of Francois Morain's ECPP program dates from April 2001 and predates the FastECPP version, I believe.

I expect that "parallel" here means that different processors investigate different paths to try to reduce the complexity of the problem, as measured by the bit length of the current prp for which a primality proof is desired. But the different paths must be compared regularly to see which one is actually making the best progress, so that the less productive paths can be pruned, and new branches can be spun off the more productive paths. So yes, ongoing communication between the various processors is necessary. Some of the papers on Morain's webpage would give more specific details, of course.

[quote=philmoore;216131]My memory may be fallible here, but I do remember Marcel Martin expanding his table of discriminants in one release of Primo. He said that it would increase the size of numbers that could be proven with the program, but that at some point, the program would run in to numbers that it could not certify. [/quote]

I have this version ... (8 tables) ,but it was also not usefuly for my 10047 digit number. The MSC-feature in the actual version is much better than the 8 tables,definite!

For the actual record number , Marcel told me : " I'm in an unknown land ! "

The 8 tables version was maybe good for 6000 digits , but at that time nobody will try a 11k digit number and will risk a runtime of factor 40 or more.
For this numbers ,the powerlaw is not 4,5-4,9. It is maybe >6. Well, a 1 GHz Athlon need maybe 15-20 years for my number,alone.

Status of 2^28978+34429:

Ph1: TEST 50 (8277/8724 digits)
Ph2: 1-22 done

Elapsed time: 150h

[quote=Cybertronic;216892]Status of 2^28978+34429:

Ph1: TEST 50 (8277/8724 digits)
Ph2: 1-22 done

Elapsed time: 150h[/quote]

Wow Norman at your pace, you would probably finish your prime before I finally finish mine. You are blasting away Norman.:smile: Good job.

Thanks engracio.

All to go according to plan. Maybe done at 10th July[U][B][/B][/U][URL="http://www.dict.cc/englisch-deutsch/plan.html"][/URL].

What is your status ?

Best,
Norman

I am just running AMD 965 4x now and just on test 275 since 14 Feb.:sad: Overall I am happy with the progress. I know I will eventually finish it.:smile:

Oh, the same maschine like me :smile:.

Your number will have 1230 TESTs total. You have maybe 24500 bits left
and 60% done. In 5-6 weeks you are done.

[quote=Cybertronic;217148]Oh, the same maschine like me :smile:.

Your number will have 1230 TESTs total. You have maybe 24500 bits left
and 60% done. In 5-6 weeks you are done.[/quote]

Thank you Sir, that is good to know.:smile:

Oopps, I meant AMD 925 4x. Couple month is not that far away.:smile:

Engracio, do you delete the lines sf= and pm= of Phase 2 manual ?
There exist a trick. I have found it during my last one.

[quote=Cybertronic;217510]Engracio, do you delete the lines sf= and pm= of Phase 2 manual ?
There exist a trick. I have found it during my last one.[/quote]

Yes I did, I was going to do the same thing on this prime. Found another shortcut? Please share.:smile:

I try to explain it.
1. create a new directory and copy all PRIMO files in the new one.
2. copy the actual tmp file in this one.
3. create a new input file with a tiny number , like 10^300+331
4. start the certification for this number and stop after 1-2 seconds.

so,...

Assumed you are at Phase 1 on TEST 301 ...
copy the last TEST of the tiny number certificate , like

[19]
Type=-4
....

and append it in the master TEMP-file of your huge number.

rewrite [19] into [301] , set to begin at line 7 "TestCount=301"

start PRIMO with this new file and you will see, PRIMO
start PHASE 2 afetr any seconds.

Stop it !

Delete all informations from TEST [301] to end of file. Continue the old procedure for Phase 2.

Why is it so ?

When PRIMO finished Phase 1 and start Phase 2 , PRIMO write automatic
a new file from memory to disc , without the line "pm=" in every TEST.
So you have not the lines "pm=" and "sf=" when PRIMO finished TESTs of PHASE 2 .