Pascal's OPN roadblock files

[henryzz]

Originally Posted by SuikaPredator

Finished t25 for composites<=10**150 in 2000_restricted. The first factors are attached.

For the composite cofactors, does this project need to factor them as deep as possible? Or we can stop after finding the first factor of each composite number?

If the answer is positive, then I will continue to factor these cofactors. Otherwise I will continue to do t30.

Multiple factors are useful but not required(most of these are not really "required"; they just help shorten the proof). Also, in general, the larger the factor, the better, as that means fewer branches on that factor. Multiple factors are also useful as often there will be a \(\sigma({x^n}) = \frac{x^{n+1}-1}{x-1}\) that has no useful factors known that will lengthen the proof without a good alternative. For an ECM pass, I wouldn't worry too much about factoring cofactors. If they are needed, the cofactors will reappear once the proof tree has been rerun again.

The aim of factoring these numbers is to shorten the proof sufficiently so that a deeper proof can be considered in a sane amount of time. There are composites that completely block the proof, but the majority of the tree is more limited by compute power. Once we have put a decent amount of effort into reducing the length of the whole proof tree, I will run portions of it much deeper, effectively allowing us to ignore that portion of the proof tree until we want to extend further. I have run much of the proof tree to 2500 in the past, although this has included some very long runs that can be shortened considerably. On other bits, I only reached 2300 mainly due to runtime, although there is a bit under 11^330 / 3^4 / 5^1 / 103^172 / 227^4 2666986681^36 that needs many factorisations to be improved to 2300(either that or very large ones).

[mataje]

c94-96 finished.

[SuikaPredator]

Originally Posted by henryzz

Multiple factors are useful but not required(most of these are not really "required"; they just help shorten the proof). Also, in general, the larger the factor, the better, as that means fewer branches on that factor. Multiple factors are also useful as often there will be a \(\sigma({x^n}) = \frac{x^{n+1}-1}{x-1}\) that has no useful factors known that will lengthen the proof without a good alternative. For an ECM pass, I wouldn't worry too much about factoring cofactors. If they are needed, the cofactors will reappear once the proof tree has been rerun again.

The aim of factoring these numbers is to shorten the proof sufficiently so that a deeper proof can be considered in a sane amount of time. There are composites that completely block the proof, but the majority of the tree is more limited by compute power. Once we have put a decent amount of effort into reducing the length of the whole proof tree, I will run portions of it much deeper, effectively allowing us to ignore that portion of the proof tree until we want to extend further. I have run much of the proof tree to 2500 in the past, although this has included some very long runs that can be shortened considerably. On other bits, I only reached 2300 mainly due to runtime, although there is a bit under 11^330 / 3^4 / 5^1 / 103^172 / 227^4 2666986681^36 that needs many factorisations to be improved to 2300(either that or very large ones).

Thanks for your detailed explanation. I will start doing t30. ETA May 9th.

[RichD]

A few more factors, if that's really all you need.

25556569658706368570429153
33762439969732650496134934812063861
11861214939725873456103559476042771841001131369604977
2354021225314267859219759601719997648330229647716959566990031

[mataje]

c97-99 finished.

[RichD]

A few more factors.

44898512899162733098135716004212530897
72707919297080088332921
18348284939757090737339114103079
97169484175318543075612267
866299577824329495009702713072389077013371318167249403611717
710370740208939975391851961944124888159297643968424605203416175219402236939673863

[mataje]

c100-101 finished.

[SuikaPredator]

Originally Posted by SuikaPredator

Thanks for your detailed explanation. I will start doing t30. ETA May 9th.

t30 done. Factors attached.

[SuikaPredator]

Some extra p-1 factors. Not efficient enough, so I will start t35, ETA "a few months later".

Input number is 2104598320219474543812427397239101630722918462694114977979508922735781932841092862647410452496442337701 (103 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=1131360803
Step 1 took 12859ms
Step 2 took 11875ms
********** Factor found in step 2: 344213958442858553966884710470461
Found prime factor of 33 digits: 344213958442858553966884710470461
Composite cofactor 6114215500557190968396922553674965767799119994014302611674186271880841 has 70 digits
Input number is 5964026232561325873924927219890165557734005697859906340413832242794737748052349996237305295618589842149 (103 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=2545655445
Step 1 took 12422ms
Step 2 took 10985ms
********** Factor found in step 2: 163537444400419909441378778509
Found prime factor of 30 digits: 163537444400419909441378778509
Composite cofactor 36468872645205725435591832369290985442480683431781676796996904145857355961 has 74 digits
Input number is 456671345906930994911229412792649624202722139083433799828564730260868306170599419217743630674119799909987 (105 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=3237737116
Step 1 took 12297ms
Step 2 took 8406ms
********** Factor found in step 2: 117258802451589272599400701596721
Found prime factor of 33 digits: 117258802451589272599400701596721
Prime cofactor 3894559183268731043692456226412265542814599309027319020801908412011752147 has 73 digits
Input number is 2304600351049741929497540242633892443993579970229201753378577163328402687977219475759928433790025664175103 (106 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=2892538102
Step 1 took 12140ms
Step 2 took 5813ms
********** Factor found in step 2: 22293105058643331586151138526983989
Found prime factor of 35 digits: 22293105058643331586151138526983989
Prime cofactor 103377270460411610648960518730861405294025705776637156167329743303526627 has 72 digits
Input number is 242566136568727192405305048460729950055255132899334499677261713271511984292999630119166737157042023337233016739 (111 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=2588141958
Step 1 took 12250ms
Step 2 took 6313ms
********** Factor found in step 2: 25158900272933498638481100893549
Found prime factor of 32 digits: 25158900272933498638481100893549
Composite cofactor 9641364842551771113904092526251783619263806574757160746459500095166727505727311 has 79 digits
Input number is 344082756699542441931989735935695089404636479500734043625079903148042410890220864326262644208479324066382487929 (111 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=3160094309
Step 1 took 12062ms
Step 2 took 6172ms
********** Factor found in step 2: 3873715076016074696074513931714813
Found prime factor of 34 digits: 3873715076016074696074513931714813
Prime cofactor 88825003890945593901141444737144334983217520761229097487214557025729249810733 has 77 digits
Input number is 423717135565056659784023345623815337641414837539489226048344463841916043607762251191080864006806497517639717877 (111 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=3277577262
Step 1 took 12547ms
Step 2 took 6187ms
********** Factor found in step 2: 33870443354896942317050998082228359
Found prime factor of 35 digits: 33870443354896942317050998082228359
Composite cofactor 12509937680039142935369013335832727958470448875366387633703960562087373079203 has 77 digits
Input number is 1793589543028063385582054884751986848986453553545865632736208094550929783640645018099617206429793747542842810091 (112 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=2755806758
Step 1 took 12406ms
Step 2 took 6375ms
********** Factor found in step 2: 233415057052322711419441276362599509
Found prime factor of 36 digits: 233415057052322711419441276362599509
Composite cofactor 7684121006066927977442124665595559778852001585769233682104587791137014734399 has 76 digits
Input number is 13006210747626311742782453093477987339187665096181060757193363219879070607945312452181827385070588287405898262479 (113 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=3372183795
Step 1 took 11984ms
Step 2 took 5969ms
********** Factor found in step 2: 923355715832346317436268413413
Found prime factor of 30 digits: 923355715832346317436268413413
Composite cofactor 14085807370458568992411137844533809360719693111967248788446570397206713984972568483 has 83 digits
Input number is 44585354968681859784240901105585273614921049444221380656504024243644593772755843452053157047489186040334783812213 (113 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=608531765
Step 1 took 11922ms
********** Factor found in step 1: 3429125976544672902789410706091721
Found prime factor of 34 digits: 3429125976544672902789410706091721
Prime cofactor 13001958887963597256534616788072895966934258280597071125057065458304323285631053 has 80 digits
Input number is 5878164161978325356022227921761786463203506036070438277128323886690328297861964552193616503110545951673073612703957 (115 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=3679736198
Step 1 took 12266ms
Step 2 took 6297ms
********** Factor found in step 2: 568646692132982609017719511
Found prime factor of 27 digits: 568646692132982609017719511
Prime cofactor 10337111326418600395425255119910212003054958491495134919279776912380082417620104037441587 has 89 digits
Input number is 11802906666001421989796147150648619876959884385793294262791849047426191447215225017220364161167499776324941278708331 (116 digits)
Using B1=100000000, B2=4537592002678, polynomial x^1, x0=2138610516
Step 1 took 12000ms
Step 2 took 6156ms
********** Factor found in step 2: 12438786026043770804377191457
Found prime factor of 29 digits: 12438786026043770804377191457
Composite cofactor 948879307135682436673337966536630110355652194716919546847232315832012032807468168918283 has 87 digits

[henryzz]

I have posted files at https://drive.google.com/drive/folde...4RYaJlVZzZhf-s with the latest factors removed.

I am going to start the process of rerunning to 2000. I am likely to run this at least twice. I believe that after I run it once, there will be a number of new composites based on our newly found factors that can be dealt with fairly easily. Depending on how many of these there are, I will likely just run some ecm on them myself before rerunning.

Does anyone use the 1500 files? If nobody does, I will retire them.

[kruoli]

Do the 1500 files have no use for larger runs?