Odd perfect related road blocks II

[chris2be8]

6 more:
sigma(10075913532196534974264023112224483068879249627249343^2)
r1=2233647098375226206004396267200587746109 (pp40)
r2=901432965375777287712709068265242936036682448835126280489 (pp57)

sigma(12794749051708719567180850925260257943250456981939899033459505718762589^2)
r1=14659349757468857368164205611241 (pp32)
r2=99468572816557302853516929596579912944397555903076167343632574289 (pp65)

sigma(146728945749970967430675586557671157044516403926191069^2)
r1=741870891337510549233708209567115165554103913213 (pp48)
r2=4915515478134903086602720135570765044721958754127 (pp49)

sigma(16505679273044843226225467853554413182713186359680961^2)
r1=1109477294403283399868083969006598600439277 (pp43)
r2=8769697222368461401697832959979560654925995138202233749 (pp55)

sigma(7255710931883617800236212603838387^4)
r1=182246129959007905993392602704102124791 (pp39)
r2=15207631256737398619141489936720163895878746551254097384179600855875162265492370959996821822923631 (pp98)

sigma(7281192133783545344470343630466889^4)
r1=55973046021203937746281033858236243395409109844364061 (pp53)
r2=980940045279294458339022045158371393319673131407116521740027241551 (pp66)

And reserving:
sigma(1727085113993512437464654140925494867107178229873217147364447040092519052075530661^2)
sigma(22235662825242282759028370550017213417493096068585212303142496929^2)
sigma(46181498689961388421722037736024247824709330424248393159589649279548351^2)
sigma(3742361194240057893199566966355314018920268076528360256893169784289227626965547117^2)
sigma(26775323154913765719823^6)
sigma(1868155402559234457844300850230116130316704032433919027624951^2)
sigma(23506223804861629238311603519722169606329449927381722054399888644233^2)
sigma(2417886500122344772439744299049627399336844777791843240805759824040508794161^2)
sigma(26935659032762675484199857024793371445721512693235718554065786902142623355952497^2)
(The first 5 are new with lower difficulty than the rest of the range so should split quickly).

Chris K

[chris2be8]

Originally Posted by apocalypse

# 100860848582065425635519047877077112241482572096184039107 | sigma(165936770074941079041373815889^2)
sigma(100860848582065425635519047877077112241482572096184039107^2)
poly:
#C108 D117 G83
type: snfs
n: 895423886690813236595276815273932699969294991769532806541199763388502776044173947098938243755544261863664237
m: 165936770074941079041373815889
c0: 74803
c1: 275
c2: 276
c3: 2
c4: 1
skew: 16.53787686227397334882784874743856953888
--
prp42 factor: 390107233242397287356015618006603288797963    
prp67 factor: 2295327567367693643024213504735796771918311722153151284381043479399

Pascal, did you notice this result. The factors are not in checkfacts.txt.

Chris K

[chris2be8]

4 more:
sigma(6679545329277832375865131410581^6)
r1=60796309575923541433684814949842433565928237741 (pp47)
r2=6783046673619438564978467325335681445646911166913 (pp49)

sigma(68559079450993435955651484647545205968410498159045489720847^2)
r1=31598463949336500829998976254635173 (pp35)
r2=8206222942406625873758079919583630774161686330201576552161653 (pp61)

sigma(11678983384265232966613390730340859^4)
r1=4373411307271557056107195650614415182091671 (pp43)
r2=1496466946671932113691859961861653500085100923652794826257574091074087830658020956460601 (pp88)

sigma(11688837754522490045674353950700583^4)
r1=109926573338026943735851521248346911 (pp36)
r2=134208197856012176380018853691668262190960871744263211097723153640561 (pp69)

And reserving:
sigma(26935659032762675484199857024793371445721512693235718554065786902142623355952497^2)
sigma(28026399389288657025491554492957859663257716446135355848930869222855656012075697^2)
sigma(2886109611694845324444633294873645513590469372621549362195473539191^2)
sigma(393982226065515082187337641362300122940985714389992426973^2)

Chris K

[chris2be8]

8 more:
sigma(26775323154913765719823^6)
r1=81675973663481284478214643775936930875300293735411413414107 (pp59)
r2=2643566058636238661059790529652952868159565618778261835950411821 (pp64)

sigma(1727085113993512437464654140925494867107178229873217147364447040092519052075530661^2)
r1=299731466926282936128786275441616670619833 (pp42)
r2=513948181800355457861365999417882907144346090613 (pp48)

sigma(22235662825242282759028370550017213417493096068585212303142496929^2)
r1=43761437174921738064158711693363468762286763 (pp44)
r2=3520140334845943593860229809896379445847690459 (pp46)

sigma(1868155402559234457844300850230116130316704032433919027624951^2)
r1=32364835517636298173368884693199 (pp32)
r2=272041737000049144086393280670927406615645201562179697826086133299 (pp66)

sigma(23506223804861629238311603519722169606329449927381722054399888644233^2)
r1=6816034294941491307209512553378710821450487 (pp43)
r2=477006897944216991354587795534467547250289377043959313 (pp54)

sigma(2417886500122344772439744299049627399336844777791843240805759824040508794161^2)
r1=7807145418305625263398574974044349916972467 (pp43)
r2=892328805339140898352292085345310595788910212803261163 (pp54)

sigma(26935659032762675484199857024793371445721512693235718554065786902142623355952497^2)
r1=2614707256740555356082443745384878920444258927 (pp46)
r2=474645333120128980511469402106527234042706210678861 (pp51)

sigma(28026399389288657025491554492957859663257716446135355848930869222855656012075697^2)
r1=262842985545295218460125102252857684162707435447 (pp48)
r2=14057545216040906430349383946253525007098617030459 (pp50)

And reserving:
sigma(43368320925136011033121^6)
sigma(51428499134255229801307^6)
sigma(69710210289691^12)
sigma(8137702419189040022504577669629191^4)
sigma(8181163353454943966963239782607889^4)
sigma(8410079421747028947607515532256625355639295434659391917170999^2)

Chris K

[chris2be8]

6 more:
sigma(46181498689961388421722037736024247824709330424248393159589649279548351^2)
r1=121623325643200032874844953 (pp27)
r2=15271055159703278968016890691021307576625684591301284987361746267 (pp65)

sigma(3742361194240057893199566966355314018920268076528360256893169784289227626965547117^2)
r1=37461693147813748715483302730672851184089 (pp41)
r2=489114348219188103139112685161386225031458123455990463 (pp54)

sigma(2886109611694845324444633294873645513590469372621549362195473539191^2)
r1=3045784831375986755970131679025402262065044811 (pp46)
r2=1254067894659920388032763379831350672640502223523423 (pp52)

sigma(393982226065515082187337641362300122940985714389992426973^2)
r1=78829077703913183385110415292521289841671 (pp41)
r2=26393106200649133293874470550237563401814913671303798433 (pp56)

sigma(43368320925136011033121^6)
r1=222391846083404924707128545641244226939013610316884331754614719 (pp63)
r2=54902477301600631000629382061641820134791407075690594257429787359 (pp65)

sigma(51428499134255229801307^6)
r1=8467302964269908769651550721644945278181 (pp40)
r2=17296988618317136178970494505390040077849429 (pp44)
r3=126330292755024667237363923002771380082295214963151893 (pp54)

I've found that sextics run 20-30% faster with sieving on the algebraic side. But it needs lss:0 in the .poly file which isn't mentioned in any of the doc.

Also reserving (all likely to be faster than the sextics above):
sigma(94129832004310937469012032249717^6)
sigma(10718708292369016715326604054594910323176586296158373643071^2)
sigma(12735509889905192785090947805974744647528326442962010464612880573^2)
sigma(131352481715827283122099191124412672476001395658247218551^2)
sigma(133723340158746769797864577818013911893784979497522041^2)
sigma(1436444320390291397906606399280142199^4)
sigma(15089118940426270597869026785179541^4)
sigma(18750312275474698293380477984859211^4)

Chris K

[chris2be8]

4 more:
sigma(10718708292369016715326604054594910323176586296158373643071^2)
r1=54394462824520095537689720217325335496509109 (pp44)
r2=554856546426239474287650125253974418685523587597671043 (pp54)

sigma(8137702419189040022504577669629191^4)
r1=848168552465278129733400144231092261 (pp36)
r2=441438709114995696966592998274693104621289064010841423629159151 (pp63)

sigma(8181163353454943966963239782607889^4)
r1=3863522147761474736762495311752707468950184874536491421 (pp55)
r2=12221391687225972100813286221346188470552057045033767273245544160513817841 (pp74)

sigma(15089118940426270597869026785179541^4)
r1=21376898440296874293284936309046747898681 (pp41)
r2=246862536924271549510790499658552804939322370951312698798001179489525071 (pp72)

And reserving:
sigma(18750312275474698293380477984859211^4)
sigma(21004289493395452945341335064971627611657694767086058109903^2)
sigma(248554705490239^16)
sigma(2591973653217041466735433632439900254868117872281608803776120270483^2)

Chris K

[alexhiggins732]

Hi,

Noob/Crank trying to get his feet wet so I hope I did this right.

Parsed all of the text files (380-1000) at http://www.lri.fr/~ochem/opn/ into an XML document and sorted by composite length.

I then picked the smallest c (c86 for sigma(129235603507054755950116424209091471032749312619279355966082026262889177 ^2).

I did not check the reservations for the above, I wanted to make sure a) I was doing this right and b) write another parser to check these on the fly. I also did not reserve it because I wanted to do a test run.

My choice was <90 digits so I ran YAFU siqs



sigma(129235603507054755950116424209091471032749312619279355966082026262889177 ^2) =
PRP42 = 706110324829400941841511584442782744845939
PRP44 = 51613471772784948754101755884156026053849953

yafu siqs(3644480531905429664714029627372819698351283468
0594381168427152858501790477578807390867) -threads 4



starting SIQS on c86: 3644480531905429664714029627372819698351283468059438116842
7152858501790477578807390867

==== sieving in progress ( 4 threads): 57580 relations needed ====
==== Press ctrl-c to abort and save state ====
58261 rels found: 19635 full + 38626 from 530220 partial, (1309.33 rels/sec)

SIQS elapsed time = 439.0909 seconds.


***factors found***

PRP42 = 706110324829400941841511584442782744845939
PRP44 = 51613471772784948754101755884156026053849953

ans = 1

Is this correct?


Also Chris, I apologize for stepping on your feet, but I accidentally put sigma(69710210289691^12) in my example.n file before running MSIEVE.

sigma(69710210289691^12) =
r1=1872396286329077709020577353455140425396501 (pp43)
r2=983399467891093542674313675313141985837450528432439539 (pp54)

In any case am I on the right path here?

[fivemack]

This is starting to be a thread filled with rather opaque postings of medium-sized prime numbers. I have devoted enough quadrillions of compute cycles to aliquot sequences that I probably shouldn't complain (and 60 quadrillion cycles to do 191^103-1), but I get the impression that the factorisations are in fact useless to the goal of proving how big an odd perfect number has to be - they won't let you sneak round the roadblocks, they serve only to make shorter the output of a program whose output is already only tens of megabytes long.

There must be a statement of the form 'either an OPN is greater than 10^481 or the factors of 191^103-1 have /some property/', but I'm not at all sure what the alternate hypothesis is ... I worry that we're doing SNFS jobs merely to confirm that numbers have no very small factors.

Would it be more useful to organise people to split 2801^79-1, which is a reasonably large but eminently practical SNFS job for which I'd be happy to do the matrix step, rather than to fiddle with these tiny little numbers?

[chris2be8]

My latest 6 results:
sigma(69710210289691^12)
r1=1872396286329077709020577353455140425396501 (pp43)
r2=983399467891093542674313675313141985837450528432439539 (pp54)

sigma(8410079421747028947607515532256625355639295434659391917170999^2)
r1=2507584176657814046668598447522773 (pp34)
r2=1073452176904869723086422034697080452669100240567372341436459761 (pp64)

sigma(12735509889905192785090947805974744647528326442962010464612880573^2)
r1=61919482629239463373061030972232007 (pp35)
r2=178068441040241701923589403152973540180423839287492239534308267 (pp63)

sigma(131352481715827283122099191124412672476001395658247218551^2)
r1=99383479935176005486219392103358338210279 (pp41)
r2=216316878381679223276820383255322311382654077727265073827 (pp57)

sigma(131352481715827283122099191124412672476001395658247218551^2)
r1=123732325288431472271998654486879 (pp33)
r2=128098977561053888128716675366545988593396115951644041921267000621 (pp66)

sigma(1436444320390291397906606399280142199^4)
r1=53647213774926770355026766225867360170169691 (pp44)
r2=1069354959198054093787923381790400331794799894307292111 (pp55)

alexhiggins732, you are on the right path. But see fivemack's comments. You might want to look at http://oddperfect.org/composites.html for some other targets.

fivemack, I agree splitting 2801^79-1 would be more help, but it's out of my range. Pascal, how much help does splitting the small fry actually do?

Reserving a few more (I'll carry on until Pascal replies):
sigma(2884158155431699570670577666164571913820879317217155062743042256541^2)
sigma(3226958732172192441631621169547522681619241918873519411412391273186619468910348410681419832069292266213968151378059834461739328162010783997^1)
sigma(460863084950616131042131723595911434951353164389087358811^2)
sigma(588761162341205094850414198053241239006032736020251463569174595598850005653^2)
sigma(644524024952624237131603886126792193057893908823223821^2)
sigma(77384683949386242687211^6)

Chris K

[wblipp]

Originally Posted by chris2be8

Pascal, how much help does splitting the small fry actually do?

Here is my understanding - I'm sure Pascal will correct any errors.

1. The 31 remaining roadblocks (see post 130) must be handled in some manner to complete a proof there is no odd perfect number less than 10¹⁰⁰⁰. Finding a factor is the best way to clear a roadblock, but there are other methods that will tried when he reaches the limit of factoring.

2. None of the other factorizations are necessary to prove there is no odd perfect number less than 10¹⁰⁰⁰.

However, the other factors aid the aesthetics of this proof and the efficiency of future extensions:

3. Composites in a proof are ugly because they make the proof longer.

4. Composites in a proof are ugly because they deviate from an "ideal" proof that will be created when all the factorizations are known.

5. Composites in a proof are inefficient for future extensions because they cause factorization work that may become unneeded when the other factorizations allow closer adherence to the ideal proof.

In summary, the way I understand it is that only the roadblock factorizations are necessary, but all the other factorizations will be used when available. When there is sufficient interest and resources to factor a roadblock, especially the lowest roadblock, that is more helpful. When that interest and resources are not available, factoring the other numbers gives tasks of varying sizes whose results will be used for a known purpose.

It sounds like now may the time to factor 2801⁷⁹-1.

William

[alexhiggins732]

Originally Posted by chris2be8

You might want to look at http://oddperfect.org/composites.html for some other targets.

Chris K

I sent an email to reserve c < 100 digits on that list, no response but here they are:

starting SIQS on c91: 4818750106967756791946311144237479116559423630612088001371
568394094429503856353036264953291

==== sieving in progress ( 4 threads):   69643 relations needed ====
====            Press ctrl-c to abort and save state            ====
70136 rels found: 19675 full + 50461 from 872657 partial, (648.48 rels/sec)

SIQS elapsed time = 1414.8972 seconds.


***factors found***

PRP45 = 523169883799520514765356620824131950759870373
PRP46 = 9210679467960944537748698585538313908343637167

ans = 1






starting SIQS on c92: 13415582603204082056089511953553542666790210640591994719901074897538510925749342168983156943

==== sieving in progress ( 4 threads):   70726 relations needed ====
====            Press ctrl-c to abort and save state            ====
SIQS elapsed time = 1641.3020 seconds.


***factors found***

PRP38 = 41389511387603778669104192124787113077
PRP54 = 324130006695900965844130272639776696252250602871310259

ans = 1




starting SIQS on c92: 44527592678752138236536639201070633129122339103682974822951900670363847684093607728326152869

==== sieving in progress ( 4 threads):   72894 relations needed ====
====            Press ctrl-c to abort and save state            ====

SIQS elapsed time = 1900.5503 seconds.


***factors found***

PRP45 = 224368947251410660487136869904116706008043197
PRP48 = 198457020119000370091810191651771745582492231177

ans = 1




starting SIQS on c93: 550362320130463963720804590080111573529190057143738148835830196709380378079668630925917243659

==== sieving in progress ( 4 threads):   77228 relations needed ====
====            Press ctrl-c to abort and save state            ====

SIQS elapsed time = 2100.6584 seconds.


***factors found***

PRP52 = 8594155600795005245007312043478653756816048153103327
PRP41 = 64039138420946499129059619125775632607317

ans = 1


Elapsed: 00:35:01.6406817



starting SIQS on c93: 804014963263071354744224934141558692779975868958332820133596413337953111689850608888500792487

==== sieving in progress ( 4 threads):   77228 relations needed ====
====            Press ctrl-c to abort and save state            ====

SIQS elapsed time = 1793.2854 seconds.


***factors found***


ans = 804014963263071354744224934141558692779975868958332820133596413337953111689850608888500792487


Elapsed: 00:30:02.1374288



starting SIQS on c94: 5740876352355082736936393996205650715612921505768820032135448250766548128674619996384650203509

==== sieving in progress ( 4 threads):   80798 relations needed ====
====            Press ctrl-c to abort and save state            ====

SIQS elapsed time = 2048.1744 seconds.


***factors found***

PRP49 = 6107723092823799052003278998495256109925761886201
PRP45 = 939937234400862280331811055999411524293487709

ans = 1


Elapsed: 00:34:11.3226607



starting SIQS on c95: 22474271429896273616849174867777965831032777381482665924222572882640481580638303454098148569851

==== sieving in progress ( 4 threads):   83284 relations needed ====
====            Press ctrl-c to abort and save state            ====

SIQS elapsed time = 2122.0958 seconds.


***factors found***

PRP52 = 1334038615602390546191830635633905589764686266522211
PRP44 = 16846792264516215089506194515713011164847241

ans = 1


Elapsed: 00:35:31.1720979

I am currently fiddling with some standalone support scripts for factsieve.py so I can automate having multiple clients run in different locations and synchronizing only the spairs.add.x files to the master. I have found that running multiple clients over a VPN takes to much of a performance hit because all of the network i/o overhead.

Should have the final kinks worked out by tonight and will start cracking away at the c115+ on that list.