4 more (even though they look small beer next to fivemack's post):
sigma(17049927741295723419455438456527^4)
r1=863597050659418830282733191300071 (pp33)
r2=4560852510952278354156342446746943616554169532779848275845292140290831660944208700091 (pp85)

sigma(1213312309461502477471^6)
r1=1733091440466168290511827770079394991558333 (pp43)
r2=22235662825242282759028370550017213417493096068585212303142496929 (pp65)

sigma(1573246909647668001337^6)
r1=94908343639604464566007348136767922803 (pp38)
r2=56213359559939340340844051525315234239648516226773487735171 (pp59)

sigma(1613833928517310528571^6)
r1=33162898421282010117752261108563691299 (pp38)
r2=8236142336691559278146274437067754660658547591364451083521915932138102569545338642983 (pp85)

Chris K

[QUOTE=fivemack;208169]191^103-1 is finished[/QUOTE]
Great, thank you very much !
Odd perfect numbers certainly do not exist, and now we know that they are > 10^540.
And even > 10^670 by using Theorem 2 in [BCR] on the remaining roadblocks.

Another 4:
sigma(25865202218735920969913319342977^4)
r1=5044422049829616608024642451977024515511 (pp40)
r2=103269206519692606299795352511949898633369679193644736365206290856905276541 (pp75)

sigma(31503547855818058003443589783807^4)
r1=30280669317751106232349128847569131600801 (pp41)
r2=55596113349323744951840911884333874068694973207577661000192821661 (pp65)

sigma(1953340318346474862709^6)
r1=261824322827367063162097688231716266639552169496273557 (pp54)
r2=35718096785654539034671456570770376772402157937930346360839793 (pp62)

sigma(2395419413743258360243^6)
r1=1799805596328158247041447530893998759 (pp37)
r2=104969660367412726519738793209432561905239018109174683323632669479085669355943407433563797827 (pp93)

Chris K

This integer doesn't seem to have been reserved in the past few days, so I have fed the RSALS BOINC grid with the first "353_97_minus1" WUs for (353^97-1)/(352*29101), using the 353*x^6-1, x=353^16 polynomial William gave me :smile:

5 more:
sigma(8058430795610571278465339811140611801264431314862899869^2)
r1=1766069678718538222688403731963047 (pp34)
r2=5550361426229339811898642111643418421848915968672729021437 (pp58)

sigma(568944611281729293283376872939^4)
r1=175441787584993677226673887329218911132861 (pp42)
r2=18313982437714629967972300468805301666587800897231657156349764561822709951 (pp74)

sigma(8379347128335604166268202471087^4)
r1=26753984207718269557180774275732499151 (pp38)
r2=394122801026240845746398503276440705671 (pp39)
r3=272434857095090294149235528111021713250041 (pp42)

sigma(653058596067301423729^6)
r1=54125735503990458636034901890174543 (pp35)
r2=143545610498352365685813166778129152838783761917312486618963077 (pp63)

sigma(39091097830253216170021088927077^4)
r1=17068334734623533591237655961584218006830811773927121 (pp53)
r2=96840666204326375049133754424260957524730989754936349718555791589721 (pp68)

And reserving a few more:
sigma(183669826628915121709213298739469^4)
sigma(233670627553369966032984993695251^4)
sigma(2651016851806986192781^6)
sigma(31045189810031713^10)
sigma(3351830668935826837813^6)
sigma(3692911306395520310951^6)
sigma(1082594347356983323042828601013538336497006202037771659433011^2)

Chris K

Another 9:
sigma(31045189810031713^10)
r1=74932907482623068229665001380469870192581329 (pp44)
r2=988801787178213634368912525432133815878028801443 (pp48)

sigma(1082594347356983323042828601013538336497006202037771659433011^2)
r1=6667548283835559647787932783644552328836487119 (pp46)
r2=47141792980071312492018890045755284228186024781 (pp47)

sigma(6503968953043892440658971030483^4)
r1=23941017738974042295830709366964297676017074971 (pp47)
r2=74743121171185670519533854946653164290451092869761131146024649790478512541211 (pp77)

sigma(55350266314895595867025212145997^4)
r1=22791396210105985803705048913080721621 (pp38)
r2=1893155564469387371268742126684310716408170769921836806623789539177405621721 (pp76)

sigma(83172085527497335812994589511133^4)
r1=13354220497777113219504373105905717024953004961651 (pp50)
r2=304886227490525087177107463821694040895066943208380400128624841342131 (pp69)

sigma(142684958271631124501863184377609^4)
r1=4636494072656480776105542525599079417128711 (pp43)
r2=10228775979039516745105634322308986703083396415131938550240339901 (pp65)

sigma(157498899221694152189827767885989^4)
r1=31356909033061788258118864416323228458342321 (pp44)
r2=583761151208079184322511793425271200200240494658102599805325889158450013805041 (pp78)

sigma(161623259620322415732121172922331^4)
r1=24148675571313376777975740862323161 (pp35)
r2=208102086301863612647270222252686038163131610541873003021191 (pp60)

sigma(165978531967050794414709318599449^4)
r1=11566916454603409176780479520777207153179929301 (pp47)
r2=6368319774505146682491066095877108030079191517521743159756841780031 (pp67)

I've noticed that degree 4 is significantly faster than degree 6 in this size range. So how many I get done depends how many of each degree I'm processing.

Also reserving some more:
sigma(244883629858151478506935326996701^4)
sigma(263043400573071174739406778532297^4)
sigma(270521868064337870143943398646563^4)
sigma(332730486894956684291903489029771^4)
sigma(391818505243975817655620850033223^4)
sigma(400429778112997955461644426806031263719^4)
sigma(5089350714503361448633^6)
sigma(5437692657064827171163^6)
sigma(56054481409340060045471850010096614414901391486475853^2)

Chris K

I'm having problems with my internet connection at home. And I can't post results from work (not allowed to copy anything from home PC to work PC).

I'll carry on factoring and post a big list when I get it fixed.

Chris K

[quote=chris2be8;208620]I'm having problems with my internet connection at home. And I can't post results from work (not allowed to copy anything from home PC to work PC).

I'll carry on factoring and post a big list when I get it fixed.

Chris K[/quote]
Or you could always write/print the factors on paper and type them in at work...though if you have a lot of results that might be more trouble than it's worth. :smile:

I'm back:
sigma(183669826628915121709213298739469^4)
r1=413161551198888423175712947354717044099008971 (pp45)
r2=430660420430018299241402140524853745148523590455553622051 (pp57)

sigma(233670627553369966032984993695251^4)
r1=455518328208580094565741935472893333994229231 (pp45)
r2=6997404848597613341939460154859051075524907980564803230187461019232550484191 (pp76)

sigma(3351830668935826837813^6)
r1=6925246896895065306713852660342246911617941329 (pp46)
r2=19303829693837121437374703269191617353677144199430472506745331712851 (pp68)

sigma(3692911306395520310951^6)
r1=4461667576867369965399918326607094515810323846919677839 (pp55)
r2=2427266953738537341166617538820878826121707766677499369689 (pp58)

sigma(244883629858151478506935326996701^4)
r1=81555888618287303069023284649123860841478361254796281 (pp53)
r2=607471681586698607375409526141779821787000788646568233551 (pp57)

sigma(263043400573071174739406778532297^4)
r1=935497740746370184053718664393312670000993495311 (pp48)
r2=7295270782762602982772292733377221245072047797495199730970163881 (pp64)

sigma(270521868064337870143943398646563^4)
r1=231917108393452114882111260311 (pp30)
r2=26490773600748331741188528875473201 (pp35)
r3=871730181206542627368454163621103541704588021858524409087825067231 (pp66)

sigma(332730486894956684291903489029771^4)
r1=638083592037566838945393312856061447503842268910251 (pp51)
r2=3104520993341957506246144402977889699058628126846635491 (pp55)

sigma(391818505243975817655620850033223^4)
r1=45734173485315820916952411776705960408161 (pp41)
r2=12903722647493402267789320847569766027061724930350222172374239192822049968421991 (pp80)

sigma(400429778112997955461644426806031263719^4)
r1=5605718536785061713066373835116391 (pp34)
r2=53590655449727341801419993473643666537557089423041939695791 (pp59)

sigma(5089350714503361448633^6)
r1=1239752011387945044984485240154888253970656464684586253 (pp55)
r2=145356275288045550488175990658692063551041257092289572686011376183 (pp66)

sigma(2651016851806986192781^6)
r1=720735372957113777041363211139030989722886783051 (pp48)
r2=19918689331707481608093934777074440675711053521139529124559411886055315388003 (pp77)

sigma(5437692657064827171163^6)
r1=258475848682057771494154360252829465378925179 (pp45)
r2=5386726188145309781114833689829930893017636163148478168241901870463 (pp67)

sigma(181095479649011274932409289484731331835274754979495389115025600401903802507601^2)
r1=11575895570039902923324482488972937005980684343 (pp47)
r2=501484376765898389876729189707203191176363605397 (pp48)

sigma(2128228199527849401129715708372387^4)
r1=799624479660932783957451351953537365001191 (pp42)
r2=9210388214797898690505385831718789936157805718992091 (pp52)

sigma(45168327939727908592049343226356563^4)
r1=15785045618167522757425457456663604900468791 (pp44)
r2=126562909973279100661542424891968606161972727227521 (pp51)

sigma(56054481409340060045471850010096614414901391486475853^2)
r1=3596769926943839408179664723721677873207191 (pp43)
r2=99095361695961099223925080051226097068789794489357 (pp50)

sigma(5951763617370629406937989269599750474693230124149234721^2)
r1=236759583225570164571357654549912853 (pp36)
r2=27976031253647021112333553007505476802597899615425414918141 (pp59)

sigma(687499744568638731597208931698745887588254541236262532971685408958846226595682426311^2)
r1=578429959605863839312110715582442874157 (pp39)
r2=1663521218376980133890596434622640837401485234568910473 (pp55)

sigma(1108172241592233039419111495698277^4)
r1=15003845879023817608671115969580188411 (pp38)
r2=178735845737718462414665103983455658694765241350242370105299364523368851 (pp72)

sigma(1311485068259788518094335674357221^4)
r1=2720449234555770172739510117700584321403535624981 (pp49)
r2=11802088193605542111263089590442885992013617719301723676590968716511 (pp68)

And reserving:
sigma(1322737349081300869636872129430093^4)
sigma(483237157246965269762015267141239^4)
sigma(485771679474531859792464342500383^4)
sigma(636509366312951605135547956211597^4)
sigma(640992247445482576119970066870663^4)
sigma(642397020588227167280642461914079^4)
sigma(6856044753913716969247^6)
sigma(7071813629821515257381^6)
sigma(707236734824410577063252238741697^4)
sigma(872153100939711875724676704162421^4)
sigma(91966303295251191104971960132273397364144023351465750399992554753980589155137853599^2)
sigma(967717215027368320902940017348223733189053844385424415479^2)

Chris K

Some more:
sigma(483237157246965269762015267141239^4)
r1=10418718936188951753594765435518985086130741 (pp44)
r2=179751638098425259360173728668764489186791667690478334023207808764299931985041 (pp78)

sigma(485771679474531859792464342500383^4)
r1=58427245818619310547371326422551 (pp32)
r2=495694630654015259822895138682386911413666372311168199306595713700059629238949797336711 (pp87)

sigma(636509366312951605135547956211597^4)
r1=104258925971558022385998681714714744682708172448769151 (pp54)
r2=18609281119753047603642396845396571364373547500060019587681 (pp59)

sigma(640992247445482576119970066870663^4)
r1=85422086483801273739245039138341 (pp32)
r2=76434357355740811597016400898438146389291 (pp41)
r3=421485268061604129218615604458323987520568661 (pp45)

sigma(642397020588227167280642461914079^4)
r1=42779208902216682310288364941583692071549873775111 (pp50)
r2=8798025253791128800509386275973435353936582487093774600531 (pp58)

sigma(1322737349081300869636872129430093^4)
r1=17336272893309523656072398698714179271 (pp38)
r2=13309850316254251270626991294588267807837718230446587518262634384524091028394923489084151 (pp89)

sigma(91966303295251191104971960132273397364144023351465750399992554753980589155137853599^2)
r1=46830858670319218866124018334595939199 (pp38)
r2=79168194720733043887500995718170185381063500566326174483 (pp56)

And reserving:
sigma(1394034488518460939015339291788339^4)
sigma(1494030148731726710157348562105207^4)
sigma(1519187846163442572072799632030733^4)
sigma(15194813938078770915091^6)
sigma(1698497861089953227001546107344598199560223472222257789665996127034306321^2)
sigma(1906580383045014957623547756949339^4)

Chris K

More results:
sigma(967717215027368320902940017348223733189053844385424415479^2)
r1=4377323673586633592671808776872309125798467 (pp43)
r2=1956388116374442931199388582235705796823780493366939 (pp52)

sigma(6856044753913716969247^6)
r1=60568177756250023780263218726671240631 (pp38)
r2=92732604493080028495937219149022534640230957385812445713 (pp56)

sigma(7071813629821515257381^6)
r1=29055889550623729087811956736914251461 (pp38)
r2=1314413045950652255429072161863091963395991145343731781541508841303023342648914801 (pp82)

sigma(707236734824410577063252238741697^4)
r1=106754485097137265099403944947401521 (pp36)
r2=2746761106586171334798175767311654589418789162027748502809857705736012951 (pp73)

sigma(872153100939711875724676704162421^4)
r1=163199587695978718693870937694833284810961 (pp42)
r2=11847468659944402703648780240680842570459049031562353686921 (pp59)

And reserving:
sigma(1944848086522004636322313228532894639^4)
sigma(12240911040103795579906843864700642393963359910824110430387939553546861^2)
sigma(2616458911833394499755349207477090939^4)
sigma(263152813162391930375710921^6)
sigma(6244756561400247183978608333534940251947919207224171630342627211^2)
sigma(65701231097378375375460212827313559961417448560515352147952562525667^2)
sigma(756067249349405037080689042255339999621^4)

Chris K