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ElevenSmooth
OddPerfect.org
Small Composites

About These Composites

These factorizations are not, strictly speaking, necessary for the Odd Perfect Number Search. In most cases the factor chain in an odd perfect proof can be extended if at least one factor is known. When factoring numbers to fill the hints file, the remaining composites are sometimes in the range where Quadratic Sieve or personal SNFS is applicable. Having these factors will make some proofs shorter, and many people feel that proofs will full factorizations are more aesthetic, so although not strictly necessary, these factorizations are of some interest. It's fun to do small factoring and hard to find candidates that anyone cares about, so these less interesting candidates are provided as a service.

Non-Qualified Composites

In addition to the composites listed here, I also have composties from 85 to 159 digits that have had very little ECM work. Experience has shown that if posted here, many people will begin GNFS or SNFS immediately and eventually find small factors that could have been found quickly with ECM. To reduce such waste of factoring power, these numbers are available only through email.

I welcome both ECM-only users and ECM-before-NFS users. Numbers receiving adequate ECM-only work will then be posted to this composite page. Send requests, including desired size of composites, to QS at odd perfect dot org.

Personal Factoring Candidates

I originally proposed numbers under 105 digits as suitable for Quadratic Sieve, but it has been pointed out that many of these small candidates are also well suited for SNFS. I'm running out of small candidates, and some people have asked about large candidates. I don't know what size numbers will appeal to people for SNFS, so I've included some variety. I'll keep all small candidates here and will update the larger ones based on interest.

These composites have arisen in the process of seeking factors for the Odd Perfect Number Search. None of these factors are necessary to clear road blocks at this time.

Email me at QS at odd perfect dot org to reserve one.

Size SNFS
Size
Previous
Work
Source Reserved
by
Decimal Representation
C142  
t45
151173-1
 
3825448166728370527527821787633309801545644890317780555184381064898427265781962786597172320044732010764117606608399144044090497346704212627947
C144  
t45
900159-1
 
294429700159407739477273904193050148580264314049395316198066966364913786569796592173189785825906944575349788156280527763231498414485097582670219
C144  
t45
267761-1
 
322966509758442431659104483201448543092825597598086096911157383349464346010571617243441898478324610642899842933452043855245216493176972939041299
C144  
t45
943761-1
 
685046394057866179296731904571322229026331893870162315685180241755774787374881994227536717435566709837347687787549550728409469021997573568453767
C145  
t45
465759-1
 
1028475751831836023215334753433222233662466587711072104910516829954929856797313363066452255200630483851409260558997034109343038921757010820778923
C145  
t45
749959-1
 
1233716641878946524604322666140512011056848415621951696065979231622977486098019955248975686044394678143565067449897216968194564768802956216558519
C145  
t45
194973-1
 
2148307759362546492355664143148804560906396639371963006062466741749055911894978377688285443598008007360523044220222043059267376524983576509600927
C145  
t45
361367-1
 
2431958173693070147630636947214658075811145079540277557617627498286585592886547442012523597190511285323613932719632382001942506869184539362057473
C146  
t45
621759-1
 
15129939143574061129310755942972423486971080973336638263993512325337078895808190538179191131269259806676886700856040384894772003178160843262695687
C146  
t45
754753-1
 
16789765718256188109372117921769560349277581196069802883559920331983391959544108269258089083632279268632505127271998614424041071746683398027123001
C146  
t45
810153-1
 
37068294014533422702964210925916265081802759372839654580640443182234849609952541356880196827657644535228988436149028359345256136574817551659537403
C146  
t45
318771-1
 
40720627946679574120093412509831516945470490736566715320077884775856312507916136221549227532953998239765529227150081606839978888123086100403788859
C146  
t45
153179-1
 
49196799546362035381086898206314773538251223244305110115967089888245972188702663055051713927300953200321699477740295556247603805926571196143518359
C147  
t45
772753-1
 
399481114629214601997759693074830116309857323771545314263933026542234715431233342275575985670985812331039356259328677034774604122138869308155242761
C147  
t45
173101-1
 
925314706251263978550363289990837545207797920656657886814331205149698473747219009816339373008096184836870712351840677665400049960976207641210901323
C149  
t50
793767-1
 
55419734797581653211363089464639361550002722833220501217659881058173280878675346508759515504183526423268156489093897021653045572216620236835183699929
C150  
t45
829753-1
 
389834497113835295724159671499385082351803085499409072074033585662727993944830126658818158293413255371529210769536679357698403048876474421023497306763
C150 185
t40
1284143-1
 
666557635936462826892509765292792453950717331697029739470440011759077739632286962531401875715803335427637206692310953790628663607493625969333290926641
C151  
2t45
54797-1
 
1077716771708737183340860457188574541025402619131148434040051046114297574429192725186342646883142367258981585221196584917539077642715811408057416693097
C151  
2t45
557359-1
 
1714797792543972819611538304727084932029048984589041418545406235272725235409754482542686061751817494542289079798471160244392285880874018065298211653599
C151 170
t40
584343-1
 
4323341835846173760419875873226927599505625762079589463445807600088523880618519314111422527898205997827929319962408383803068918006176259581841692918267
C152 175
t40
769943-1
 
12097796458701306188898278066653984736851085680175709921021761271843998523899313944933715440955615251717069592933051719633467885980525554560302250488511
C152 182
3t40
186687129-1
 
17539918483329965916214061448098989736757501472558593526872970463720821376589315612492421386452424640147862245218574001863083147136355959974863810065633
C152  
3t45
216173-1
 
18672379111643128908055041945768832266013596366339132141561976530714356750924837914129594916349894947953942071980788492597010007944546896510097664783293
C153  
t50
556959-1
 
284747666023364783826529324435694084204792244444836385238821770653673323421600417113539353868385695402116138903303782941312948804080553828747040963204349
C153  
t50
505959-1
 
385622140727458627105089341877664230612112746667625647490194243266184745063433055708086310861876511643857492887794501432600813004232248239718107563019059
C153  
t50
38989-1
 
407786459471981564546066737155810542763170629277822610081627121759757759993477229534375510348895609185143147421152333194071245142668599212304343816178713
C153  
t50
213167-1
 
511231899614856303885304107631124928204341668531871725881220835209766119098562043744242833911259750467985982273202402570285542813111235559648017904824329
C154  
t50
557361-1
 
1282269253228518606762853913152088385394641123428287011315463409169699709189665924323785606096905355310474848145907705015869754331684505472937102616424667
C154  
t50
703959-1
 
7623672036135134427926587044694450006126731921704248863446138318601309883989609332458779114355940362406609844312513403610923142114303374670225374468058257
C155 186
3t40
2645625123-1
 
14692327297165659070093470273300830659971332058152538145391766860960308234053790569403304349832247169847830109362591655039919164674864579103245906916526111
C155  
t45
436213933622906865609478311-1
 
16594272456394514001936463361811410698912954370150505302029321613645440871661478234593777439429022803034081524545312328731745925586855081207085223892202619
C156  
t50
76983-1
 
671361921235421282007172502994278422827187253751609851566967577985623870134569344398353107010905783399836800962756078009456088066074992799704427509414361187
C157 180
t40
3417932806317-1
 
1070942825591251162854166090464609243084337688376284493407383932927133892915649630161913272331560281358588340760817613862548245205418003456048462393517526731
C157  
t50
4531971-1
 
1820370852083805056581119339306379646157416037651391884748204846926841867036951341501040276053909839705345008775632527545355622052323325959132345806511651337
C157  
t50
87779-1
 
3787388118933512063249259173231597770049112435945032094640277541632460519045009491164974276597271170346757143570242916437315466248541421375702840232794402591
C157  
t50
559161-1
 
4916719472909163222402421363155781932008792951205476182592544160016798076460852151259767846729725962180353503005873964597669829852264052181548887277838146847
C157  
t50
421101-1
 
7545709641397498353067070440069426912947573375927447640888942311863554120213198748831464013566826952330033623830454475465232632544099520354726347375557061459
C158 213
t45
730545731-1
 
47660519055208779858312307235079067666364023222518053347031526934830142740526020735129924905403514247411661890035910525610504688648062473036468491693762805323

+SNFS polynomial x6+3x5+5x4+6x3+7x2+6x+3 comes from Φ35(x))/Φ3(-x)