by Toshio Yamaguchi

Factorizations of integers of the form (10^n) + 1. The factorizations are complete up to 10^171 + 1.

Observations:

  • all numbers of the form (10^j) + 1, where j = 2k + 1 (meaning j is an odd integer, k can be any integer) are divisible by 11
  • all numbers of the form (10^q) + 1, where q = 4r + 2 (r can be any integer) are divisible by 101
  • all numbers of the form (10^t) + 1, where t = 6u + 3 (u can be ????) are divisible by 13 (these numbers are also divisible by 11)
  • all numbers of the form ???? are divisible by 73
  • there are repeatedly numbers with only two factors, 11 and a factor of the form 90909......091


11 = prime

101 = prime

1001 = 7 x 11 x 13

10001 = 73 x 137

100001 = 11 x 9091

1000001 = 101 x 9901

10000001 = 11 x 909091

100000001 = 17 x 5882353

1000000001 = 7 x 11 x 13 x 19 x 52579

10000000001 = 101 x 3541 x 27961

100000000001 = 11^2 x 23 x 4093 x 8779

1000000000001 = 73 x 137 x 99990001

10000000000001 = 11 x 859 x 1058313049

100000000000001 = 29 x 101 x 281 x 121499449

1000000000000001 = 7 x 11 x 13 x 211 x 241 x 2161 x 9091

10000000000000001 = 353 x 449 x 641 x 1409 x 69857

100000000000000001 = 11 x 103 x 4013 x 21993833369

1000000000000000001 = 101 x 9901 x 999999000001

10000000000000000001 = 11 x 909090909090909091

100000000000000000001 = 73 x 137 x 1676321 x 5964848081

1000000000000000000001 = 7^2 x 11 x 13 x 127 x 2689 x 459691 x 909091

10000000000000000000001 = 89 x 101 x 1052788969 x 1056689261

100000000000000000000001 = 11 x 47 x 139 x 2531 x 549797184491917

1000000000000000000000001 = 17 x 5882353 x 9999999900000001

10000000000000000000000001 = 11 x 251 x 5051 x 9091 x 78875943472201

100000000000000000000000001 = 101 x 521 x 1900381976777332243781

1000000000000000000000000001 = 7 x 11 x 13 x 19 x 52579 x 70541929 x 14175966169

10000000000000000000000000001 = 73 x 137 x 7841 x 127522001020150503761

100000000000000000000000000001 = 11 x 59 x 154083204930662557781201849

1000000000000000000000000000001 = 61 x 101 x 3541 x 9901 x 27961 x 4188901 x 39526741

10000000000000000000000000000001 = 11 x 909090909090909090909090909091

100000000000000000000000000000001 = 19841 x 976193 x 6187457 x 834427406578561

1000000000000000000000000000000001 = 7 x 11^2 x 13 x 23 x 4093 x 8779 x 599144041 x 183411838171

10000000000000000000000000000000001 = 101 x 28559389 x 1491383821 x 2324557465671829

100000000000000000000000000000000001 = 11 x 9091 x 909091 x 4147571 x 265212793249617641

1000000000000000000000000000000000001 = 73 x 137 x 3169 x 98641 x 99990001 x 3199044596370769

10000000000000000000000000000000000001 = 11 x 7253 x 422650073734453 x 296557347313446299

100000000000000000000000000000000000001 = 101 x 722817036322379041 x 1369778187490592461

1000000000000000000000000000000000000001 = 7 x 11 x 13^2 x 157 x 859 x 6397 x 216451 x 1058313049 x 388847808493

10000000000000000000000000000000000000001 = 17 x 5070721 x 5882353 x 19721061166646717498359681

100000000000000000000000000000000000000001 = 11 x 2670502781396266997 x 3404193829806058997303

1000000000000000000000000000000000000000001 = 29 x 101 x 281 x 9901 x 226549 x 121499449 x 4458192223320340849

10000000000000000000000000000000000000000001 = 11 x 57009401 x 2182600451 x 7306116556571817748755241

100000000000000000000000000000000000000000001 = 73 x 137 x 617 x 16205834846012967584927082656402106953

1000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 19 x 211 x 241 x 2161 x 9091 x 29611 x 52579 x 3762091 x 8985695684401

10000000000000000000000000000000000000000000001 = 101 x 1289 x 18371524594609 x 4181003300071669867932658901

100000000000000000000000000000000000000000000001 = 11 x 6299 x 4855067598095567 x 297262705009139006771611927

1000000000000000000000000000000000000000000000001 = 97 x 353 x 449 x 641 x 1409 x 69857 x 206209 x 66554101249 x 75118313082913

10000000000000000000000000000000000000000000000001 = 11 x 197 x 909091 x 5076141624365532994918781726395939035533

100000000000000000000000000000000000000000000000001 = 101 x 3541 x 27961 x 60101 x 7019801 x 14103673319201 x 1680588011350901

1000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 103 x 4013 x 21993833369 x 291078844423 x 377526955309799110357

10000000000000000000000000000000000000000000000000001 = 73 x 137 x 1580801 x 632527440202150745090622412245443923049201

100000000000000000000000000000000000000000000000000001 = 11 x 9090909090909090909090909090909090909090909090909091

1000000000000000000000000000000000000000000000000000001 = 101 x 109 x 9901 x 153469 x 999999000001 x 59779577156334533866654838281

10000000000000000000000000000000000000000000000000000001 = 11^2 x
23 x 331 x 4093 x 5171 x 8779 x 9091 x 20163494891 x 318727841165674579776721

100000000000000000000000000000000000000000000000000000001 = 17 x 113
x 5 882353 x 73765755896403138401 x 119968369144846370226083377

1000000000000000000000000000000000000000000000000000000001 = 7 x 11
x 13 x 1458973 x 909090909090909091 x 753201806271328462547977919407

10000000000000000000000000000000000000000000000000000000001 = 101 x
349 x 38861 x 618049 x 11811806375201836408679635736258669583187541

100000000000000000000000000000000000000000000000000000000001 = 11 x 1889 x 1090805842068098677837 x 4411922770996074109644535362851087

1000000000000000000000000000000000000000000000000000000000001 = 73
x 137 x 1676321 x 99990001 x 5964848081 x 100009999999899989999000000010001

10000000000000000000000000000000000000000000000000000000000001 = 11
x 81131 x 11205222530116836855321528257890437575145023592596037161

100000000000000000000000000000000000000000000000000000000000001 = 101 x 2049349 x 483128549554512237305554588359039822397307149685578249

1000000000000000000000000000000000000000000000000000000000000001 = 7^2 x 11 x 13 x 19 x 127 x 2689 x 52579 x 459691 x 909091 x 5274739 x 189772422673235585874485732659

10000000000000000000000000000000000000000000000000000000000000001 = 1265011073 x 15343168188889137818369 x 515217525265213267447869906815873

100000000000000000000000000000000000000000000000000000000000000001 = 11 x 131 x 859 x 9091 x 1058313049 x 8396862596258693901610602298557167100076327481

1000000000000000000000000000000000000000000000000000000000000000001 = 89 x 101 x 9901 x 1052788969 x 1056689261 x 5419170769 x 789390798020221 x 2361000305507449

10000000000000000000000000000000000000000000000000000000000000000001 = 11 x 909090909090909090909090909090909090909090909090909090909090909091

100000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 152533657 x 65552746171882583264230070868884366877803237222654400793

1000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 47 x 139 x 2531 x 31051 x 143574021480139 x 549797184491917 x 24649445347649059192745899

10000000000000000000000000000000000000000000000000000000000000000000001 = 29 x 101 x 281 x 421 x 3541 x 27961 x 3471301 x 13489841 x 121499449 x 60368344121 x 848654483879497562821

100000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 290249 x 31321069464181068355415209323405389541706979493156189716729115659

1000000000000000000000000000000000000000000000000000000000000000000000001 = 17 x 8929 x 5882353 x 9999999900000001 x 111994624258035614290513943330720125433979169

10000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 293 x 10826684964539959837294043117 x 286578888976194997999922592330908602103011

100000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 149 x 3109 x 111149 x 708840373781 x 669031686661427842829 x 40548140514062774758071840361

1000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 211 x 241 x 251 x 2161 x 5051 x 9091 x 78875943472201 x 10000099999999989999899999000000000100001

10000000000000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 457 x 1403417 x 5240808656722481737 x 297478330786365628414805305290302483555043017

100000000000000000000000000000000000000000000000000000000000000000000000000001 = 11^2 x 23 x 463 x 4093 x 8779 x 24179 x 590437 x 909091 x 7444361 x 4539402627853030477 x 4924630160315726207887

1000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 521 x 3121 x 9901 x 53397071018461 x 1900381976777332243781 x 6060517860310398033985611921721

10000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 1423 x 9615060929 x 66443174541490579097997510158021076958392938976011506949065646573

100000000000000000000000000000000000000000000000000000000000000000000000000000001 = 353 x 449 x 641 x 1409 x 69857 x 1634881 x 18453761 x 947147262401 x 349954396040122577928041596214187605761

1000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 19 x 1459 x 52579 x 70 541929 x 2458921051 x 14175966169 x 456502382570032651 x 610600386089858349939139

10000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 68389 x 1447745997018511893740076606031686237538345362413531560645573104006506749609

100000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 167 x 997 x 3565183 x 2097307081 x 7742098247001476863 x 943176903141330068482602900960294299878841

1000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 7841 x 99990001 x 11189053009 x 603812429055411913 x 127522001020150503761 x 148029423400750506553

10000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 103 x 4013 x 9091 x 87211 x 787223761 x 21993833369 x 160220794821014452066741918303580917664386555934641

100000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 338669 x 2923500556298303355222653948542706598448925085853709961673200056984872843366529

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 59 x 638453709757 x 135080726389891 x 154083204930662557781201849 x 1274194732898148471766404179653

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 17 x 5882353 x 10100113 x 9900879227786858424257223656804730798555422102713108259184822982673560177

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 179 x 12147237304901893 x 4180967272673252032291190917188955510245874180001164839931077197586653

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 61 x 101 x 181 x 3541 x 9901 x 27961 x 4188901 x 39526741 x 999999000001 x 4999437541453012143121 x 1105097795002994798105101

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 859 x 909091 x 21705503 x 1058313049 x 50678387411703889101759125785290439894389920385627096501794498837

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 2393 x 4178437150016715837818641871709193476807772628503969494400330129962348520684914375257

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 373 x 44641 x 3590254957 x 909090909090909090909090909091 x 18381907262281244633158190677786966663091011

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 45121 x 2144906157509411684424913774078958939881 x 1023037643093214557651333120422980213172396059301

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 9091 x 1812604116731 x 121450506296081 x 909090909090909091 x 4996731930447843676185843959746621491531100801

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 193 x 769 x 19841 x 976193 x 6187457 x 834427406578561 x 1253224535459902849 x 53763491189967221358575546107279034709697

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 102527361354613106010527 x 323338434891034089173475790125293 x 27422699366054621683295623079471066588881

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 29 x 101 x 281 x 121 499449 x 999999999999990000000000000099999999999999000000000000009999999999999900000000000001

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11^2 x 13 x 19 x 23 x 4093 x 8779 x 52579 x 599144041 x 7093127053 x 183411838171 x 141122524877886182282233539317796144938305111168717

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 401 x 1201 x 1601 x 1676321 x 5964848081 x 129694419029057750551385771184564274499075700947656757821537291527196801

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 607 x 809 x 1213 x 1327067281 x 11500490394117824585468796003575163076836624586334794818271756072956027758946488969

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 409 x 3061 x 9901 x 5969449 x 28559389 x 134703241 x 1491383821 x 225974065503889 x 2324557465671829 x 44398000479007997569751764249

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 1237 x 44092859 x 102860539 x 984385009 x 612053256358933 x 182725114866521155647161 x 1471865453993855302660887614137521979

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 17 x 1249 x 49297 x 300977 x 648961 x 5882353 x 249227787818677482257 x 333632766438409011274705987026407639670042305536743429073

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 ^ 2 x 11 x 13 x 127 x 211 x 241 x 2161 x 2689 x 9091 x 459691 x 909091 x 4147571 x 29970369241 x 1661378260814161 x 265212793249617641 x 18276168846821336356291

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 1061 x 5051749 x 245391150214875249502685807421982149521 x 75277048352808729626679875852901448034540173569840168229

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 1499 x 28463 x 74687 x 392263 x 795653 x 9140689231828972552925524522037823147045937571379494322686226282352288670801988451

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 3169 x 98641 x 99990001 x 3199044596370769 x 1726290008991504500177463302688697 x 579276943498154282123686999881829009033

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 3338786746233023 x 14060959683864286267405933000927102019 x 19364383321148719295180578853325741855858987848620134943

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 89 x 101 x 661 x 3541 x 18041 x 27961 x 148721 x 1052788969 x 1056689261 x 1121407321 x 1395900370916327245555441901 x 36380545029953205956377406702261

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 223 x 4663 x 7253 x 422650073734453 x 296557347313446299 x 21606064498691505246200058094681 x 48911689110891303706174193415115219

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 353 x 449 x 641 x 673 x 1409 x 69857 x 43735845217 x 217860610452031121598489279950204653537 x 155944009296214054100626916003794407157304353

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 4973 x 4426889 x 412943108813978385999641617982242667485519119709940711942693553709517240114281629255685010553886849303

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 229 x 2281 x 4789 x 9901 x 304077901 x 52875286008709 x 722817036322379041 x 739653893349540289 x 1369778187490592461 x 33950736420661075851541

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 47 x 139 x 691 x 2531 x 9091 x 549797184491917 x 15918798843849477568899983937931966555877132981347465830696251648192619376266439940521

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 233 x 355193 x 21591416633 x 17468739848498438039329935679794457 x
320326994163169943384295066992439316655840979654890345228609

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 ^ 2 x 19 x 157 x 859 x 6397 x 52579 x 216451 x 461917 x 60034573 x 1058313049 x 388847808493 x 36096800156828895568286578224818258719817914995401933354161

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 430148941 x 230175856669373992253976277974612031182496625023886807386072581333871027940087154579555293851089822885094561

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 103 x 4013 x 909091 x 1868879293 x 21993833369 x 5673320472670315859129 x 103746647830421551242486430622636901002236971549990724717454338463

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 17 x 5070721 x 5882353 x 1132716961 x 9999999900000001 x 19721061166646717498359681 x 281259985248437790051014401 x 31388506438433752927908678241

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 ^ 3 x 23 x 4093 x 4357 x 8779 x 25169 x 1485397 x 102502981431359171598893 x 544471001372579296332291652675646774644208265246405598834086237345 292487

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 1587221 x 81183810541 x 101444162656037151745878558385892753596849 x
75743388768260974116327848920184337528059461788181539337429709

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 739 x 148339 x 16419517 x 2670502781396266997 x 3404193829806058997303 x 61051796035522969271171274876554178504544683763248923853725596423

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 1489 x 640543322297 x 27908132670449 x 384705444182230291105649 x 97645954668018846467287180866355758374263120864803042536883990817097

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 251 x 5051 x 9091 x 21001 x 162251 x 10893295001 x 78875943472201 x 269409792871731627664586194662281233853701011108906726055753272681082282441709251

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 29 x 101 x 281 x 1009 x 9901 x 226549 x 121499449 x 43266855241 x 999999000001 x 4458192223320340849 x 22906246896437231227899575633620139766044690040039603689929

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 3557 x 857772733 x 1094479651 x 1125629957 x 616896149073719728613 x 10860110813777339731289 x 36099531273603138218699301565567581705151216702113889

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 257 x 15361 x 453377 x 55871187633753621225794775009016131346430842253464047463157158784732544216230781165223702155223678309562822667655169

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 57009401 x 2182600451 x 7306116556571817748755241 x 304768036847074491064894608014695867632997 x 3605696680890791382725432167911038465896663

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 521 x 3541 x 27961 x 2311921 x 1031498834064949381 x 12763852652999774041 x 1900381976777332243781 x 12119730504567977254081 x 2737820036624672031089487008281

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 263 x 1397382241 x 306662501757259 x 525786373041914526306757 x 112506283680098168752627601991569 x 1363608083180796048411168783196497071688492468691

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 617 x 2377 x 16369 x 432961 x 99990001 x 6796152793 x 24387741577 x 126197002179733470481 x 283830826522232279893972777 x 16205834846012967584927082656402106953

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 909091 x 909090909090909091 x 247025236977306025681323889 x 61828645758322140842666144519962696417487 x 72021403933746126426491665754465510017877

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 269 x 4021 x 260587121 x 94927228208573594069 x 2302527353565357450759725122262880394277261 x 16071030565277594576986582552521799177065559188277159741

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 19 x 211 x 241 x 2161 x 6481 x 9091 x 29611 x 52579 x 3762091 x 70541929 x 14175966169 x 577603663291 x 8985695684401 x 31023833790241 x 8610583349234340055547908764091017276717091

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 17 ^ 2 x 5882353 x 13355595217 x 440441087557478776852171834625638618412949059374084837579531425633661269203803741415744566525108430933975383194546209

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 364393423 x 117651465889 x 441651480271681 x 676321006412903 x 218801242136856556680173235529 x 3244569580634956101009646791013296826459859399717968478099

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 829 x 1289 x 9901 x 1569889 x 18371524594609 x 536430531035337769 x 757108543129939106221 x 4181003300071669867932658901 x 19108466176791400681292709171992566565029

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 557 x 2503 x 652065570931334169846518762110895357104035953330623783530923329412897765703841859492780362601926814638167836591846272150911969126521

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 7841 x 851761 x 1676321 x 5964848081 x 127522001020150503761 x 1174155661036370531158387153086358732085761158354280249987966107746175275693416345665039841

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 6299 x 344887 x 9127213 x 4855067598095567 x 1160803383934463712259 x 297262705009139006771611927 x 30073566270559048948142559741512708796590524703892560552659

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 569 x 7669 x 380623849488714809 x 7716926518833508778689508504941 x 93611382287513950329431625811490669 x 82519882659061966708762483486719446639288430446081

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 ^ 2 x 23 x 859 x 4093 x 8779 x 51767 x 1058313049 x 22144088539 x 264752347289 x 104730101107272149081 x 34607524609209512562213651270561528862879196390936320471942325254862879783

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 97 x 353 x 449 x 641 x 1409 x 13249 x 69857 x 206209 x 1067329 x 66554101249 x 75118313082913 x 70716147055257711374123575798428 608590219877617672752248112085912824160137075376116481

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 59 x 1451 x 9091 x 30 104611 x 58765601 x 2433146345771 x 17996132431060961 x 154083204930662557781201849 x 97862727665480231246011008935563207741144491224418517422691228321

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 5911541 x 16692085818029 x 5774294197526381 x 182202742802607835615596881 x 9537037576103752545861071409 967321761728 999089417907986752766348817191016093460769

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 ^ 3 x 11 x 13 x 127 x 197 x 2689 x 459691 x 909091 x 5076141624365532994918781726395939035533 x 142857157142857142856999999985714285714285857142857142855714285571428571428572857143

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 61544617 x 16444765848115921 x 987958734776503660730847298429926744644928427487850380038560428638070909650210480224210297181360032908354907525523774393

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 2087 x 9615683031450065714899 x 165459609176797865866134365329792270635207840943 x 2737869430252705432917439814481839640694075521336313521691938014929169431049

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 61 x 101 x 601 x 3541 x 9901 x 27961 x 60101 x 261301 x 3903901 x 4188901 x 7019801 x 39526741 x 168290119201 x 14103673319201 x 1680588011350901 x 25074091038628125301 x 38654658795718156456729958859629701

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 181288487 x 153653579173 x 12331942624071394811 x 2646756758131654397378192081701748003041997 x 999882306178377345161889846655198592766347086896770989636138585751423

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 17 x 134369 x 5882353 x 31735795756961 x 234504682039452385472228601837391217101263308508305719138749905156540866534427238711769806579683320997636600725852987602204289

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 19 x 103 x 4013 x 52579 x 2142001 x 5364487 x 832339891 x 21993833369 x 276402747619 x 291078844423 x 2405782797823 x 377526955309799110357 x 157393477257579000092993572752789683416120273639369

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 29 x 89 x 101 x 281 x 121499449 x 1052788969 x 1056689261 x 39511854229 x 25561948931738399180959860493035633005346674997219855227412314112685523898853595360610683149167147379131162769

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 9091 x 11161 x 3925963357681 x 5167617497664851 x 909090909090909090909090909091 x 4857900688365130469291831549890842547443917376935406225054646143856579892970236911030721

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 313 x 1101673 x 1580801 x 99990001 x 1358074433371719716641 x 291593563046646669491593 x 632527440202150745090622412245443923049201 x 7323941687838105624847742701467683590147273

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 4397 x 3641773 x 56772494575417679209143612613936371702842084190817259161711159777577563483338093894447335028905724214106839545113870547643014663862360146330362411

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 5689 x 507998564486483655774880939989709 x 646301962916453492325383567253991760083617720844121 x
530084044837791203267418958734478905892862260111193658629289735929681

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 3499 x 2784091 x 54137839415767 x 917813298871770308465539 x 26526333976234009593263527 x 8558521377558885170560719135529 x 9090909090909090909090909090909090909090909090909091

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 19841 x 976193 x 6187457 x 834427406578561 x 99999999999999999999999999999999000000000000000000000000000000009999999999999999999999999999999900000000000000000000000000000001

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 47 x 139 x 967 x 2531 x 909091 x 1569936761 x 549797184491917 x 1203881882727712699967 x 23391028206417273637358380573 x 7775058388319250595762800404689 x 3309383964775818489317002654646529291847

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 109 x 9901 x 153469 x 2925721 x 999999000001 x 59779577156334533866654838281 x 341796090604674881849636380229010216626944264336893367139245334739710314141368913850637159182300704681

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 653 x 13693 x 14286890032106357 x 66953479943839030979655991920753816099754871899 x 106288106156544189601112452124463274118441603168767263777500290285464677481570934480831778653

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 121 553521 x 36637591407529194237097 x 2245236606248397162554620353530247131809555439174332456262048578539955402631665831489925370072038825037489223972536291929859656473

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 ^ 2 x 13 x 23 x 211 x 241 x 331 x 2161 x 4093 x 5171 x 8779 x 9091 x 599144041 x 4124507971 x 20163494891 x 183411838171 x 318727841165674579776721 x 19835636682880495867311241 x 1112314101311286003379752617807870409611285281

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 23023967955265160767768376873521136169786061 x 4300297028838474156015268798064619519844286165272568941158694953418333634388515222398381949374346543672407516659353137441

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 63716179 x 116011189311149998139 x 272828068791212993437 x 301525294918950432087520298129941558711551656822567015411 x 14950128044255312629457887411604300692966728690551568705030373

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 17 x 113 x 337 x 5882353 x 9999999900000001 x 73765755896403138401 x 119968369144846370226083377 x 2070270028985341766616009080161 x 1433319827159466789806966856379479179916136529424792832495021393

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 677 x 859 x 987001237 x 1058313049 x 1592730232155679902273246343099578009020762979379345291 x 939618179300167110691422839525295363729230399945945616908880764779647712170590547747265739

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 3541 x 26861 x 27961 x 28559389 x 1491383821 x 7568346838961 x 2324557465671829 x 237612993541791006121 x 1988731184935761442996825520561 x 1051361091529803074497312148085134194834726090632313891925201

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 19 ^ 2 x 2053 x 52579 x 1458973 x 4410785971 x 2911579215499 x 909090909090909091 x 307010852070382484317401373 x 753201806271328462547977919407 x 6508684267533856834852965580950145565983063793936631379

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 277641151780258438310079109077611969 x 2645778409917434965592366282025495569 x
38993135849791157061060738352944105076217 x 34908493290773859017057784025792153817150916131843303273

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 9689 x 16864733 x 55635102055543836835465457049148501469803488052399095459738250346232835862545261814302848982434784577390375138359139691388144380289619426750242614561569128075543

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 349 x 9901 x 38861 x 618049 x 997369 x 15565833747318241 x 157002934023127338801841 x 4477350074169470752905544969081 x 925473240150495502771483432977308389 x 11811806375201836408679635736258669583187541

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 251 x 5051 x 9091 x 909091 x 4147571 x 3612546001 x 299547376801 x 78875943472201 x 265212793249617641 x 924113758530847383764787530400912659976463549693743820952869672176334445090649182638712486115217201

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 353 x 449 x 641 x 1409 x 11969 x 69857 x 4913921 x 470909313601 x 361057759540097288072937247979725352972055181853408265699800478521559326591153094457376181755912540092512773699689532234798987224827675649

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 1889 x 60247408327 x 968385024074451409 x 2676157881043509853 x 1090805842068098677837 x 3203031926532314264104769060847481 x 4411922770996074109644535362851087 x 219734968010040680865912320713950289

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 101 x 38449 x 138841 x 18547092770394661955046893866403953444141877738854819606028843831344546174591125346548473015452312338456023705554686130669604243301021812682716262365263155956618360389

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 523661705392754764972834211810001059 x 17360270948380236765442123580448180934246742941840774929827069381097446101825710313953633305039247538221205037054245870292654737645806593390849

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 73 x 137 x 3169 x 98641 x 1676321 x 99990001 x 265183201 x 5964848081 x 3199044596370769 x 100009999999899989999000000010001 x 95853807664312827399794371014650641 x 39340929985040037939860550511566010202173435808159761

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 11 x 13757 x 1467439874822650361 x 57813769227978665304109403799291636496876923883191635824278127299864929561 x 778918424933155393480511088578762495409547716376329687166271120021739022042090054703

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 29 x 101 x 281 x 521 x 121499449 x 654721485601 x 1900381976777332243781 x 3571618567996393297210217238290456648947344377957590363519828421 x 431916413820617754546053476804635449461410533962843828981966782964481

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 7 x 11 x 13 x 367 x 81131 x 51745081 x 40498340376691 x 42936744040512685057308971520417028077990465463 x 33277993916065498965234812212436587255656671587921 x 11205222530116836855321528257890437575145023592596037161

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
= 17 x 5882353 x 120553054891405588545727822543281066162803459003848166118314367809 x 829510285658710111215121966308351445187741335558528775675039806142270659943202818322753067885238020768017585089