### 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 11all numbers of the form (10^q) + 1, where q = 4r + 2 (r can be any integer) are divisible by 101all 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 73there are repeatedly numbers with only two factors, 11 and a factor of the form 90909......09111 = prime101 = prime1001 = 7 x 11 x 1310001 = 73 x 137100001 = 11 x 90911000001 = 101 x 990110000001 = 11 x 909091100000001 = 17 x 58823531000000001 = 7 x 11 x 13 x 19 x 5257910000000001 = 101 x 3541 x 27961100000000001 = 11^2 x 23 x 4093 x 87791000000000001 = 73 x 137 x 9999000110000000000001 = 11 x 859 x 1058313049100000000000001 = 29 x 101 x 281 x 1214994491000000000000001 = 7 x 11 x 13 x 211 x 241 x 2161 x 909110000000000000001 = 353 x 449 x 641 x 1409 x 69857100000000000000001 = 11 x 103 x 4013 x 219938333691000000000000000001 = 101 x 9901 x 99999900000110000000000000000001 = 11 x 909090909090909091100000000000000000001 = 73 x 137 x 1676321 x 59648480811000000000000000000001 = 7^2 x 11 x 13 x 127 x 2689 x 459691 x 90909110000000000000000000001 = 89 x 101 x 1052788969 x 1056689261100000000000000000000001 = 11 x 47 x 139 x 2531 x 5497971844919171000000000000000000000001 = 17 x 5882353 x 999999990000000110000000000000000000000001 = 11 x 251 x 5051 x 9091 x 78875943472201100000000000000000000000001 = 101 x 521 x 19003819767773322437811000000000000000000000000001 = 7 x 11 x 13 x 19 x 52579 x 70541929 x 1417596616910000000000000000000000000001 = 73 x 137 x 7841 x 127522001020150503761100000000000000000000000000001 = 11 x 59 x 1540832049306625577812018491000000000000000000000000000001 = 61 x 101 x 3541 x 9901 x 27961 x 4188901 x 3952674110000000000000000000000000000001 = 11 x 909090909090909090909090909091100000000000000000000000000000001 = 19841 x 976193 x 6187457 x 8344274065785611000000000000000000000000000000001 = 7 x 11^2 x 13 x 23 x 4093 x 8779 x 599144041 x 18341183817110000000000000000000000000000000001 = 101 x 28559389 x 1491383821 x 2324557465671829100000000000000000000000000000000001 = 11 x 9091 x 909091 x 4147571 x 2652127932496176411000000000000000000000000000000000001 = 73 x 137 x 3169 x 98641 x 99990001 x 319904459637076910000000000000000000000000000000000001 = 11 x 7253 x 422650073734453 x 296557347313446299100000000000000000000000000000000000001 = 101 x 722817036322379041 x 13697781874905924611000000000000000000000000000000000000001 = 7 x 11 x 13^2 x 157 x 859 x 6397 x 216451 x 1058313049 x 38884780849310000000000000000000000000000000000000001 = 17 x 5070721 x 5882353 x 19721061166646717498359681100000000000000000000000000000000000000001 = 11 x 2670502781396266997 x 34041938298060589973031000000000000000000000000000000000000000001 = 29 x 101 x 281 x 9901 x 226549 x 121499449 x 445819222332034084910000000000000000000000000000000000000000001 = 11 x 57009401 x 2182600451 x 7306116556571817748755241100000000000000000000000000000000000000000001 = 73 x 137 x 617 x 162058348460129675849270826564021069531000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 19 x 211 x 241 x 2161 x 9091 x 29611 x 52579 x 3762091 x 898569568440110000000000000000000000000000000000000000000001 = 101 x 1289 x 18371524594609 x 4181003300071669867932658901100000000000000000000000000000000000000000000001 = 11 x 6299 x 4855067598095567 x 2972627050091390067716119271000000000000000000000000000000000000000000000001 = 97 x 353 x 449 x 641 x 1409 x 69857 x 206209 x 66554101249 x 7511831308291310000000000000000000000000000000000000000000000001 = 11 x 197 x 909091 x 5076141624365532994918781726395939035533100000000000000000000000000000000000000000000000001 = 101 x 3541 x 27961 x 60101 x 7019801 x 14103673319201 x 16805880113509011000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 103 x 4013 x 21993833369 x 291078844423 x 37752695530979911035710000000000000000000000000000000000000000000000000001 = 73 x 137 x 1580801 x 632527440202150745090622412245443923049201100000000000000000000000000000000000000000000000000001 = 11 x 90909090909090909090909090909090909090909090909090911000000000000000000000000000000000000000000000000000001 = 101 x 109 x 9901 x 153469 x 999999000001 x 5977957715633453386665483828110000000000000000000000000000000000000000000000000000001 = 11^2 x 23 x 331 x 4093 x 5171 x 8779 x 9091 x 20163494891 x 318727841165674579776721100000000000000000000000000000000000000000000000000000001 = 17 x 113 x 5 882353 x 73765755896403138401 x 1199683691448463702260833771000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 1458973 x 909090909090909091 x 75320180627132846254797791940710000000000000000000000000000000000000000000000000000000001 = 101 x 349 x 38861 x 618049 x 11811806375201836408679635736258669583187541100000000000000000000000000000000000000000000000000000000001 = 11 x 1889 x 1090805842068098677837 x 44119227709960741096445353628510871000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 1676321 x 99990001 x 5964848081 x 10000999999989998999900000001000110000000000000000000000000000000000000000000000000000000000001 = 11 x 81131 x 11205222530116836855321528257890437575145023592596037161100000000000000000000000000000000000000000000000000000000000001 = 101 x 2049349 x 4831285495545122373055545883590398223973071496855782491000000000000000000000000000000000000000000000000000000000000001 = 7^2 x 11 x 13 x 19 x 127 x 2689 x 52579 x 459691 x 909091 x 5274739 x 18977242267323558587448573265910000000000000000000000000000000000000000000000000000000000000001 = 1265011073 x 15343168188889137818369 x 515217525265213267447869906815873100000000000000000000000000000000000000000000000000000000000000001 = 11 x 131 x 859 x 9091 x 1058313049 x 83968625962586939016106022985571671000763274811000000000000000000000000000000000000000000000000000000000000000001 = 89 x 101 x 9901 x 1052788969 x 1056689261 x 5419170769 x 789390798020221 x 236100030550744910000000000000000000000000000000000000000000000000000000000000000001 = 11 x 909090909090909090909090909090909090909090909090909090909090909091100000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 152533657 x 655527461718825832642300708688843668778032372226544007931000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 47 x 139 x 2531 x 31051 x 143574021480139 x 549797184491917 x 2464944534764905919274589910000000000000000000000000000000000000000000000000000000000000000000001 = 29 x 101 x 281 x 421 x 3541 x 27961 x 3471301 x 13489841 x 121499449 x 60368344121 x 848654483879497562821100000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 290249 x 313210694641810683554152093234053895417069794931561897167291156591000000000000000000000000000000000000000000000000000000000000000000000001 = 17 x 8929 x 5882353 x 9999999900000001 x 11199462425803561429051394333072012543397916910000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 293 x 10826684964539959837294043117 x 286578888976194997999922592330908602103011100000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 149 x 3109 x 111149 x 708840373781 x 669031686661427842829 x 405481405140627747580718403611000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 211 x 241 x 251 x 2161 x 5051 x 9091 x 78875943472201 x 1000009999999998999989999900000000010000110000000000000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 457 x 1403417 x 5240808656722481737 x 297478330786365628414805305290302483555043017100000000000000000000000000000000000000000000000000000000000000000000000000001 = 11^2 x 23 x 463 x 4093 x 8779 x 24179 x 590437 x 909091 x 7444361 x 4539402627853030477 x 49246301603157262078871000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 521 x 3121 x 9901 x 53397071018461 x 1900381976777332243781 x 606051786031039803398561192172110000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 1423 x 9615060929 x 66443174541490579097997510158021076958392938976011506949065646573100000000000000000000000000000000000000000000000000000000000000000000000000000001 = 353 x 449 x 641 x 1409 x 69857 x 1634881 x 18453761 x 947147262401 x 3499543960401225779280415962141876057611000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 19 x 1459 x 52579 x 70 541929 x 2458921051 x 14175966169 x 456502382570032651 x 61060038608985834993913910000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 68389 x 1447745997018511893740076606031686237538345362413531560645573104006506749609100000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 167 x 997 x 3565183 x 2097307081 x 7742098247001476863 x 9431769031413300684826029009602942998788411000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 7841 x 99990001 x 11189053009 x 603812429055411913 x 127522001020150503761 x 14802942340075050655310000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 103 x 4013 x 9091 x 87211 x 787223761 x 21993833369 x 160220794821014452066741918303580917664386555934641100000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 338669 x 29235005562983033552226539485427065984489250858537099616732000569848728433665291000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 59 x 638453709757 x 135080726389891 x 154083204930662557781201849 x 127419473289814847176640417965310000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 17 x 5882353 x 10100113 x 9900879227786858424257223656804730798555422102713108259184822982673560177100000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 179 x 12147237304901893 x 41809672726732520322911909171889555102458741800011648399310771975866531000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 61 x 101 x 181 x 3541 x 9901 x 27961 x 4188901 x 39526741 x 999999000001 x 4999437541453012143121 x 110509779500299479810510110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 859 x 909091 x 21705503 x 1058313049 x 50678387411703889101759125785290439894389920385627096501794498837100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 2393 x 41784371500167158378186418717091934768077726285039694944003301299623485206849143752571000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11 x 13 x 373 x 44641 x 3590254957 x 909090909090909090909090909091 x 1838190726228124463315819067778696666309101110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 45121 x 2144906157509411684424913774078958939881 x 1023037643093214557651333120422980213172396059301100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 9091 x 1812604116731 x 121450506296081 x 909090909090909091 x 49967319304478436761858439597466214915311008011000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 193 x 769 x 19841 x 976193 x 6187457 x 834427406578561 x 1253224535459902849 x 5376349118996722135857554610727903470969710000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 102527361354613106010527 x 323338434891034089173475790125293 x 27422699366054621683295623079471066588881100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 29 x 101 x 281 x 121 499449 x 9999999999999900000000000000999999999999990000000000000099999999999999000000000000011000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 7 x 11^2 x 13 x 19 x 23 x 4093 x 8779 x 52579 x 599144041 x 7093127053 x 183411838171 x 14112252487788618228223353931779614493830511116871710000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 73 x 137 x 401 x 1201 x 1601 x 1676321 x 5964848081 x 129694419029057750551385771184564274499075700947656757821537291527196801100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 607 x 809 x 1213 x 1327067281 x 115004903941178245854687960035751630768366245863347948182717560729560277589464889691000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 101 x 409 x 3061 x 9901 x 5969449 x 28559389 x 134703241 x 1491383821 x 225974065503889 x 2324557465671829 x 4439800047900799756975176424910000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 1237 x 44092859 x 102860539 x 984385009 x 612053256358933 x 182725114866521155647161 x 1471865453993855302660887614137521979100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 17 x 1249 x 49297 x 300977 x 648961 x 5882353 x 249227787818677482257 x 3336327664384090112747059870264076396700423055367434290731000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 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 1827616884682133635629110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 101 x 1061 x 5051749 x 245391150214875249502685807421982149521 x 75277048352808729626679875852901448034540173569840168229100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 11 x 1499 x 28463 x 74687 x 392263 x 795653 x 91406892318289725529255245220378231470459375713794943226862262823522886708019884511000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 73 x 137 x 3169 x 98641 x 99990001 x 3199044596370769 x 1726290008991504500177463302688697 x 57927694349815428212368699988182900903310000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 3338786746233023 x 14060959683864286267405933000927102019 x 19364383321148719295180578853325741855858987848620134943100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 89 x 101 x 661 x 3541 x 18041 x 27961 x 148721 x 1052788969 x 1056689261 x 1121407321 x 1395900370916327245555441901 x 363805450299532059563774067022611000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 7 x 11 x 13 x 223 x 4663 x 7253 x 422650073734453 x 296557347313446299 x 21606064498691505246200058094681 x 4891168911089130370617419341511521910000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 353 x 449 x 641 x 673 x 1409 x 69857 x 43735845217 x 217860610452031121598489279950204653537 x 155944009296214054100626916003794407157304353100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 4973 x 4426889 x 4129431088139783859996416179822426674855191197099407119426935537095172401142816292556850105538868493031000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 101 x 229 x 2281 x 4789 x 9901 x 304077901 x 52875286008709 x 722817036322379041 x 739653893349540289 x 1369778187490592461 x 3395073642066107585154110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 47 x 139 x 691 x 2531 x 9091 x 549797184491917 x 15918798843849477568899983937931966555877132981347465830696251648192619376266439940521100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 73 x 137 x 233 x 355193 x 21591416633 x 17468739848498438039329935679794457 x 3203269941631699433842950669924393166558409796548903452286091000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 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 3609680015682889556828657822481825871981791499540193335416110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 101 x 430148941 x 230175856669373992253976277974612031182496625023886807386072581333871027940087154579555293851089822885094561100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 103 x 4013 x 909091 x 1868879293 x 21993833369 x 5673320472670315859129 x 1037466478304215512424864306226369010022369715499907247174543384631000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 17 x 5070721 x 5882353 x 1132716961 x 9999999900000001 x 19721061166646717498359681 x 281259985248437790051014401 x 3138850643843375292790867824110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 ^ 3 x 23 x 4093 x 4357 x 8779 x 25169 x 1485397 x 102502981431359171598893 x 544471001372579296332291652675646774644208265246405598834086237345 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x 78875943472201 x 2694097928717316276645861946622812338537010111089067260557532726810822824417092511000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 29 x 101 x 281 x 1009 x 9901 x 226549 x 121499449 x 43266855241 x 999999000001 x 4458192223320340849 x 2290624689643723122789957563362013976604469004003960368992910000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 3557 x 857772733 x 1094479651 x 1125629957 x 616896149073719728613 x 10860110813777339731289 x 36099531273603138218699301565567581705151216702113889100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 257 x 15361 x 453377 x 558711876337536212257947750090161313464308422534640474631571587847325442162307811652237021552236783095628226676551691000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 7 x 11 x 13 x 57009401 x 2182600451 x 7306116556571817748755241 x 304768036847074491064894608014695867632997 x 360569668089079138272543216791103846589666310000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 101 x 521 x 3541 x 27961 x 2311921 x 1031498834064949381 x 12763852652999774041 x 1900381976777332243781 x 12119730504567977254081 x 2737820036624672031089487008281100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 263 x 1397382241 x 306662501757259 x 525786373041914526306757 x 112506283680098168752627601991569 x 13636080831807960484111687831964970716884924686911000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 73 x 137 x 617 x 2377 x 16369 x 432961 x 99990001 x 6796152793 x 24387741577 x 126197002179733470481 x 283830826522232279893972777 x 1620583484601296758492708265640210695310000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 909091 x 909090909090909091 x 247025236977306025681323889 x 61828645758322140842666144519962696417487 x 72021403933746126426491665754465510017877100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 101 x 269 x 4021 x 260587121 x 94927228208573594069 x 2302527353565357450759725122262880394277261 x 160710305652775945769865825525217991770655591882771597411000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 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 861058334923434005554790876409101727671709110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 17 ^ 2 x 5882353 x 13355595217 x 440441087557478776852171834625638618412949059374084837579531425633661269203803741415744566525108430933975383194546209100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 364393423 x 117651465889 x 441651480271681 x 676321006412903 x 218801242136856556680173235529 x 32445695806349561010096467910132968264598593997179684780991000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 101 x 829 x 1289 x 9901 x 1569889 x 18371524594609 x 536430531035337769 x 757108543129939106221 x 4181003300071669867932658901 x 1910846617679140068129270917199256656502910000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 557 x 2503 x 652065570931334169846518762110895357104035953330623783530923329412897765703841859492780362601926814638167836591846272150911969126521100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 73 x 137 x 7841 x 851761 x 1676321 x 5964848081 x 127522001020150503761 x 11741556610363705311583871530863587320857611583542802499879661077461752756934163456650398411000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 7 x 11 x 13 x 6299 x 344887 x 9127213 x 4855067598095567 x 1160803383934463712259 x 297262705009139006771611927 x 3007356627055904894814255974151270879659052470389256055265910000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 101 x 569 x 7669 x 380623849488714809 x 7716926518833508778689508504941 x 93611382287513950329431625811490669 x 82519882659061966708762483486719446639288430446081100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 ^ 2 x 23 x 859 x 4093 x 8779 x 51767 x 1058313049 x 22144088539 x 264752347289 x 104730101107272149081 x 346075246092095125622136512705615288628791963909363204719423252548628797831000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 97 x 353 x 449 x 641 x 1409 x 13249 x 69857 x 206209 x 1067329 x 66554101249 x 75118313082913 x 70716147055257711374123575798428 60859021987761767275224811208591282416013707537611648110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 59 x 1451 x 9091 x 30 104611 x 58765601 x 2433146345771 x 17996132431060961 x 154083204930662557781201849 x 97862727665480231246011008935563207741144491224418517422691228321100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 101 x 5911541 x 16692085818029 x 5774294197526381 x 182202742802607835615596881 x 9537037576103752545861071409 967321761728 9990894179079867527663488171910160934607691000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 7 ^ 3 x 11 x 13 x 127 x 197 x 2689 x 459691 x 909091 x 5076141624365532994918781726395939035533 x 14285715714285714285699999998571428571428585714285714285571428557142857142857285714310000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 73 x 137 x 61544617 x 16444765848115921 x 987958734776503660730847298429926744644928427487850380038560428638070909650210480224210297181360032908354907525523774393100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 2087 x 9615683031450065714899 x 165459609176797865866134365329792270635207840943 x 27378694302527054329174398144818396406940755213363135216919380149291694310491000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 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 3865465879571815645672995885962970110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 181288487 x 153653579173 x 12331942624071394811 x 2646756758131654397378192081701748003041997 x 999882306178377345161889846655198592766347086896770989636138585751423100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 17 x 134369 x 5882353 x 31735795756961 x 2345046820394523854722286018373912171012633085083057191387499051565408665344272387117698065796833209976366007258529876022042891000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 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 15739347725757900009299357275278968341612027363936910000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 29 x 89 x 101 x 281 x 121499449 x 1052788969 x 1056689261 x 39511854229 x 25561948931738399180959860493035633005346674997219855227412314112685523898853595360610683149167147379131162769100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 9091 x 11161 x 3925963357681 x 5167617497664851 x 909090909090909090909090909091 x 48579006883651304692918315498908425474439173769354062250546461438565798929702369110307211000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 73 x 137 x 313 x 1101673 x 1580801 x 99990001 x 1358074433371719716641 x 291593563046646669491593 x 632527440202150745090622412245443923049201 x 732394168783810562484774270146768359014727310000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 11 x 4397 x 3641773 x 56772494575417679209143612613936371702842084190817259161711159777577563483338093894447335028905724214106839545113870547643014663862360146330362411100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 101 x 5689 x 507998564486483655774880939989709 x 646301962916453492325383567253991760083617720844121 x 5300840448377912032674189587344789058928622601111936586292897359296811000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 7 x 11 x 13 x 3499 x 2784091 x 54137839415767 x 917813298871770308465539 x 26526333976234009593263527 x 8558521377558885170560719135529 x 909090909090909090909090909090909090909090909090909110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001= 19841 x 976193 x 6187457 x 834427406578561 x 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