Factorizations of 99...991 2008-06-15(Sun) 00:02
Last update
Jun 15, 2008 00:02 JST
Sequence
1, 91, 991, 9991, 99991, ...
General term
10n -9
Algebraic factorizations 102k -9 = (10k -3)(10k +3)
See also 100...003 , 99...997 .
Room for prime numbers
upper limit of periods: 10000
upper limit of periodical factors: 4294967296
checked terms: 100000000
terms divided by periodical factors: 81984016
room for prime numbers: 18.02%
Prime numbers
103 -9 = 991 is prime. (Makoto Kamada / May 29, 2003)
105 -9 = 99991 is prime. (Makoto Kamada / May 29, 2003)
107 -9 = 9999991 is prime. (Makoto Kamada / May 29, 2003)
1033 -9 = ( 9) 32 1<33> is prime. (Makoto Kamada / May 29, 2003)
1045 -9 = ( 9) 44 1<45> is prime. (Makoto Kamada / May 29, 2003)
10105 -9 = ( 9) 104 1<105> is prime. (Makoto Kamada / PPSIQS / May 29, 2003)
10197 -9 = ( 9) 196 1<197> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
10199 -9 = ( 9) 198 1<199> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
10281 -9 = ( 9) 280 1<281> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
10301 -9 = ( 9) 300 1<301> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
10317 -9 = ( 9) 316 1<317> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
101107 -9 = ( 9) 1106 1<1107> is prime. (searched by Makoto Kamada / May 29, 2003) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 13, 2006)
101657 -9 = ( 9) 1656 1<1657> is prime. (searched by Makoto Kamada / May 29, 2003) (certified by Makoto Kamada / pock 0.2.1 / Aug 18, 2003)
103395 -9 = ( 9) 3394 1<3395> is PRP. (Makoto Kamada / May 29, 2003)
Searched:
References:
Condition
n≤200
Status
Completed up to n=100. (May 29, 2003)
Completed up to n=150. (Jul 10, 2004)
The following numbers are not factored yet. (n≤200)
n= 191 , 193 (2/200)
Factorization results
101 -9 =1
102 -9 =91 = 7 · 13
103 -9 =991 = definitely prime number
104 -9 =9991 = 97 · 103
105 -9 =99991 = definitely prime number
106 -9 =999991 = 17 · 59 · 997
107 -9 =9999991 = definitely prime number
108 -9 =99999991 = 7 · 13 · 769 · 1429
109 -9 =999999991 = 67 · 14925373
1010 -9 =9999999991<10> = 192 · 277 · 100003
1011 -9 =99999999991<11> = 83 · 1289 · 934693
1012 -9 =999999999991<12> = 757 · 1321 · 1000003
1013 -9 =9999999999991<13> = 31 · 3391 · 95128471
1014 -9 =99999999999991<14> = 7 · 13 · 769231 · 1428571
1015 -9 =999999999999991<15> = 653 · 718321 · 2131907
1016 -9 =9999999999999991<16> = 643 · 1297 · 77101 · 155521
1017 -9 =99999999999999991<17> = 43 · 19387 · 119955712351<12>
1018 -9 =999999999999999991<18> = 23 · 71 · 307 · 2251 · 6257 · 141623
1019 -9 =9999999999999999991<19> = 5441 · 1837897445322551<16>
1020 -9 =99999999999999999991<20> = 7 · 13 · 769230769 · 1428571429<10>
1021 -9 =999999999999999999991<21> = 17839 · 19813 · 237877 · 11893969
1022 -9 =9999999999999999999991<22> = 17 · 5882352941<10> · 100000000003<12>
1023 -9 =99999999999999999999991<23> = 479 · 857839 · 243365325222311<15>
1024 -9 =999999999999999999999991<24> = 61 · 5507 · 14221 · 1152763 · 181587071
1025 -9 =9999999999999999999999991<25> = 107 · 21569 · 390110923 · 11107033999<11>
1026 -9 =99999999999999999999999991<26> = 72 · 13 · 29 · 547 · 56527 · 3610339 · 48492137
1027 -9 =999999999999999999999999991<27> = 41947 · 3192187 · 5818399 · 1283533681<10>
1028 -9 =9999999999999999999999999991<28> = 19 · 31 · 613 · 839 · 276964579 · 119189511323<12>
1029 -9 =99999999999999999999999999991<29> = 5197 · 19241870309794111987685203<26>
1030 -9 =999999999999999999999999999991<30> = 599 · 2131 · 3733 · 209861 · 14902357 · 67103479
1031 -9 =9999999999999999999999999999991<31> = 64332799 · 1883470517<10> · 82529407366277<14>
1032 -9 =99999999999999999999999999999991<32> = 7 · 13 · 433 · 39323 · 45177491 · 1428571428571429<16>
1033 -9 =999999999999999999999999999999991<33> = definitely prime number
1034 -9 =9999999999999999999999999999999991<34> = 99999999999999997<17> · 100000000000000003<18>
1035 -9 =99999999999999999999999999999999991<35> = 2308769 · 13259446279<11> · 3266586248147987441<19>
1036 -9 =999999999999999999999999999999999991<36> = 47 · 1283 · 949261 · 17469877 · 1000000000000000003<19>
1037 -9 =9999999999999999999999999999999999991<37> = 1787 · 10076191 · 555365703265382231555726123<27>
1038 -9 =99999999999999999999999999999999999991<38> = 7 · 13 · 17 · 43 · 103 · 9431 · 18679 · 155027 · 9486361 · 56335953419<11>
1039 -9 =999999999999999999999999999999999999991<39> = 757 · 22111 · 1299187 · 45985834253851859338253959<26>
1040 -9 =9999999999999999999999999999999999999991<40> = 23 · 373 · 19031 · 155773 · 859249 · 265883581 · 1721071782307<13>
1041 -9 =99999999999999999999999999999999999999991<41> = 2801 · 14489 · 970867 · 192390028511<12> · 13191864450781787<17>
1042 -9 =999999999999999999999999999999999999999991<42> = 67 · 1164288119<10> · 858893931563<12> · 14925373134328358209<20>
1043 -9 =9999999999999999999999999999999999999999991<43> = 31 · 89 · 163 · 631 · 1123 · 31379901759227182253273005491071<32>
1044 -9 =99999999999999999999999999999999999999999991<44> = 7 · 13 · 157 · 601 · 1031137 · 14682887281<11> · 769230769230769230769<21>
1045 -9 =999999999999999999999999999999999999999999991<45> = definitely prime number
1046 -9 =9999999999999999999999999999999999999999999991<46> = 19 · 113 · 3049 · 983513 · 2972507 · 1800293893<10> · 290244589115247419<18>
1047 -9 =99999999999999999999999999999999999999999999991<47> = 3701884489<10> · 27013268592563045799563304526436832319<38>
1048 -9 =999999999999999999999999999999999999999999999991<48> = 3529 · 821461 · 838069 · 411605923 · 37967337697<11> · 26338428255901<14>
1049 -9 =9999999999999999999999999999999999999999999999991<49> = 258551 · 1542917 · 25067510989169360187582443013884314573<38>
1050 -9 =99999999999999999999999999999999999999999999999991<50> = 7 · 13 · 7668629 · 100308773475776339<18> · 1428571428571428571428571<25>
1051 -9 =999999999999999999999999999999999999999999999999991<51> = 481639 · 1001431 · 2204507 · 179488118809<12> · 5239744793907523162973<22>
1052 -9 =9999999999999999999999999999999999999999999999999991<52> = 83 · 223 · 6947 · 161377320703<12> · 2778770221987<13> · 173430153607087049797<21>
1053 -9 =99999999999999999999999999999999999999999999999999991<53> = 71 · 191 · 587 · 12562329568445036102250830275767002453548588013<47>
1054 -9 =999999999999999999999999999999999999999999999999999991<54> = 17 · 29 · 1335869 · 813219713 · 1229679979486675331<19> · 1518410537203064741<19>
1055 -9 =9999999999999999999999999999999999999999999999999999991<55> = 2701593300560063647774277<25> · 3701519395212785560731843555083<31>
1056 -9 =99999999999999999999999999999999999999999999999999999991<56> = 7 · 132 · 109 · 199 · 571 · 89779 · 140035456540965619<18> · 542858693881982519950057<24>
1057 -9 =999999999999999999999999999999999999999999999999999999991<57> = 10037 · 8675911 · 2086949124287147<16> · 5502614973976617719498047337479<31>
1058 -9 =9999999999999999999999999999999999999999999999999999999991<58> = 31 · 223283 · 228859 · 5834659 · 10928153 · 335398307039<12> · 295183134022089846821<21>
1059 -9 =99999999999999999999999999999999999999999999999999999999991<59> = 43 · 313921897407961<15> · 7408152838496002619265064701228387953553517<43>
1060 -9 =999999999999999999999999999999999999999999999999999999999991<60> = 24551 · 1514197 · 1859827 · 26899761675796814351<20> · 537684419034673655130289<24>
1061 -9 =9999999999999999999999999999999999999999999999999999999999991<61> = 174637 · 878473364729<12> · 31773852594137837<17> · 2051470437966151140949832791<28>
1062 -9 =99999999999999999999999999999999999999999999999999999999999991<62> = 7 · 13 · 23 · 1063 · 1453 · 2089 · 17021 · 95633 · 167826727 · 40083104483<11> · 1352315810743633261969<22>
1063 -9 =999999999999999999999999999999999999999999999999999999999999991<63> = 14499216344898896752959323769763<32> · 68969244696581083712684424134557<32>
1064 -9 =9999999999999999999999999999999999999999999999999999999999999991<64> = 19 · 59 · 6271 · 4814471 · 36799991 · 9566469711577703<16> · 839285264668608213245600047<27>
1065 -9 =99999999999999999999999999999999999999999999999999999999999999991<65> = 197 · 3319 · 12227 · 5653746453683<13> · 2212433780585198050210908345776014868486357<43>
1066 -9 =999999999999999999999999999999999999999999999999999999999999999991<66> = 151 · 439 · 757 · 66883 · 4492009 · 5338459457<10> · 42250012204817<14> · 294078654564558761050369<24>
1067 -9 =9999999999999999999999999999999999999999999999999999999999999999991<67> = 1321 · 5437 · 19597 · 161831 · 20738805713683<14> · 21169119569691551954355564217157401643<38>
1068 -9 =99999999999999999999999999999999999999999999999999999999999999999991<68> = 72 · 13 · 210019 · 971729379975436624732980913<27> · 769230769230769230769230769230769<33>
1069 -9 =999999999999999999999999999999999999999999999999999999999999999999991<69> = 63397 · 381757 · 626947971773213<15> · 2170339093195963<16> · 30365832264283391654982456041<29>
1070 -9 =9999999999999999999999999999999999999999999999999999999999999999999991<70> = 17 · 2111 · 3759289 · 26793961 · 1501972065791<13> · 8389656836773<13> · 219540251670011409967913819<27>
1071 -9 =99999999999999999999999999999999999999999999999999999999999999999999991<71> = 78881595557<11> · 1267722835648523341138988112316740317428617451159045144870763<61>
1072 -9 =999999999999999999999999999999999999999999999999999999999999999999999991<72> = 103 · 1811 · 922639 · 5963471 · 69425387 · 3480881723167<13> · 3023024732613877<16> · 1333718356890134051<19>
1073 -9 =9999999999999999999999999999999999999999999999999999999999999999999999991<73> = 31 · 4341008533<10> · 263305661205877<15> · 282219793586905741966296113640065805999889291921<48>
1074 -9 =99999999999999999999999999999999999999999999999999999999999999999999999991<74> = 7 · 13 · 5779 · 702780737 · 40483675109<11> · 8688593630053<13> · 769230769230769230769230769230769231<36>
1075 -9 =999999999999999999999999999999999999999999999999999999999999999999999999991<75> = 67 · 6666551 · 49052929 · 831859001 · 54866761472622933343355173670712591013912519245187<50>
1076 -9 =9999999999999999999999999999999999999999999999999999999999999999999999999991<76> = 2399 · 34367 · 76417717 · 50954499311257<14> · 25681678366581487<17> · 1212908750097169152242159463709<31>
1077 -9 =99999999999999999999999999999999999999999999999999999999999999999999999999991<77> = 1111680721<10> · 286073245559406853963<21> · 3819624664305357584639<22> · 82323152627172493323691403<26>
1078 -9 =999999999999999999999999999999999999999999999999999999999999999999999999999991<78> = 107 · 827 · 1093 · 187423 · 55165513569618566444754607<26> · 1000000000000000000000000000000000000003<40>
1079 -9 =9999999999999999999999999999999999999999999999999999999999999999999999999999991<79> = 277 · 293 · 613 · 119591 · 1680713307247928623333378139199916888933751555253361302265955410357<67>
1080 -9 =99999999999999999999999999999999999999999999999999999999999999999999999999999991<80> = 7 · 13 · 43 · 661 · 4787 · 48239 · 5853526052603<13> · 569085301052150111<18> · 50261106447997346213579545740119923<35>
1081 -9 =999999999999999999999999999999999999999999999999999999999999999999999999999999991<81> = 518729 · 2567713237<10> · 750780443939323421019040060823110255867754708718152845260302358467<66>
1082 -9 =9999999999999999999999999999999999999999999999999999999999999999999999999999999991<82> = 19 · 29 · 47 · 149 · 44909 · 1046191 · 6387259 · 18348412175865138486980597873<29> · 470659572629542911224468953859<30>
1083 -9 =99999999999999999999999999999999999999999999999999999999999999999999999999999999991<83> = 227 · 5678824643<10> · 365174417962746309511512440803<30> · 212429750392986068412353843621587493937877<42>
1084 -9 =999999999999999999999999999999999999999999999999999999999999999999999999999999999991<84> = 23 · 61 · 1597 · 9865301191<10> · 3369415196267<13> · 132459430228679414184601<24> · 101365379590466879644202035797733<33>
1085 -9 =9999999999999999999999999999999999999999999999999999999999999999999999999999999999991<85> = 3033644667696760540431621340129571927071<40> · 3296364965377543000577028480024125464906676521<46> (Makoto Kamada / SNFS / 0:28:18:37)
1086 -9 =99999999999999999999999999999999999999999999999999999999999999999999999999999999999991<86> = 7 · 13 · 17 · 63473 · 71861 · 1004537 · 6948583 · 2639420403553807201<19> · 769230769230769230769230769230769230769231<42>
1087 -9 =999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<87> = 89 · 30724787 · 2408107211722250575505321<25> · 151860663916435588509393477939479396484360673953474797<54>
1088 -9 =9999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<88> = 31 · 71 · 467 · 2293 · 5113 · 13825941769007037889<20> · 218137357234515008089<21> · 275142993946312101483059532532768657<36>
1089 -9 =99999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<89> = 12919 · 16167474982347553799533<23> · 478772176962247587352907492838496717461481419429473558642556133<63>
1090 -9 =999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<90> = 1511 · 2621 · 26190869 · 143091007 · 202758977 · 7084864849<10> · 7665370631<10> · 2039334898823<13> · 35230144787557<14> · 85164473749219<14>
1091 -9 =9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<91> = 1877 · 3129911 · 306588651529<12> · 5551977068631901091589255759952253908919377717783066915271868552132757<70>
1092 -9 =99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<92> = 7 · 13 · 44029 · 44436195239<11> · 74716684251563<14> · 774717324390885241<18> · 231687279868248212917<21> · 41881272672179231514961<23>
1093 -9 =999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<93> = 83 · 757 · 1559760415307<13> · 2656685632389043<16> · 3840855484347303588648524752054204879903713883726897884305161<61>
1094 -9 =9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<94> = 397 · 409 · 967 · 66977 · 230999 · 26846177 · 9450382559<10> · 198266889049<12> · 64414344031291<14> · 1270455041555076682580419086613351<34>
1095 -9 =99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<95> = 28002119 · 183521111 · 80159620523<11> · 6812318414609<13> · 35634648700779351974316488534173284861604554506730720757<56>
1096 -9 =999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<96> = 8737 · 106669 · 726599 · 4378837 · 69080527 · 1127952811<10> · 554508243299<12> · 2663156190955741239949<22> · 2930857126525877256434827<25>
1097 -9 =9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<97> = 928307 · 90591614701069919<17> · 2477758575530044609237440495439<31> · 47991175334310938360645484759471530531608093<44>
1098 -9 =99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<98> = 7 · 13 · 464459 · 551342479 · 5952808865209<13> · 168557936063381<15> · 10024665283411171<17> · 845440161194356421<18> · 504621641480758757819<21>
1099 -9 =999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991<99> = 60089 · 3663323155566124987<19> · 5639339932759193074579906236439<31> · 805566723873756259384442313420944670580411883<45>
10100 -9 =9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 <100> = 19 · 97 · 283 · 14627 · 3674333699<10> · 994327748569<12> · 61236769827829<14> · 44848033061277421<17> · 3148809563627188687<19> · 41488023184722935209<20>
10101 -9 =( 9) 100 1<101> = 43 · 1951013 · 1191986622000385035518638564374173230629064145436957800300259046108652989677074017088725488449<94>
10102 -9 =( 9) 101 1<102> = 17 · 3187 · 144203 · 1353383 · 1991177 · 273871783 · 1876732427<10> · 6775887552190427787707<22> · 13637925013200840085919638391816980569079<41>
10103 -9 =( 9) 102 1<103> = 31 · 1289 · 109811749013<12> · 2278959357036763169790259713957172311789365105706462004361509988932771734012673210727773<88>
10104 -9 =( 9) 103 1<104> = 7 · 13 · 179 · 5290477824748729<16> · 1947862590871197811021597<25> · 2206202131092079878657863<25> · 270026919286686265519817460570276301<36>
10105 -9 =( 9) 104 1<105> = definitely prime number
10106 -9 =( 9) 105 1<106> = 23 · 103 · 28966193 · 4116417953254772568899<22> · 1056215898465504263474971028839<31> · 33517479718779992603489942082562596233732843<44>
10107 -9 =( 9) 106 1<107> = 5549373285559157092001363028537319<34> · 18020052869794279776876644915664872171366200606040049218496910334177029489<74> (Robert Backstrom / NFSX v1.8)
10108 -9 =( 9) 107 1<108> = 67 · 21518801375655714851137<23> · 46470989835488840363806434126781<32> · 14925373134328358208955223880597014925373134328358209<53>
10109 -9 =( 9) 108 1<109> = 2252231 · 5021879364791<13> · 420996486880249365031<21> · 2100111342215991523137439256807739714502295190739810518118318630550641<70>
10110 -9 =( 9) 109 1<110> = 72 · 13 · 29 · 3989 · 2290143001<10> · 3696549175591577<16> · 90865194024447148790098749503<29> · 1764175903156622301759112718314562795753064064813<49>
10111 -9 =( 9) 110 1<111> = 311 · 19843 · 339520660770777220429931419842789373<36> · 477272126034520940722669910353174573124220865322990922519656783471879<69> (Robert Backstrom / NFSX v1.8)
10112 -9 =( 9) 111 1<112> = 313 · 3941689 · 19336103 · 4191836705988181479348939975589788043307<40> · 100000000000000000000000000000000000000000000000000000003<57>
10113 -9 =( 9) 112 1<113> = 50894932942368973<17> · 1964832139836696397682583169637882971162304383697587052901592370317534325799462577219143296115667<97>
10114 -9 =( 9) 113 1<114> = 1439 · 2448952313317<13> · 113619994412549<15> · 3593891055967117960201170304091<31> · 694927032661570535093815149409312022237665045170257123<54>
10115 -9 =( 9) 114 1<115> = 431 · 761 · 47521 · 117144283957<12> · 33326319321401<14> · 331925529497713410796178426929591703479<39> · 495111931006187446021416144073444010100227<42>
10116 -9 =( 9) 115 1<116> = 7 · 13 · 1033 · 173219 · 171132083 · 3214902282801317877541<22> · 8071642288696029355717<22> · 1382934587194025722583321808878440049785645138984926013<55>
10117 -9 =( 9) 116 1<117> = 547 · 6987367889<10> · 109039799172580020244441<24> · 2399462798624315554649709206087096815106848663696985921484062707559204417437731797<82>
10118 -9 =( 9) 117 1<118> = 17 · 19 · 312 · 1249 · 4345511 · 57041926629930666036665011901733531105845315401<47> · 104058272632674297606659729448491155046826222684703433923<57>
10119 -9 =( 9) 118 1<119> = 340352021759490884489<21> · 113148498830123776919173<24> · 713773037869037412947173769<27> · 3638000295246258667246145912935370160176949991387<49>
10120 -9 =( 9) 119 1<120> = 1932 · 719 · 757 · 6755603 · 3171548632838023<16> · 33362320576752631<17> · 253721783490136061838019<24> · 271963805968702864258461551790513043662751795453<48>
10121 -9 =( 9) 120 1<121> = 245669593284788565157<21> · 40705078175497523585658176359797372933442555843803048351858849905659364452055101437395616728774464363 <101>
10122 -9 =( 9) 121 1<122> = 7 · 13 · 432 · 59 · 131 · 157 · 167 · 1321 · 4656167 · 279376131961211<15> · 247777638479293206997639471109<30> · 6888100737095659876606563395668348970470023329997196543<55>
10123 -9 =( 9) 122 1<123> = 71 · 643 · 4523 · 1211599 · 198625207849<12> · 31841595447419671637<20> · 631998430051830557700888487084817052140637940611464801026449689276201645624747<78>
10124 -9 =( 9) 123 1<124> = 163 · 9661 · 3625031 · 603220214617<12> · 4092282467463097<16> · 120127553010300307<18> · 129176073645540570328399<24> · 45731177968650786903285932397336219226657811<44>
10125 -9 =( 9) 124 1<125> = 443 · 119003827 · 239025992477781293791695002659636001203014815071<48> · 7935790893211144760583231282378683537340883150482218186749879931561<67> (Robert Backstrom / NFSX v1.8)
10126 -9 =( 9) 125 1<126> = 1346919923<10> · 99582738067633474259<20> · 259449246196264501631<21> · 2279800480953691053649<22> · 4404728007638875844033<22> · 2861579460492886363697385972683569<34>
10127 -9 =( 9) 126 1<127> = 1279 · 4481 · 481067 · 975991 · 78121039 · 92152509519425281345483<23> · 516211832437885012830316711233981950839391966071710578960440252992807200434681<78>
10128 -9 =( 9) 127 1<128> = 7 · 13 · 23 · 47 · 5676423007<10> · 36627147032611375348033<23> · 6871065942231129106260647628859<31> · 711591830925780972034441044616807799046466946559453497473849<60>
10129 -9 =( 9) 128 1<129> = 1009 · 77477 · 13641424747<11> · 80755181161<11> · 362949074802653<15> · 376154756266432204449733<24> · 85053787774507451964167307670996633539178013275162506825756889<62>
10130 -9 =( 9) 129 1<130> = 613 · 34625917 · 640113583 · 168988305737<12> · 27879282336387712355695204432176867365129339<44> · 156222274695895650131829806836015851268070966711543754259<57>
10131 -9 =( 9) 130 1<131> = 89 · 107 · 929 · 161985391 · 625730947759680608316517<24> · 4173470555635270048745347<25> · 26720812783453188342897986088256735447149625712703020502970430010797<68>
10132 -9 =( 9) 131 1<132> = 3923 · 2546962972527613<16> · 52234229988717651520074139707847<32> · 19144534153485086423317835475736549<35> · 100082710942204725571854029984014199096850397403<48>
10133 -9 =( 9) 132 1<133> = 31 · 906121 · 4251769 · 305012901698475689<18> · 274513836604759106468014028146903884058523985192147532823372067829573046278727191808481524623176990401 <102>
10134 -9 =( 9) 133 1<134> = 7 · 132 · 17 · 83 · 4462531 · 18699520487<11> · 1300152148179033332753<22> · 52308679461327694413683<23> · 143165945597753855112098594619101<33> · 73734181764135557483526518495064769<35>
10135 -9 =( 9) 134 1<135> = 306763 · 8464241 · 3421887940693<13> · 112549409303150618674183268133025591762701233598641472560443313845767714664563979024974638179818758103720133889 <111>
10136 -9 =( 9) 135 1<136> = 19 · 181 · 8269 · 25867 · 10927079 · 1008934873<10> · 1407477156450817<16> · 16618414584512959499<20> · 2161655080961323535207341<25> · 24388450615853296712957638559087522557098904525303<50>
10137 -9 =( 9) 136 1<137> = 5165311746933052842465538744631<31> · 19359915702934259182946897176045257949017142531937648447023760144426052319383724069748135763227304525002561 <107> (Robert Backstrom / GMP-ECM 5.0c)
10138 -9 =( 9) 137 1<138> = 29 · 347 · 911 · 240347 · 797489219 · 6719463889<10> · 9278852153<10> · 56916658697<11> · 724445935328640404936057<24> · 2703789257357684025009811<25> · 81873532684973362089980292505983625333<38>
10139 -9 =( 9) 138 1<139> = 2266591 · 2107924908563<13> · 12726436311211289<17> · 164461745696618591896009005886435914358832505722141167532684801621204516924694144596831699353270813308043 <105>
10140 -9 =( 9) 139 1<140> = 7 · 13 · 103 · 2838853 · 609124139649827<15> · 12036938568862646965703<23> · 36956589665321881667605033<26> · 13869625520110957004160887656033287101248266296809986130374479889043<68>
10141 -9 =( 9) 140 1<141> = 67 · 151 · 7213 · 20641 · 663898341873149124755823694157220929460057755228744437893664294783209177859251794012695675122759673986348215698104475317933187831 <129>
10142 -9 =( 9) 141 1<142> = 4957 · 390869 · 1398779 · 10900801759<11> · 911624502096187117724092068409<30> · 56615306657739612877438471735301<32> · 6558317755506364692997595133084191555668163745537318023<55>
10143 -9 =( 9) 142 1<143> = 43 · 4987 · 8103911869384742969083926875701596043<37> · 57543658086818917236653328425662353297036755376057033707756606095232065216600744427923471045358733757 <101> (Tetsuya Kobayashi / NFSX / 62 hours)
10144 -9 =( 9) 143 1<144> = 61 · 4919 · 72103 · 349051 · 725437 · 14120947 · 928059349171<12> · 102778173667843<15> · 483601316311322078135288401<27> · 280235709382592215021783942116823254062739685689808590303568199<63>
10145 -9 =( 9) 144 1<145> = 5521133 · 30320243 · 306989367187882350122759<24> · 362929801125787433471130910799<30> · 162964976215164129227941885578492094157<39> · 3290022525160979923646398846777354649597<40> (Robert Backstrom / GMP-ECM 5.0c, PPSIQS Ver 1.1)
10146 -9 =( 9) 145 1<146> = 7 · 13 · 5527003 · 31820483 · 37830550701787<14> · 3678953376089882824379299271733196192314658634813671<52> · 44894712269811510134166455882251333879142294243975761506466492937<65>
10147 -9 =( 9) 146 1<147> = 757 · 83719 · 2529649 · 564188459973277<15> · 1989051072783415478046060199<28> · 5558398631776347251250612449996615477873378707620847736764219298064172335941129476440400951<91> (Robert Backstrom / GMP-ECM 5.0c)
10148 -9 =( 9) 147 1<148> = 31 · 191 · 277 · 9619 · 445792777 · 2600441047<10> · 20025961396631<14> · 227647200762466824679<21> · 566498878475024033576724763236475512079<39> · 211719305898683240805292394343293049479508278233<48>
10149 -9 =( 9) 148 1<149> = 5598934639<10> · 24622603363924497961<20> · 9406652544628197783013757175083<31> · 17015077596097981289004980562402392680515791<44> · 4532017689917763060723550614008624077237163293<46> (Robert Backstrom / GMP-ECM 5.0c, PPSIQS Ver 1.1)
10150 -9 =( 9) 149 1<150> = 17 · 23 · 593 · 3019 · 29593547 · 1228340719<10> · 203287386737<12> · 235122042143<12> · 231740870573890406759791<24> · 649616931789157865019702753163<30> · 5461674546661760187240499608772098204986115329557<49>
10151 -9 =( 9) 150 1<151> = 4065209 · 1054947908341869962347<22> · 2331772124791830137648157620024086292452822488119665231195374868127084505089199354203662189352272288259806743791305159760717 <124>
10152 -9 =( 9) 151 1<152> = 72 · 13 · 47843 · 695017 · 657565957 · 18660707022367378937999<23> · 4583778702733702837221245869057<31> · 67708151357480212958271175141825303<35> · 1239694634341423432349916056158844097321901<43>
10153 -9 =( 9) 152 1<153> = 7351 · 12177173 · 4869339071<10> · 1717538402791591<16> · 212160165998317320103944607230187712351218102168603<51> · 6296029889857224726698251701700348692740511088455095303322626184799<67> (Makoto Kamada / GGNFS-0.77.1-20050930-pentium4 / 36.60 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Oct 12, 2005)
10154 -9 =( 9) 153 1<154> = 19 · 9770545391<10> · 50670908789<11> · 492691725102017033<18> · 21577127639648878849780469624000867189<38> · 185554311496620532371770351611143673123<39> · 538925768921415130739706333069119686561<39>
10155 -9 =( 9) 154 1<155> = 199 · 359 · 2820400404223072081249<22> · 77307199863851638605347<23> · 6419803921831371590190563637961411585509868203087940243856771169107672745149713980380003017961449703927917 <106>
10156 -9 =( 9) 155 1<156> = 659 · 37657 · 82507 · 117361 · 7062049 · 1174699424012203549<19> · 273991272661126875657939650707603352993489342536453<51> · 1830880745642327756127708628460154103036454601740305990569843647<64>
10157 -9 =( 9) 156 1<157> = 1182138400863175552253848266595264231758705488091359346888751281045582124679<76> · 8459246390015065347380115262012913546306699962332583936149204215042988678809171729<82> (Makoto Kamada / GGNFS-0.54.4-k1 / 182.16596 hours / Sep 27, 2004)
10158 -9 =( 9) 157 1<158> = 7 · 13 · 71 · 113 · 11273 · 66457829 · 227601541763<12> · 13755478715667106004852653<26> · 855791776632840528315673335967<30> · 68236562514926748050140226135968174467243038164709414598530184443428477847<74>
10159 -9 =( 9) 158 1<159> = 557 · 787 · 66522203560881529<17> · 463502940459739711<18> · 5179103681557614987753607571009<31> · 14285529639955355530391178145824057096420000669920946451104886135613114248058746965615319<89> (Makoto Kamada / GMP-ECM 5.0.3 B1=100550, sigma=3289701478)
10160 -9 =( 9) 159 1<160> = 2663 · 130960381 · 87144781633537<14> · 4110612782962333<16> · 3455312701687993075561<22> · 1634764941685338629653189<25> · 2535895350921026674019960278106110759<37> · 5588135774935638678380176533658718987<37>
10161 -9 =( 9) 160 1<161> = 37871278906453241<17> · 21025652136804630508221938561<29> · 125585804992968912808788945390634517801861766554822671111449018351172498773938268560062296220409535778931448185975791 <117> (Wataru Sakai / GMP-ECM B1=10000000, sigma=696853086)
10162 -9 =( 9) 161 1<162> = 619 · 1759 · 28477 · 572435189 · 3777480038153<13> · 82711432890473<14> · 9232332226415328725291695187328474787743613722899413<52> · 19531869160556511907230090805735936797585412429882883916315932831<65>
10163 -9 =( 9) 162 1<163> = 31 · 197 · 12803410721<11> · 46745703973<11> · 836469155018551<15> · 17629888376681459284632404389201355683<38> · 185526180890784762356394559001150584399176683003863408727544883590129373766517842415517<87> (Patrick Keller / GMP-ECM B1=1000000, sigma=1966041121 for P38 / May 28, 2005)
10164 -9 =( 9) 163 1<164> = 7 · 13 · 43 · 109 · 1151 · 12973 · 432661 · 6702143138293367<16> · 872912117122274214886393<24> · 26915104249006886077344416513524151206136145229903<50> · 230472904760975218695860182014530586110889780505824741637<57>
10165 -9 =( 9) 164 1<165> = 56290473873165148381086844809790940629420103915155210253<56> · 17764995232643102887053101422297754638281216307353274409711866004077365678936425580088372114246263483737897747 <110> (Tetsuya Kobayashi / GGNFS 0.54.4 / 4PCs*2days/sieve+1PC*0.5days/linear)
10166 -9 =( 9) 165 1<166> = 17 · 29 · 6133 · 6286051 · 2384189546677451999<19> · 23823584851228754531<20> · 230082359474216559463433395796447020827820649934059530357<57> · 40259743299929784472838712049504899249693041902211136407533<59>
10167 -9 =( 9) 166 1<167> = 1693 · 251081 · 235249761719633225013599965162333286462954974186008359040388274273923782742394126426981239323174861244338605681202231109681148048384561882123999429538147810827 <159>
10168 -9 =( 9) 167 1<168> = 29059 · 136039691 · 152199469 · 13631181661<11> · 21392516536095359<17> · 16775491065354149113<20> · 1502670426032911987830107685541<31> · 3464655614694615820134361459503031<34> · 65259858139040767607584620036276601603<38>
10169 -9 =( 9) 168 1<169> = 94211591202708488915524241578569786726705726654902440361<56> · 106144051621882701124925887117325659671531292461815961898361365027825862303359296356795774245471393139352946460831 <114> (Makoto Kamada / GGNFS-0.77.1 / 168.51 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Sep 30, 2005)
10170 -9 =( 9) 169 1<170> = 7 · 13 · 4073 · 19471 · 29063 · 64849 · 1848031 · 33819758330585864983<20> · 159924045213327762917315647618256183211961766315464550981<57> · 735561004054368499805948808599092871902963794530535645906012138636137<69>
10171 -9 =( 9) 170 1<171> = 307 · 1341257227<10> · 119089804935077063337409<24> · 345902145520852319930047561079359<33> · 58955144714945402926154900462795557653240056734408286929929832931465190563110621663093933530297499871449 <104> (Patrick Keller / GMP-ECM B1=1000000, sigma=3663717252 for P33 / May 29, 2005)
10172 -9 =( 9) 171 1<172> = 19 · 23 · 997 · 967681309615663<15> · 5455303132259154458842540374893027723704662896639359296193937202067<67> · 4347826086956521739130434782608695652173913043478260869565217391304347826086956521739<85>
10173 -9 =( 9) 172 1<173> = 401 · 2528185841<10> · 938580727415304869460365420846237262713037883<45> · 105093292974603519781220816145515742537483095614362298755215504949519619870717052285912811121252640366779911913175797 <117> (Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 / 255.28 hours on windows xp professional, 1 gig RAM, 3.2 ghz p4, cygwin / Sep 27, 2006)
10174 -9 =( 9) 173 1<174> = 47 · 67 · 103 · 257 · 757 · 113123 · 824281 · 4632613 · 625148401 · 95226283921568354649911469910374171419599375062477580588497655609249<68> · 616267018056359185441747698615843643683296258084651274651119987076887<69>
10175 -9 =( 9) 174 1<175> = 83 · 89 · 277590538396397099817467<24> · 896295447371381022541530417241001<33> · 61949583081432845501932022855183580890650237564733399<53> · 87828944454424628608061572314719937855686216572417491650902721<62> (Patrick Keller / GMP-ECM B1=50000, sigma=3752722861 for P33 / May 29, 2005) (Makoto Kamada / GGNFS-0.77.1-20050930-pentium4 gnfs / 54.99 hours on Pentium 4 3.06GHz, Windows XP and Cygwin for P53 x P62 / Oct 15, 2005)
10176 -9 =( 9) 175 1<176> = 7 · 13 · 12097 · 302303497 · 15968813857743312100267<23> · 7395228897021612341523232889578455213960269146595764004311471<61> · 2544564574556572962069409237534454425346031538731320831426673073619023437129577<79>
10177 -9 =( 9) 176 1<177> = 1321 · 2376752857145462309881481<25> · 166539912927088863044604457888822597127041055210868917788027<60> · 1912470850607748174543437500075957519331332156283120157980757697449058309385972258440240133<91> (matsui / GGNFS-0.77.1-20060513-prescott snfs / May 6, 2008)
10178 -9 =( 9) 177 1<178> = 31 · 269 · 1663 · 3253 · 8803 · 711780703 · 751414214574205487<18> · 50085008861179389314983865307479<32> · 6270490382978711525333242984143695967656023<43> · 149914670527656837997920618197642940784707574042657246252776461<63>
10179 -9 =( 9) 178 1<179> = 569 · 8951 · 944482695820147111<18> · 546906270091264303592773419636796433846880957980999<51> · 38010997664106318499368894010475771853596823493322466917536870017901952887416421331572081502939677862201 <104> (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / 378.09 hours / May 18, 2008)
10180 -9 =( 9) 179 1<180> = 59 · 166303 · 1981462151<10> · 403895669461<12> · 5427392805973<13> · 6775211799337<13> · 8974986752701<13> · 78160868906623597<17> · 2976176599680018387033042268965119689<37> · 1658810987591830795547164323164711490089752199766030492869341<61>
10181 -9 =( 9) 180 1<181> = 613 · 4721990197<10> · 118046288030005689138006772776064145473173086074955176614021148886231992477409<78> · 29265915150079883819125682044728327718073357005292178916251770323960139756081440411297901759<92> (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / May 12, 2008)
10182 -9 =( 9) 181 1<182> = 7 · 13 · 17 · 1223 · 611557 · 622802562607<12> · 541191531367411<15> · 53040230332956067<17> · 3920505864836767714747<22> · 4945904653788016124568903613721692237248629<43> · 249316864069717043485091626653147919697908905053883660187580519<63>
10183 -9 =( 9) 182 1<183> = 49314675241585004778040302476198275634070752715382741171333<59> · 27179661213248372553517898319953454110361829996769269348594493<62> · 746070354608195431221196594309881696831382401936346066887929639<63> (Wataru Sakai / GGNFS-0.77.1-20060513-pentium4 / 693.77 hours on Pentium 4 3GHz, Windows XP and Cygwin / Oct 9, 2006)
10184 -9 =( 9) 183 1<184> = 107 · 841801 · 3557017 · 211480670972866622535223234753759<33> · 76772438105837719738754548269930764941<38> · 3422354146951056095066841448159662200272103243<46> · 561719994649737610867659787910638005737532777151667317<54>
10185 -9 =( 9) 184 1<185> = 43 · 68239 · 2538313576960440629507448895847540063266132079<46> · 29377049543046125556029128856057470051512089568061282636870001<62> · 457030771896922620319211488891391699946102749496004569879285614325665077<72> (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / May 17, 2008)
10186 -9 =( 9) 185 1<186> = 233 · 419 · 10744219 · 291653535584641<15> · 52792348845059647<17> · 5459780369426989258506416918868167807<37> · 25943645194741155506563259922410371213134407504184593<53> · 437130192678284489192380500009849205232710912361559391<54>
10187 -9 =( 9) 186 1<187> = 381467 · 252250919 · 573590921 · 2468421133<10> · 28220407597<11> · 7739992696481<13> · 623469605000773495978145688789573442397<39> · 538976246538898546343223750880120388579184821372415393352789944003119846089632154549645112111<93> (Patrick Keller / GMP-ECM B1=1000000, sigma=4006704447 for P39 / May 28, 2005)
10188 -9 =( 9) 187 1<188> = 7 · 13 · 151548409 · 487606042003<12> · 1465865413328343894556166417276893<34> · 3462670511054145557735868404409558124203646135593037<52> · 2929765641752731346391547040207212875979805414190271980235225659141284583284855143<82>
10189 -9 =( 9) 188 1<189> = 680546965633716247679<21> · 210016417538123401200815971279<30> · 8147900155250040965434833800626154533552907527597<49> · 858702947397860145236409007951942850049599814990863975327405594646045661188912043740978083<90> (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=72668037 for P30 / Mar 12, 2005) (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / 1147.35 hours / Jun 14, 2008)
10190 -9 =( 9) 189 1<190> = 19 · 509 · 2591 · 11279 · 37728203 · 718809580057632062928074197<27> · 15232652842182146291582535453277<32> · 9132939882670122379669592086842575587<37> · 9378307897647822189773362682835304573974710330908432747151623394481317471521<76>
10191 -9 =( 9) 190 1<191> = 25890181282711<14> · 19215578593700683<17> · [201007120753913992913726676871999752197866484593647274473058062430107124951627993332234694165639979396161961186666496539291615060870044793869267715322527456739907 <162> ] SUBMIT/RESERVE
10192 -9 =( 9) 191 1<192> = 1861 · 38604899 · 67135031 · 3339133451<10> · 75802272361<11> · 1274839317373<13> · 371370564511057<15> · 3210299262702817<16> · 1002960752029899359<19> · 537345513164965072541644277270284793121977431488447071466953250940354648038688876947877485223<93>
10193 -9 =( 9) 192 1<193> = 31 · 71 · 397 · 31039 · 7333825763352817867<19> · [50274891495756964747055055496890986637122321939508209584006709525221053605515373965266365474014162871727873923935469195773083682555289322275596819198059208928831231 <164> ] SUBMIT/RESERVE
10194 -9 =( 9) 193 1<194> = 72 · 13 · 232 · 29 · 2281 · 56978387 · 24702593883547<14> · 572041744923931<15> · 441830682536309401<18> · 4594143404942642691414177378188955640856825123859977753777753<61> · 2744989966329896961448749127879070039002143600805487375898998297932229<70>
10195 -9 =( 9) 194 1<195> = 1289 · 283435121 · 190918276279<12> · 1608873192799<13> · 387312818354664563<18> · 1079504646683992390751<22> · 296827436308088224012637591<27> · 71801525491886233491994351008708055401003967702537009426787904436648333892829264331597536123173<95> (Wataru Sakai / GMP-ECM B1=2500000, sigma=1727198373)
10196 -9 =( 9) 195 1<196> = 97 · 227 · 105199 · 135288787 · 5127030864793921<16> · 378919599206831707<18> · 4907420475243384479<19> · 3616709145802705022310102159175743619073157102612973<52> · 925441856044986409718150197395729413167764668894414882028382058169268699297<75>
10197 -9 =( 9) 196 1<197> = definitely prime number
10198 -9 =( 9) 197 1<198> = 172 · 367 · 1517627 · 2113775865581<13> · 10526423190323<14> · 48012016357931<14> · 3591932541314891<16> · 80691749292003731118629647616252267832462124947404914376760456191<65> · 20064301263767150482328850050963655988361397950026433927658752114587<68>
10199 -9 =( 9) 198 1<199> = definitely prime number
10200 -9 =( 9) 199 1<200> = 7 · 13 · 157 · 769 · 2593 · 596275259857<12> · 4888946572366141<16> · 27089835581037121<17> · 220030935994058489226133<24> · 4242036622639156527888055237578804493024993216233097<52> · 47621545764299677617779790257997285086538394033923200643767527821353377<71>