Factorizations of 988...883

Table of contents

1. About 988...883
   • First ten terms
   • General term
2. Prime numbers of the form 988...883
   • Last update
   • Searched up to
   • Difficulty of search
   • Results
3. Factorizations of 988...883
   • Last update
   • Completed up to
   • Range
   • Results
4. References

1. About 988...883

First ten terms

93, 983, 9883, 98883, 988883, 9888883, 98888883, 988888883, 9888888883, 98888888883

General term

(89·10ⁿ-53)/9

2. Prime numbers of the form 988...883

Last update

Jan 18, 2009

Searched up to

n≤10000

Difficulty of search

15.69%

Results

1. (89·10²-53)/9 = 983 is prime. (Makoto Kamada / Dec 7, 2004)
2. (89·10³-53)/9 = 9883 is prime. (Makoto Kamada / Dec 7, 2004)
3. (89·10³²-53)/9 = 9(8)₃₁3_<33> is prime. (Makoto Kamada / PPSIQS / Dec 7, 2004)
4. (89·10⁴²-53)/9 = 9(8)₄₁3_<43> is prime. (Makoto Kamada / PPSIQS / Dec 7, 2004)
5. (89·10⁷⁵-53)/9 = 9(8)₇₄3_<76> is prime. (Makoto Kamada / PPSIQS / Dec 7, 2004)
6. (89·10³⁶⁸-53)/9 = 9(8)₃₆₇3_<369> is prime. (searched by Makoto Kamada / Dec 7, 2004) (certified by Makoto Kamada / PPSIQS / Jan 8, 2005)
7. (89·10¹³⁹²-53)/9 = 9(8)₁₃₉₁3_<1393> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 7, 2006)

3. Factorizations of 988...883

Last update

Oct 23, 2009

Completed up to

• n≤100 / Jan 8, 2005

Range

n≤100

Results

(89·10¹-53)/9 =

93

= 3 · 31

(89·10²-53)/9 =

983

= definitely prime number

(89·10³-53)/9 =

9883

= definitely prime number

(89·10⁴-53)/9 =

98883

= 3² · 10987

(89·10⁵-53)/9 =

988883

= 7 · 141269

(89·10⁶-53)/9 =

9888883

= 17 · 581699

(89·10⁷-53)/9 =

98888883

= 3 · 167 · 197383

(89·10⁸-53)/9 =

988888883

= 47 · 151 · 139339

(89·10⁹-53)/9 =

9888888883_<10>

= 113 · 2441 · 35851

(89·10¹⁰-53)/9 =

98888888883_<11>

= 3 · 32962962961_<11>

(89·10¹¹-53)/9 =

988888888883_<12>

= 7 · 27479 · 5141011

(89·10¹²-53)/9 =

9888888888883_<13>

= 19 · 23 · 1277 · 2143 · 8269

(89·10¹³-53)/9 =

98888888888883_<14>

= 3³ · 1019 · 1319 · 2724989

(89·10¹⁴-53)/9 =

988888888888883_<15>

= 397 · 829 · 3004709291_<10>

(89·10¹⁵-53)/9 =

9888888888888883_<16>

= 14143 · 699207303181_<12>

(89·10¹⁶-53)/9 =

98888888888888883_<17>

= 3 · 31 · 467 · 563 · 4044261911_<10>

(89·10¹⁷-53)/9 =

988888888888888883_<18>

= 7 · 141269841269841269_<18>

(89·10¹⁸-53)/9 =

9888888888888888883_<19>

= 4864147 · 2033016043489_<13>

(89·10¹⁹-53)/9 =

98888888888888888883_<20>

= 3 · 32962962962962962961_<20>

(89·10²⁰-53)/9 =

988888888888888888883_<21>

= 83 · 11914323962516733601_<20>

(89·10²¹-53)/9 =

9888888888888888888883_<22>

= 29 · 340996168582375478927_<21>

(89·10²²-53)/9 =

98888888888888888888883_<23>

= 3² · 17 · 199 · 809629 · 4011593641441_<13>

(89·10²³-53)/9 =

988888888888888888888883_<24>

= 7 · 149 · 523 · 569 · 3186025397836763_<16>

(89·10²⁴-53)/9 =

9888888888888888888888883_<25>

= 716959 · 14687287 · 939099469051_<12>

(89·10²⁵-53)/9 =

98888888888888888888888883_<26>

= 3 · 32962962962962962962962961_<26>

(89·10²⁶-53)/9 =

988888888888888888888888883_<27>

= 131 · 357107 · 21138678727076174699_<20>

(89·10²⁷-53)/9 =

9888888888888888888888888883_<28>

= 307 · 4931 · 6532420291811288213099_<22>

(89·10²⁸-53)/9 =

98888888888888888888888888883_<29>

= 3 · 32962962962962962962962962961_<29>

(89·10²⁹-53)/9 =

988888888888888888888888888883_<30>

= 7 · 11941 · 48121 · 245852209127357610329_<21>

(89·10³⁰-53)/9 =

9888888888888888888888888888883_<31>

= 19 · 635287 · 819264106234363274426311_<24>

(89·10³¹-53)/9 =

98888888888888888888888888888883_<32>

= 3² · 31 · 354440461967343687773795300677_<30>

(89·10³²-53)/9 =

988888888888888888888888888888883_<33>

= definitely prime number

(89·10³³-53)/9 =

9888888888888888888888888888888883_<34>

= 1459 · 3041 · 7079210008649_<13> · 314840786813593_<15>

(89·10³⁴-53)/9 =

98888888888888888888888888888888883_<35>

= 3 · 23 · 9293 · 154220628724579805103247245299_<30>

(89·10³⁵-53)/9 =

988888888888888888888888888888888883_<36>

= 7 · 12753053 · 6865494527_<10> · 1613479557556816199_<19>

(89·10³⁶-53)/9 =

9888888888888888888888888888888888883_<37>

= 929 · 2729 · 13921 · 280193343790992211130779003_<27>

(89·10³⁷-53)/9 =

98888888888888888888888888888888888883_<38>

= 3 · 17921 · 19564468823_<11> · 42970333261_<11> · 2187898746547_<13>

(89·10³⁸-53)/9 =

988888888888888888888888888888888888883_<39>

= 17 · 269 · 216245110187817382219306557815195471_<36>

(89·10³⁹-53)/9 =

9888888888888888888888888888888888888883_<40>

= 107 · 139 · 2027 · 288403 · 733009457 · 783915127 · 1979323469_<10>

(89·10⁴⁰-53)/9 =

98888888888888888888888888888888888888883_<41>

= 3³ · 3359 · 1090369586284375738909164862656311831_<37>

(89·10⁴¹-53)/9 =

988888888888888888888888888888888888888883_<42>

= 7² · 2503 · 72821031039943_<14> · 110721954617496041087123_<24>

(89·10⁴²-53)/9 =

9888888888888888888888888888888888888888883_<43>

= definitely prime number

(89·10⁴³-53)/9 =

98888888888888888888888888888888888888888883_<44>

= 3 · 14957 · 1389991267942171_<16> · 1585512523884672146743663_<25>

(89·10⁴⁴-53)/9 =

988888888888888888888888888888888888888888883_<45>

= 1039 · 19259 · 49419485133477781490902464154923000583_<38>

(89·10⁴⁵-53)/9 =

9888888888888888888888888888888888888888888883_<46>

= 13582607 · 117686977652731561_<18> · 6186370873801367983829_<22>

(89·10⁴⁶-53)/9 =

98888888888888888888888888888888888888888888883_<47>

= 3 · 31 · 363573919 · 1115680567_<10> · 175676616653_<12> · 14921689537377299_<17>

(89·10⁴⁷-53)/9 =

988888888888888888888888888888888888888888888883_<48>

= 7 · 493853 · 344005819 · 2074878607_<10> · 400768223117883764784181_<24>

(89·10⁴⁸-53)/9 =

9888888888888888888888888888888888888888888888883_<49>

= 19 · 22811 · 20925761 · 1090355982923519834584275420804010867_<37>

(89·10⁴⁹-53)/9 =

98888888888888888888888888888888888888888888888883_<50>

= 3² · 29 · 378884631758194976585781183482332907620263942103_<48>

(89·10⁵⁰-53)/9 =

988888888888888888888888888888888888888888888888883_<51>

= 1153 · 857665992097908836850727570588802158620025055411_<48>

(89·10⁵¹-53)/9 =

9888888888888888888888888888888888888888888888888883_<52>

= 1009 · 759791947727_<12> · 12899166375099095935574718380685422381_<38>

(89·10⁵²-53)/9 =

98888888888888888888888888888888888888888888888888883_<53>

= 3 · 55351 · 18793174844203_<14> · 31688422271610429736885917783131237_<35>

(89·10⁵³-53)/9 =

988888888888888888888888888888888888888888888888888883_<54>

= 7 · 59 · 49477073 · 3583954471_<10> · 268124632649617_<15> · 50360988698015081081_<20>

(89·10⁵⁴-53)/9 =

9888888888888888888888888888888888888888888888888888883_<55>

= 17 · 47 · 61 · 46008189791568104915021_<23> · 4409971032448651919313160757_<28>

(89·10⁵⁵-53)/9 =

98888888888888888888888888888888888888888888888888888883_<56>

= 3 · 1423 · 155861 · 823969 · 19675133 · 9167593217769925317732412472508031_<34>

(89·10⁵⁶-53)/9 =

988888888888888888888888888888888888888888888888888888883_<57>

= 23 · 6829 · 13611613 · 82648322311_<11> · 497984732143_<12> · 11238358596379771016101_<23>

(89·10⁵⁷-53)/9 =

9888888888888888888888888888888888888888888888888888888883_<58>

= 109 · 54419 · 1667133745092890163478198451817184211479174905163973_<52>

(89·10⁵⁸-53)/9 =

98888888888888888888888888888888888888888888888888888888883_<59>

= 3² · 719 · 15281855801095485842820103367159463589690757052834011573_<56>

(89·10⁵⁹-53)/9 =

988888888888888888888888888888888888888888888888888888888883_<60>

= 7 · 191 · 171659 · 8456671631869_<13> · 509506869992389892755778937748192548629_<39>

(89·10⁶⁰-53)/9 =

9888888888888888888888888888888888888888888888888888888888883_<61>

= 823 · 87689697914347_<14> · 1435868927561888761_<19> · 95429860863798082268209063_<26>

(89·10⁶¹-53)/9 =

98888888888888888888888888888888888888888888888888888888888883_<62>

= 3 · 31 · 83 · 639378590071453_<15> · 20099034452337719_<17> · 996903617740360140492650351_<27>

(89·10⁶²-53)/9 =

988888888888888888888888888888888888888888888888888888888888883_<63>

= 4133 · 5903 · 83063 · 487979633113513950818911851254299829180743411819759_<51>

(89·10⁶³-53)/9 =

9888888888888888888888888888888888888888888888888888888888888883_<64>

= 311 · 836726062961_<12> · 693468981375227_<15> · 54799522123015017042855391205494799_<35>

(89·10⁶⁴-53)/9 =

98888888888888888888888888888888888888888888888888888888888888883_<65>

= 3 · 3407 · 14033 · 57859499 · 178222601 · 66859963839969466090041081903286851954469_<41>

(89·10⁶⁵-53)/9 =

988888888888888888888888888888888888888888888888888888888888888883_<66>

= 7 · 212377445659806551_<18> · 107919454463472009612929_<24> · 6163697591024095811147411_<25>

(89·10⁶⁶-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888883_<67>

= 19 · 2293957 · 8876274456157_<13> · 2547464240934497693_<19> · 10033900837797637611630108101_<29>

(89·10⁶⁷-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888883_<68>

= 3⁴ · 31153 · 39188857577432008763156943404728826975777807455631718439770931_<62>

(89·10⁶⁸-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888883_<69>

= 193723 · 3930355727_<10> · 6146212227305239_<16> · 211313332906119898673540260182813559057_<39>

(89·10⁶⁹-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888883_<70>

= 661013822471617_<15> · 10774578363303568622377_<23> · 1388470547890854670517849622336187_<34>

(89·10⁷⁰-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888883_<71>

= 3 · 17 · 6101 · 1654963 · 2780223426593_<13> · 3077626697685763795843_<22> · 22443592162487524798759909_<26>

(89·10⁷¹-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888883_<72>

= 7 · 8971 · 5548381516123_<13> · 111503627147388481075219_<24> · 25453838795496089228327967421247_<32>

(89·10⁷²-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888883_<73>

= 499 · 4777975457_<10> · 200913394693721207_<18> · 330485615852279183333_<21> · 62465696019329138695451_<23>

(89·10⁷³-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888883_<74>

= 3 · 22669 · 2752105696820529809_<19> · 3763117398865567019855489_<25> · 140404492279720416933164869_<27>

(89·10⁷⁴-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888888883_<75>

= 4793 · 11182851391_<11> · 12363519527799995545938839_<26> · 1492263084221348467488984270094388819_<37>

(89·10⁷⁵-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888888883_<76>

= definitely prime number

(89·10⁷⁶-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888888883_<77>

= 3² · 31 · 512741 · 67504755133997_<14> · 29576141074171759_<17> · 2162915091816339611_<19> · 160077355682928828049_<21>

(89·10⁷⁷-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888888888883_<78>

= 7 · 29 · 3052297 · 324306413 · 4921178667520913018774065745023564573383054909000306462850901_<61>

(89·10⁷⁸-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888888888883_<79>

= 23 · 2155465937166071723_<19> · 199470417698430853325349900419688695856801475148969114034127_<60>

(89·10⁷⁹-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888888888883_<80>

= 3 · 977 · 557143402733_<12> · 60557046632752917253518514219435371527228494395883398105400490021_<65>

(89·10⁸⁰-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888888888888883_<81>

= 864051389 · 19910993129_<11> · 1271053778818424582011_<22> · 45222136433360272648662894414117672349013_<41>

(89·10⁸¹-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888888888888883_<82>

= 3643 · 22899523 · 192833194570426296283_<21> · 614723893488671267836044357162967144114069542144409_<51>

(89·10⁸²-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888888888888883_<83>

= 3 · 32962962962962962962962962962962962962962962962962962962962962962962962962962962961_<83>

(89·10⁸³-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888888888888888883_<84>

= 7² · 151 · 1447 · 3299 · 8627862549629_<13> · 12031930826212490870231_<23> · 269702566389834474674885768034696266611_<39>

(89·10⁸⁴-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<85>

= 19 · 331 · 487 · 827 · 617094001 · 85046093459_<11> · 74391914893966694644043863917869462772298992284356595317_<56>

(89·10⁸⁵-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<86>

= 3² · 139 · 3329 · 182681 · 129981939247623180852613653749109538681494472267136732874246098594049528217_<75>

(89·10⁸⁶-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<87>

= 17² · 3421760861207227989234909650134563629373317954632833525567089580930411380238369857747_<85>

(89·10⁸⁷-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<88>

= 11338755509671273_<17> · 80186688083722447_<17> · 54615688798783175611_<20> · 199141793726284208943757446301471663_<36>

(89·10⁸⁸-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<89>

= 3 · 2239051025426909_<16> · 10357809363756554655839725228501_<32> · 1421328086760662019981612783841118246714929_<43> (Makoto Kamada / msieve 0.83 / 8.2 minutes)

(89·10⁸⁹-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<90>

= 7 · 2411 · 2703443946943178431_<19> · 21673790814799834736679232705652583797693721651286973741604797887009_<68>

(89·10⁹⁰-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<91>

= 346857761 · 25138784121890565013841_<23> · 1134101206210223191225275835753974295513581117532593881478883_<61>

(89·10⁹¹-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<92>

= 3 · 31 · 145551387263_<12> · 7305470637532930453285376063211334542358713808910523498883342026243054276969137_<79>

(89·10⁹²-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<93>

= 97 · 107 · 227 · 409 · 956006174555116169_<18> · 1073450747590866901695567106495753827797330558510001242909386955731_<67>

(89·10⁹³-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<94>

= 3677 · 2689390505544979300758468558305381802798174840600731272474541443809869156619224609434019279_<91>

(89·10⁹⁴-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<95>

= 3³ · 1803421003_<10> · 2030890975671540466691506516552725010228362138574852104937224932790259905271761312443_<85>

(89·10⁹⁵-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<96>

= 7 · 179 · 2297 · 36587 · 12890939 · 316638595195371797514615232297893667_<36> · 2300701243578046381863477177422820162555773_<43> (Makoto Kamada / GGNFS-0.71.4 / 0.46 hours)

(89·10⁹⁶-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<97>

= 181 · 107171 · 509790383988952693451431488247850965748335424132625599935214234167767971415583475228331533_<90>

(89·10⁹⁷-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<98>

= 3 · 233 · 472097277757986731_<18> · 1391652815776934267_<19> · 215331676965666954711206807063791606865360222443258682377921_<60>

(89·10⁹⁸-53)/9 =

988888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<99>

= 347 · 133665968850589185451999_<24> · 21320489514226137379753190745165393076803488259511749344105229767338757911_<74>

(89·10⁹⁹-53)/9 =

9888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<100>

= 16091 · 614560244166856558876942942569690441171393256409725243234658435702497600452979236149952699576713_<96>

(89·10¹⁰⁰-53)/9 =

98888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<101>

= 3 · 23 · 47 · 86183 · 88411 · 191563 · 395152271 · 21267866027_<11> · 2485836783999475484739042658415094766827727969055908317482345147_<64>

4. References

• A103108 (On-Line Encyclopedia of Integer Sequences)