Factorizations of 788...883

Table of contents

1. About 788...883
   • First ten terms
   • General term
2. Prime numbers of the form 788...883
   • Last update
   • Searched up to
   • Difficulty of search
   • Results
3. Factorizations of 788...883
   • Last update
   • Completed up to
   • Range
   • Results
4. References

1. About 788...883

First ten terms

73, 783, 7883, 78883, 788883, 7888883, 78888883, 788888883, 7888888883, 78888888883

General term

(71·10ⁿ-53)/9

2. Prime numbers of the form 788...883

Last update

Jan 18, 2009

Searched up to

n≤10000

Difficulty of search

16.28%

Results

1. (71·10¹-53)/9 = 73 is prime. (Makoto Kamada / Dec 6, 2004)
2. (71·10³-53)/9 = 7883 is prime. (Makoto Kamada / Dec 6, 2004)
3. (71·10⁶-53)/9 = 7888883 is prime. (Makoto Kamada / Dec 6, 2004)
4. (71·10⁶⁰-53)/9 = 7(8)₅₉3_<61> is prime. (Makoto Kamada / PPSIQS / Dec 6, 2004)
5. (71·10²⁸⁸-53)/9 = 7(8)₂₈₇3_<289> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PPSIQS / Jan 7, 2005)
6. (71·10¹³¹⁴-53)/9 = 7(8)₁₃₁₃3_<1315> is prime. (searched by Makoto Kamada / PFGW / Dec 23, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 10, 2006)
7. (71·10¹⁷²⁸-53)/9 = 7(8)₁₇₂₇3_<1729> is prime. (searched by Makoto Kamada / PFGW / Dec 23, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Jul 25, 2006)
8. (71·10²⁴⁹³-53)/9 = 7(8)₂₄₉₂3_<2494> is PRP. (Makoto Kamada / PFGW / Dec 23, 2004)

3. Factorizations of 788...883

Last update

Oct 21, 2009

Completed up to

• n≤100 / Jan 7, 2005

Range

n≤100

Results

(71·10¹-53)/9 =

73

= definitely prime number

(71·10²-53)/9 =

783

= 3³ · 29

(71·10³-53)/9 =

7883

= definitely prime number

(71·10⁴-53)/9 =

78883

= 7 · 59 · 191

(71·10⁵-53)/9 =

788883

= 3 · 439 · 599

(71·10⁶-53)/9 =

7888883

= definitely prime number

(71·10⁷-53)/9 =

78888883

= 5717 · 13799

(71·10⁸-53)/9 =

788888883

= 3 · 619 · 424819

(71·10⁹-53)/9 =

7888888883_<10>

= 73 · 108066971

(71·10¹⁰-53)/9 =

78888888883_<11>

= 7 · 7187 · 1568087

(71·10¹¹-53)/9 =

788888888883_<12>

= 3² · 87654320987_<11>

(71·10¹²-53)/9 =

7888888888883_<13>

= 103 · 78539 · 975199

(71·10¹³-53)/9 =

78888888888883_<14>

= 23 · 40471 · 84750851

(71·10¹⁴-53)/9 =

788888888888883_<15>

= 3 · 19 · 13840155945419_<14>

(71·10¹⁵-53)/9 =

7888888888888883_<16>

= 17 · 3801377 · 122074787

(71·10¹⁶-53)/9 =

78888888888888883_<17>

= 7 · 11269841269841269_<17>

(71·10¹⁷-53)/9 =

788888888888888883_<18>

= 3 · 73 · 3602232369355657_<16>

(71·10¹⁸-53)/9 =

7888888888888888883_<19>

= 457 · 499 · 46723 · 740403347

(71·10¹⁹-53)/9 =

78888888888888888883_<20>

= 402416101 · 196038102583_<12>

(71·10²⁰-53)/9 =

788888888888888888883_<21>

= 3² · 87654320987654320987_<20>

(71·10²¹-53)/9 =

7888888888888888888883_<22>

= 5126123 · 1538958173436121_<16>

(71·10²²-53)/9 =

78888888888888888888883_<23>

= 7 · 27352524349_<11> · 412021981081_<12>

(71·10²³-53)/9 =

788888888888888888888883_<24>

= 3 · 262962962962962962962961_<24>

(71·10²⁴-53)/9 =

7888888888888888888888883_<25>

= 61297 · 4130714659_<10> · 31156697921_<11>

(71·10²⁵-53)/9 =

78888888888888888888888883_<26>

= 73 · 173 · 433 · 673 · 769 · 53617 · 519894311

(71·10²⁶-53)/9 =

788888888888888888888888883_<27>

= 3 · 607 · 433217401915919214107023_<24>

(71·10²⁷-53)/9 =

7888888888888888888888888883_<28>

= 88609 · 89030334265016972191187_<23>

(71·10²⁸-53)/9 =

78888888888888888888888888883_<29>

= 7² · 1609977324263038548752834467_<28>

(71·10²⁹-53)/9 =

788888888888888888888888888883_<30>

= 3³ · 741563 · 39400707688874409406283_<23>

(71·10³⁰-53)/9 =

7888888888888888888888888888883_<31>

= 29 · 4973 · 20639 · 3575011513_<10> · 741367060957_<12>

(71·10³¹-53)/9 =

78888888888888888888888888888883_<32>

= 17 · 70501 · 65822085868526594857552199_<26>

(71·10³²-53)/9 =

788888888888888888888888888888883_<33>

= 3 · 19 · 47 · 421 · 137558021 · 1078486021_<10> · 4714770857_<10>

(71·10³³-53)/9 =

7888888888888888888888888888888883_<34>

= 73 · 97229551 · 249414002141_<12> · 4456294333081_<13>

(71·10³⁴-53)/9 =

78888888888888888888888888888888883_<35>

= 7 · 1554014939947507_<16> · 7252080388765086967_<19>

(71·10³⁵-53)/9 =

788888888888888888888888888888888883_<36>

= 3 · 23 · 22699 · 503686166912089525037423527493_<30>

(71·10³⁶-53)/9 =

7888888888888888888888888888888888883_<37>

= 89 · 953 · 1048942459_<10> · 1061832787_<10> · 83507433360803_<14>

(71·10³⁷-53)/9 =

78888888888888888888888888888888888883_<38>

= 794249 · 483093217 · 205602420356466274555451_<24>

(71·10³⁸-53)/9 =

788888888888888888888888888888888888883_<39>

= 3² · 167 · 524876173578768389147630664596732461_<36>

(71·10³⁹-53)/9 =

7888888888888888888888888888888888888883_<40>

= 83² · 149 · 1291 · 7643 · 58567 · 13299346636677874958993_<23>

(71·10⁴⁰-53)/9 =

78888888888888888888888888888888888888883_<41>

= 7 · 409 · 363473554841153_<15> · 75809157955613315167997_<23>

(71·10⁴¹-53)/9 =

788888888888888888888888888888888888888883_<42>

= 3 · 73 · 113 · 151 · 211113659342182325903411100171855439_<36>

(71·10⁴²-53)/9 =

7888888888888888888888888888888888888888883_<43>

= 803989 · 4994932897_<10> · 1964427812240252486414311751_<28>

(71·10⁴³-53)/9 =

78888888888888888888888888888888888888888883_<44>

= 1973 · 7243 · 2896151720310601_<16> · 1906114387166315003597_<22>

(71·10⁴⁴-53)/9 =

788888888888888888888888888888888888888888883_<45>

= 3 · 9661 · 391249 · 26267849 · 2648468127231186733319641901_<28>

(71·10⁴⁵-53)/9 =

7888888888888888888888888888888888888888888883_<46>

= 1129 · 8963 · 92311 · 108140765526697_<15> · 78095427325186339687_<20>

(71·10⁴⁶-53)/9 =

78888888888888888888888888888888888888888888883_<47>

= 7 · 103 · 2739281003891_<13> · 66073224839737_<14> · 604530872848958969_<18>

(71·10⁴⁷-53)/9 =

788888888888888888888888888888888888888888888883_<48>

= 3² · 17 · 233 · 4042531277_<10> · 6444170741_<10> · 849470027637337029980131_<24>

(71·10⁴⁸-53)/9 =

7888888888888888888888888888888888888888888888883_<49>

= 1936756725893704373_<19> · 4073247188672397698302770060871_<31>

(71·10⁴⁹-53)/9 =

78888888888888888888888888888888888888888888888883_<50>

= 73 · 250499 · 4314067963571499718829101436212163747947529_<43>

(71·10⁵⁰-53)/9 =

788888888888888888888888888888888888888888888888883_<51>

= 3 · 19 · 61 · 701 · 65239 · 414269 · 11975768692815442346576601885707369_<35>

(71·10⁵¹-53)/9 =

7888888888888888888888888888888888888888888888888883_<52>

= 6779 · 1163724574257101178476012522332038484863385291177_<49>

(71·10⁵²-53)/9 =

78888888888888888888888888888888888888888888888888883_<53>

= 7 · 193 · 227 · 11095199 · 114794921406755449201_<21> · 201965347909506567721_<21>

(71·10⁵³-53)/9 =

788888888888888888888888888888888888888888888888888883_<54>

= 3 · 4007 · 321619 · 276192403 · 30845280619_<11> · 23951520605415565535762381_<26>

(71·10⁵⁴-53)/9 =

7888888888888888888888888888888888888888888888888888883_<55>

= 324456850125972484049_<21> · 24314138800971458690480228182262467_<35>

(71·10⁵⁵-53)/9 =

78888888888888888888888888888888888888888888888888888883_<56>

= 109 · 923137 · 71808303744649_<14> · 197875574597237_<15> · 55176776680503208427_<20>

(71·10⁵⁶-53)/9 =

788888888888888888888888888888888888888888888888888888883_<57>

= 3⁵ · 401 · 2713 · 2833 · 71537 · 14724416762811657441476600693852035015897_<41>

(71·10⁵⁷-53)/9 =

7888888888888888888888888888888888888888888888888888888883_<58>

= 23 · 73 · 1275053447_<10> · 3684993731897356190717191033168308149998290491_<46>

(71·10⁵⁸-53)/9 =

78888888888888888888888888888888888888888888888888888888883_<59>

= 7 · 29 · 191413 · 2030244634384410139200692287112929821411589576004597_<52>

(71·10⁵⁹-53)/9 =

788888888888888888888888888888888888888888888888888888888883_<60>

= 3 · 347 · 1217 · 7233526871_<10> · 47987365541_<11> · 1793897085072918516416629023234449_<34>

(71·10⁶⁰-53)/9 =

7888888888888888888888888888888888888888888888888888888888883_<61>

= definitely prime number

(71·10⁶¹-53)/9 =

78888888888888888888888888888888888888888888888888888888888883_<62>

= 7561 · 97491861573409502385862399_<26> · 107020811080260748405016889538597_<33>

(71·10⁶²-53)/9 =

788888888888888888888888888888888888888888888888888888888888883_<63>

= 3 · 59 · 2851 · 482855159 · 3237639423711766779892581683193185599137396901831_<49>

(71·10⁶³-53)/9 =

7888888888888888888888888888888888888888888888888888888888888883_<64>

= 17 · 131 · 16035908922967_<14> · 670387648035011_<15> · 329515643711270374026374972930317_<33>

(71·10⁶⁴-53)/9 =

78888888888888888888888888888888888888888888888888888888888888883_<65>

= 7 · 163 · 181 · 8046640215418713649635036997_<28> · 47471946177305089906484007137359_<32>

(71·10⁶⁵-53)/9 =

788888888888888888888888888888888888888888888888888888888888888883_<66>

= 3² · 73 · 307 · 10644899 · 15761323 · 294104996686187_<15> · 6879637256293453_<16> · 11521524220648511_<17>

(71·10⁶⁶-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888883_<67>

= 313420260427153431973_<21> · 25170322040244939639615573978149551256648295671_<47>

(71·10⁶⁷-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888883_<68>

= 1825433063_<10> · 43216533373861043563715099033948465788739189112018888029141_<59>

(71·10⁶⁸-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888883_<69>

= 3 · 19 · 173 · 1489 · 441388859 · 2392381088641281235387_<22> · 50880158432416738260438194665919_<32>

(71·10⁶⁹-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888883_<70>

= 1304915169097_<13> · 6045518571408739281397870836302076443842448331471707645339_<58>

(71·10⁷⁰-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888883_<71>

= 7² · 1609977324263038548752834467120181405895691609977324263038548752834467_<70>

(71·10⁷¹-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888883_<72>

= 3 · 14159699 · 18571225487417703085564386853347868691485812160481869209434675339_<65>

(71·10⁷²-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888883_<73>

= 537224491 · 14684529504982841314449472648649014940178683865864352205954975513_<65>

(71·10⁷³-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888883_<74>

= 73 · 617 · 533894457988996296102269_<24> · 3280593366314463113099788302313368109468504927_<46>

(71·10⁷⁴-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888888883_<75>

= 3² · 229 · 164531 · 322649 · 48475491399551114989_<20> · 148743352768186602173279794219528886190433_<42>

(71·10⁷⁵-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888888883_<76>

= 15733922798311_<14> · 501393644167094982434203396130827489820520570953592586155914453_<63>

(71·10⁷⁶-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888888883_<77>

= 7 · 179 · 194891 · 103620997 · 46206240964493_<14> · 4725587521956703_<16> · 14278045710389109600452570051867_<32>

(71·10⁷⁷-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888888888883_<78>

= 3 · 12143 · 143569 · 13754911 · 10966047670408472141602705194333537119761226595124300971302353_<62>

(71·10⁷⁸-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888888888883_<79>

= 47 · 362531858218741_<15> · 8165052876694508776989181_<25> · 56703883381645309860007103714259198109_<38>

(71·10⁷⁹-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888888888883_<80>

= 17 · 23² · 293 · 794509 · 37682942215008931892135074754326219168584130679872422137044234429363_<68>

(71·10⁸⁰-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888888888888883_<81>

= 3 · 83 · 89 · 103 · 1637 · 10883 · 16529 · 115742489 · 2701272901_<10> · 43813509081992161_<17> · 85679328778432199564042370391_<29>

(71·10⁸¹-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888888888888883_<82>

= 73 · 23369 · 51151 · 90406305515081432808336758173854080588002365776136196375743173782562509_<71>

(71·10⁸²-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888888888888883_<83>

= 7 · 2647 · 2696590037689_<13> · 1578879304765717167812204155931147563381259752721614320833575795243_<67>

(71·10⁸³-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888888888888888883_<84>

= 3³ · 266891 · 419343875800380067_<18> · 261064512996407877717199820823791166164984487362742216278857_<60>

(71·10⁸⁴-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<85>

= 48438421 · 1531954260792897367_<19> · 106311455209622110396407908759263208048909991308961226078769_<60>

(71·10⁸⁵-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<86>

= 97 · 236115971761_<12> · 7866336755073949133_<19> · 437871022352979486087770921163017181651497987767589903_<54>

(71·10⁸⁶-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<87>

= 3 · 19 · 29 · 1747 · 8107980031821999835186657_<25> · 33692823760512818972181214113607470590721804345539694109_<56>

(71·10⁸⁷-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<88>

= 29569 · 239144043851461229726543491693319_<33> · 1115628584669577777387862231772195162159213614596853_<52> (Makoto Kamada / GGNFS-0.70.3 / 0.20 hours)

(71·10⁸⁸-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<89>

= 7 · 11269841269841269841269841269841269841269841269841269841269841269841269841269841269841269_<89>

(71·10⁸⁹-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<90>

= 3 · 73 · 4133 · 393605191069176604241_<21> · 2214346100177818168840921071256426600093037415033131408173240069_<64>

(71·10⁹⁰-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<91>

= 419 · 438211 · 677781193 · 3069286741_<10> · 20653400373350278617903853427151256108253616475522796198272376599_<65>

(71·10⁹¹-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<92>

= 6089 · 10247 · 75575993323_<11> · 130160940004216905662036450239_<30> · 128531207825325417373843039084768963495089433_<45> (Makoto Kamada / msieve 0.83)

(71·10⁹²-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<93>

= 3² · 90397 · 82394454851_<11> · 1643319794418761353_<19> · 7161421584002448440374397431401453638918264887525524389557_<58>

(71·10⁹³-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<94>

= 21011513 · 67019837 · 1228770843268804553_<19> · 59826646484963034729354433_<26> · 76206074049950997679268411452530607_<35>

(71·10⁹⁴-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<95>

= 7 · 11213 · 1005069229451642721953967829291114763334508273418466943839279521077434213972160997934653513_<91>

(71·10⁹⁵-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<96>

= 3 · 17 · 1163 · 74747 · 1175617 · 669854450171_<12> · 8659443584653_<13> · 1604953551347700694039_<22> · 16258235945681196518456461595099537_<35>

(71·10⁹⁶-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<97>

= 15493 · 1255559 · 3989562827_<10> · 101652457939590160704983830509437106024659154665928938458722120235294202849267_<78>

(71·10⁹⁷-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<98>

= 73 · 520552803688777_<15> · 492789105511202561202598111_<27> · 4212763619193651848092838192444280221117308460291752093_<55>

(71·10⁹⁸-53)/9 =

788888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<99>

= 3 · 214684699 · 2818685199685414171954694448349178786411_<40> · 434557166954572548941364634455272738941803072794249_<51> (Makoto Kamada / GGNFS-0.71.4 / 0.39 hours)

(71·10⁹⁹-53)/9 =

7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<100>

= 191 · 1399 · 199883891 · 147702199481403441820901026222957657263733663282915977746228959528619080557081995465657_<87>

(71·10¹⁰⁰-53)/9 =

78888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<101>

= 7 · 331 · 14821971463573_<14> · 2297120791586324236880387607934892114434587736386197750902221535885105002368934194563_<85>

4. References

• A103066 (On-Line Encyclopedia of Integer Sequences)