Factorizations of 200...003

Table of contents

1. About 200...003
   • First ten terms
   • General term
   • Related tables
2. Prime numbers of the form 200...003
   • Last update
   • Searched up to
   • Difficulty of search
   • Results
3. Factorizations of 200...003
   • Last update
   • Completed up to
   • Range
   • Terms which have not been factored yet
   • Results
4. References

1. About 200...003

First ten terms

23, 203, 2003, 20003, 200003, 2000003, 20000003, 200000003, 2000000003, 20000000003

General term

2·10ⁿ+3

Related tables

• Factorizations of 399...991

2. Prime numbers of the form 200...003

Last update

Jan 18, 2009

Searched up to

n≤10000

Difficulty of search

23.69%

Results

1. 2·10¹+3 = 23 is prime. (Makoto Kamada / Sep 27, 2004)
2. 2·10³+3 = 2003 is prime. (Makoto Kamada / Sep 27, 2004)
3. 2·10⁵+3 = 200003 is prime. (Makoto Kamada / Sep 27, 2004)
4. 2·10⁶+3 = 2000003 is prime. (Makoto Kamada / Sep 27, 2004)
5. 2·10⁷+3 = 20000003 is prime. (Makoto Kamada / Sep 27, 2004)
6. 2·10¹²+3 = 2(0)₁₁3_<13> is prime. (Makoto Kamada / Sep 27, 2004)
7. 2·10¹⁶+3 = 2(0)₁₅3_<17> is prime. (Makoto Kamada / PPSIQS / Sep 27, 2004)
8. 2·10¹⁷+3 = 2(0)₁₆3_<18> is prime. (Makoto Kamada / PPSIQS / Sep 27, 2004)
9. 2·10²²+3 = 2(0)₂₁3_<23> is prime. (Makoto Kamada / PPSIQS / Sep 27, 2004)
10. 2·10²⁴+3 = 2(0)₂₃3_<25> is prime. (Makoto Kamada / PPSIQS / Sep 27, 2004)
11. 2·10³⁵+3 = 2(0)₃₄3_<36> is prime. (Makoto Kamada / PPSIQS / Sep 27, 2004)
12. 2·10¹¹⁵+3 = 2(0)₁₁₄3_<116> is prime. (Makoto Kamada / PPSIQS / Sep 27, 2004)
13. 2·10¹²⁰+3 = 2(0)₁₁₉3_<121> is prime. (Makoto Kamada / PPSIQS / Sep 27, 2004)
14. 2·10³⁵⁸+3 = 2(0)₃₅₇3_<359> is prime. (searched by Makoto Kamada / Sep 27, 2004) (certified by Makoto Kamada / PPSIQS / Dec 30, 2004)
15. 2·10¹⁴⁸⁸+3 = 2(0)₁₄₈₇3_<1489> is prime. (searched by Makoto Kamada / Sep 27, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Aug 25, 2006)
16. 2·10¹⁸¹⁹+3 = 2(0)₁₈₁₈3_<1820> is prime. (searched by Makoto Kamada / Sep 27, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Jun 29, 2006)
17. 2·10⁴⁶⁷⁹+3 = 2(0)₄₆₇₈3_<4680> is PRP. (Makoto Kamada / PFGW / Dec 18, 2004)
18. 2·10⁹⁸²¹+3 = 2(0)₉₈₂₀3_<9822> is PRP. (Makoto Kamada / PFGW / Jan 3, 2005)

3. Factorizations of 200...003

Last update

May 8, 2009

Completed up to

• n≤100 / Sep 27, 2004
• n≤150 / May 22, 2007

Range

n≤200

Terms which have not been factored yet

n=177, 179, 180, 181, 182, 186, 190, 192, 193, 194, 196, 198, 199, 200 (14/200)

Results

2·10¹+3 =

23

= definitely prime number

2·10²+3 =

203

= 7 · 29

2·10³+3 =

2003

= definitely prime number

2·10⁴+3 =

20003

= 83 · 241

2·10⁵+3 =

200003

= definitely prime number

2·10⁶+3 =

2000003

= definitely prime number

2·10⁷+3 =

20000003

= definitely prime number

2·10⁸+3 =

200000003

= 7 · 31 · 223 · 4133

2·10⁹+3 =

2000000003_<10>

= 17 · 211 · 233 · 2393

2·10¹⁰+3 =

20000000003_<11>

= 79 · 253164557

2·10¹¹+3 =

200000000003_<12>

= 47 · 1171 · 3633919

2·10¹²+3 =

2000000000003_<13>

= definitely prime number

2·10¹³+3 =

20000000000003_<14>

= 617 · 64879 · 499621

2·10¹⁴+3 =

200000000000003_<15>

= 7 · 8431 · 3388854059_<10>

2·10¹⁵+3 =

2000000000000003_<16>

= 19 · 105263157894737_<15>

2·10¹⁶+3 =

20000000000000003_<17>

= definitely prime number

2·10¹⁷+3 =

200000000000000003_<18>

= definitely prime number

2·10¹⁸+3 =

2000000000000000003_<19>

= 107 · 1279 · 14614221098551_<14>

2·10¹⁹+3 =

20000000000000000003_<20>

= 21977 · 910042316967739_<15>

2·10²⁰+3 =

200000000000000000003_<21>

= 7 · 173 · 2339 · 81971 · 861381217

2·10²¹+3 =

2000000000000000000003_<22>

= 11850947 · 168762884518849_<15>

2·10²²+3 =

20000000000000000000003_<23>

= definitely prime number

2·10²³+3 =

200000000000000000000003_<24>

= 23² · 31 · 79 · 174456743 · 884907301

2·10²⁴+3 =

2000000000000000000000003_<25>

= definitely prime number

2·10²⁵+3 =

20000000000000000000000003_<26>

= 17 · 61 · 181 · 106554713181350794099_<21>

2·10²⁶+3 =

200000000000000000000000003_<27>

= 7 · 3793020318169_<13> · 7532632618541_<13>

2·10²⁷+3 =

2000000000000000000000000003_<28>

= 1433 · 6053 · 335676199 · 686898522953_<12>

2·10²⁸+3 =

20000000000000000000000000003_<29>

= 944220544009_<12> · 21181492106794667_<17>

2·10²⁹+3 =

200000000000000000000000000003_<30>

= 541 · 2659 · 139031879314767479609237_<24>

2·10³⁰+3 =

2000000000000000000000000000003_<31>

= 29 · 199 · 8837 · 1632417869_<10> · 24023856568681_<14>

2·10³¹+3 =

20000000000000000000000000000003_<32>

= 8898053 · 723962431 · 3104695253724121_<16>

2·10³²+3 =

200000000000000000000000000000003_<33>

= 7² · 227 · 13326490787_<11> · 1349249466612248603_<19>

2·10³³+3 =

2000000000000000000000000000000003_<34>

= 19 · 376757 · 279392706425459492737396141_<27>

2·10³⁴+3 =

20000000000000000000000000000000003_<35>

= 241 · 3229088693532413_<16> · 25699991466148591_<17>

2·10³⁵+3 =

200000000000000000000000000000000003_<36>

= definitely prime number

2·10³⁶+3 =

2000000000000000000000000000000000003_<37>

= 59 · 79 · 120943 · 3547890075714688351659371161_<28>

2·10³⁷+3 =

20000000000000000000000000000000000003_<38>

= 5049497107807891_<16> · 3960790465465279655633_<22>

2·10³⁸+3 =

200000000000000000000000000000000000003_<39>

= 7 · 31 · 348331826708401_<15> · 2645922409342926726059_<22>

2·10³⁹+3 =

2000000000000000000000000000000000000003_<40>

= 211 · 2341 · 88033849 · 45993497522560350084477797_<26>

2·10⁴⁰+3 =

20000000000000000000000000000000000000003_<41>

= 6770723 · 2359303200251_<13> · 1252019786340070350611_<22>

2·10⁴¹+3 =

200000000000000000000000000000000000000003_<42>

= 17 · 11764705882352941176470588235294117647059_<41>

2·10⁴²+3 =

2000000000000000000000000000000000000000003_<43>

= 473476023375163705877_<21> · 4224078731047546560439_<22>

2·10⁴³+3 =

20000000000000000000000000000000000000000003_<44>

= 6263 · 2187467868975357653_<19> · 1459842158613772062977_<22>

2·10⁴⁴+3 =

200000000000000000000000000000000000000000003_<45>

= 7 · 419 · 1091 · 1115911 · 22068793 · 2537961573918528140906387_<25>

2·10⁴⁵+3 =

2000000000000000000000000000000000000000000003_<46>

= 23 · 83 · 5281 · 1137872495299_<13> · 174346928210271221879232893_<27>

2·10⁴⁶+3 =

20000000000000000000000000000000000000000000003_<47>

= 601 · 10825259 · 734482643 · 4185387670524992598018391019_<28>

2·10⁴⁷+3 =

200000000000000000000000000000000000000000000003_<48>

= 176905403 · 1130547719902031482893713540224658938201_<40>

2·10⁴⁸+3 =

2000000000000000000000000000000000000000000000003_<49>

= 6871 · 10949 · 26584934299123232854555060648941702283057_<41>

2·10⁴⁹+3 =

20000000000000000000000000000000000000000000000003_<50>

= 79 · 253164556962025316455696202531645569620253164557_<48>

2·10⁵⁰+3 =

200000000000000000000000000000000000000000000000003_<51>

= 7 · 6491 · 237151 · 1153609 · 8988086730774101_<16> · 1790067864550241141_<19>

2·10⁵¹+3 =

2000000000000000000000000000000000000000000000000003_<52>

= 19 · 197 · 159239027032849_<15> · 3355526347347494765062846183242829_<34>

2·10⁵²+3 =

20000000000000000000000000000000000000000000000000003_<53>

= 409 · 4335631 · 10342885269851_<14> · 1090467352009655798670870606607_<31>

2·10⁵³+3 =

200000000000000000000000000000000000000000000000000003_<54>

= 31 · 829 · 14753 · 527513318280406704433683764738692440130410049_<45>

2·10⁵⁴+3 =

2000000000000000000000000000000000000000000000000000003_<55>

= 1129 · 5536417031655899_<16> · 319968523864926281807959061371083793_<36>

2·10⁵⁵+3 =

20000000000000000000000000000000000000000000000000000003_<56>

= 947 · 630641640613593647_<18> · 33488629391928160215301711261193567_<35>

2·10⁵⁶+3 =

200000000000000000000000000000000000000000000000000000003_<57>

= 7 · 87796968481_<11> · 9368987878212461_<16> · 34734396543207627172561909369_<29>

2·10⁵⁷+3 =

2000000000000000000000000000000000000000000000000000000003_<58>

= 17² · 47 · 47161 · 381357863 · 1982502477023_<13> · 4129570129161813841531043869_<28>

2·10⁵⁸+3 =

20000000000000000000000000000000000000000000000000000000003_<59>

= 29 · 133373771 · 830083951270177_<15> · 8577012162065861_<16> · 726279061919048761_<18>

2·10⁵⁹+3 =

200000000000000000000000000000000000000000000000000000000003_<60>

= 36382287863_<11> · 1715548838023451276899_<22> · 3204327551100096307916697319_<28>

2·10⁶⁰+3 =

2000000000000000000000000000000000000000000000000000000000003_<61>

= 97 · 3347 · 89627 · 13472671 · 195022804897_<12> · 26159207707463133368869943944733_<32>

2·10⁶¹+3 =

20000000000000000000000000000000000000000000000000000000000003_<62>

= 197689 · 493060093873981_<15> · 2608655530952645899_<19> · 78655827078856343401733_<23>

2·10⁶²+3 =

200000000000000000000000000000000000000000000000000000000000003_<63>

= 7 · 79 · 67187 · 5382940938022136860142931615845020393406317220316048073_<55>

2·10⁶³+3 =

2000000000000000000000000000000000000000000000000000000000000003_<64>

= 173 · 709 · 123805374165243868085316016373_<30> · 131703755921620208014649133623_<30>

2·10⁶⁴+3 =

20000000000000000000000000000000000000000000000000000000000000003_<65>

= 241 · 82987551867219917012448132780082987551867219917012448132780083_<62>

2·10⁶⁵+3 =

200000000000000000000000000000000000000000000000000000000000000003_<66>

= 250214207989_<12> · 799315121261189397901309758464692809702923108613928727_<54>

2·10⁶⁶+3 =

2000000000000000000000000000000000000000000000000000000000000000003_<67>

= 5045396267_<10> · 269952174593306396039669287_<27> · 1468411861087106185253786003407_<31>

2·10⁶⁷+3 =

20000000000000000000000000000000000000000000000000000000000000000003_<68>

= 23 · 3083 · 474717736202574865914293_<24> · 594145999077637914442282147060469278819_<39>

2·10⁶⁸+3 =

200000000000000000000000000000000000000000000000000000000000000000003_<69>

= 7 · 31 · 179 · 289067 · 12221768408569_<14> · 1457419800611451039734374629295231356806366627_<46>

2·10⁶⁹+3 =

2000000000000000000000000000000000000000000000000000000000000000000003_<70>

= 19 · 211 · 58676451232029416603_<20> · 2067397236615734055061_<22> · 4112502436486078502075149_<25>

2·10⁷⁰+3 =

20000000000000000000000000000000000000000000000000000000000000000000003_<71>

= 193 · 1009 · 9015029 · 318197099659911533_<18> · 35802897529245969120774911383627717355267_<41>

2·10⁷¹+3 =

200000000000000000000000000000000000000000000000000000000000000000000003_<72>

= 107 · 155731 · 110242819 · 108873161835557496912230201617128500051561735049298977361_<57>

2·10⁷²+3 =

2000000000000000000000000000000000000000000000000000000000000000000000003_<73>

= 149 · 13422818791946308724832214765100671140939597315436241610738255033557047_<71>

2·10⁷³+3 =

20000000000000000000000000000000000000000000000000000000000000000000000003_<74>

= 17 · 151 · 7759 · 28481543869_<11> · 35256146990949820675155255501335850511972129326274272679_<56>

2·10⁷⁴+3 =

200000000000000000000000000000000000000000000000000000000000000000000000003_<75>

= 7² · 23909542862637059743_<20> · 170711446743697725633505677829515883121491856455923629_<54>

2·10⁷⁵+3 =

2000000000000000000000000000000000000000000000000000000000000000000000000003_<76>

= 79 · 331 · 10206815431870182840270817231_<29> · 7493498919620788902689385842385931447646537_<43>

2·10⁷⁶+3 =

20000000000000000000000000000000000000000000000000000000000000000000000000003_<77>

= 103035186006031_<15> · 1934982246763493955490755927821_<31> · 100315363558355014647859823017153_<33>

2·10⁷⁷+3 =

200000000000000000000000000000000000000000000000000000000000000000000000000003_<78>

= 7159 · 6478104454016753760887_<22> · 4312505747417765608582777589439413779944095761779091_<52>

2·10⁷⁸+3 =

2000000000000000000000000000000000000000000000000000000000000000000000000000003_<79>

= 5693 · 1237661 · 2486863 · 114139310551026338652399651844405362963557000608503422372020997_<63>

2·10⁷⁹+3 =

20000000000000000000000000000000000000000000000000000000000000000000000000000003_<80>

= 4561 · 685978596651857_<15> · 6392332516138127241768447324856462524373231004706954463263139_<61>

2·10⁸⁰+3 =

200000000000000000000000000000000000000000000000000000000000000000000000000000003_<81>

= 7 · 6299 · 414473453 · 19966584998152201_<17> · 548100043780603304955338234337098221979945589533507_<51>

2·10⁸¹+3 =

2000000000000000000000000000000000000000000000000000000000000000000000000000000003_<82>

= 1277 · 1523 · 2530899979_<10> · 133940570111507996479098559_<27> · 3033556371527318787524930840338672101713_<40>

2·10⁸²+3 =

20000000000000000000000000000000000000000000000000000000000000000000000000000000003_<83>

= 825611 · 8812588523511893_<16> · 2748849941029302910494614920725892417409755520329614893557061_<61>

2·10⁸³+3 =

200000000000000000000000000000000000000000000000000000000000000000000000000000000003_<84>

= 31 · 113 · 229 · 24979 · 5278397362612613211007287739_<28> · 1890937814311875696421686100672206606653923849_<46>

2·10⁸⁴+3 =

2000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<85>

= 10689751 · 30870029 · 174101240977_<12> · 27501614868292675787_<20> · 1265800626727778453024504210132287247243_<40>

2·10⁸⁵+3 =

20000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<86>

= 61 · 263 · 784009 · 730869849769_<12> · 188791641851297_<15> · 92965737425275667_<17> · 123958877689262908298519237788099_<33>

2·10⁸⁶+3 =

200000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<87>

= 7 · 29 · 83 · 6271 · 3708068388463_<13> · 803341897652669_<15> · 606376773754238324363_<21> · 1047920541237702507248025832637_<31>

2·10⁸⁷+3 =

2000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<88>

= 19 · 2633 · 13351343 · 9391183921538689_<16> · 60685815889202975701_<20> · 5254035963287563578959421946859218396907_<40>

2·10⁸⁸+3 =

20000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<89>

= 79 · 9712441 · 98836273 · 160330424167_<12> · 259333214069_<12> · 636360516185020985689_<21> · 9967375987265890256911580767_<28>

2·10⁸⁹+3 =

200000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<90>

= 17 · 23 · 293 · 31220972566629346037_<20> · 55916398361587507836687691938105593431350598515146351210658005213_<65>

2·10⁹⁰+3 =

2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<91>

= 1153 · 1612351060219207303_<19> · 1075823634240573613236619945236180905716293882720442899436436921102117_<70>

2·10⁹¹+3 =

20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<92>

= 14341 · 225859 · 751763 · 45186538905301_<14> · 181770388080836974514656491761082559023131975054065757127548899_<63>

2·10⁹²+3 =

200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<93>

= 7 · 9241 · 162557 · 90668547845459_<14> · 188080429537884826493_<21> · 6577596128333935936571_<22> · 169566414790523540512576421_<27>

2·10⁹³+3 =

2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<94>

= 7321913 · 159129109 · 4211620326587_<13> · 175746623295851659_<18> · 2319100651175680426597602137387367174469580704823_<49>

2·10⁹⁴+3 =

20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<95>

= 59 · 241 · 94427 · 3614470427_<10> · 19340062151882758570550401967047_<32> · 213089577421509928559482959036656417177388199_<45>

2·10⁹⁵+3 =

200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<96>

= 1097 · 2777 · 323537 · 3184710803_<10> · 63716737888419215547415929687932010189450906872448170069806562750426211617_<74>

2·10⁹⁶+3 =

2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<97>

= 13387084763939_<14> · 6888003416488249330043_<22> · 21689554339683136588679658930304369012462798870108076460065939_<62>

2·10⁹⁷+3 =

20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<98>

= 109 · 347 · 787429 · 784377317 · 145923420596482481004347_<24> · 5866952744783258583080885755055224630524999042809897791_<55>

2·10⁹⁸+3 =

200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<99>

= 7 · 31 · 26891720626840241453_<20> · 34272964492098008972146833105500148126083732893462398747862634497615158084103_<77>

2·10⁹⁹+3 =

2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<100>

= 211 · 79382035150980920346405340690307261392830949801_<47> · 119405769425714490171006230771951087269574666783273_<51> (Makoto Kamada / GGNFS-0.54.5b)

2·10¹⁰⁰+3 =

20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<101>

= 170547889 · 2351903621_<10> · 49861360773942694081325021246938997255965585182246410257045279125241288931457688087_<83>

2·10¹⁰¹+3 =

2(0)₁₀₀3_<102>

= 79 · 383 · 617 · 774799 · 1690313 · 216954797 · 18484717176979_<14> · 176407766384435368999_<21> · 11562800031772242924518824714175876232173_<41>

2·10¹⁰²+3 =

2(0)₁₀₁3_<103>

= 439 · 701 · 5551873 · 322353810266010223_<18> · 3631408672796406702085696216743007169009354928263686873187008923205595863_<73>

2·10¹⁰³+3 =

2(0)₁₀₂3_<104>

= 47 · 2068430377411_<13> · 71811408358293195292411_<23> · 77125858976287579050890129854699_<32> · 37144778449564313154341134715055031_<35> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1191110923 for P35 / May 15, 2007)

2·10¹⁰⁴+3 =

2(0)₁₀₃3_<105>

= 7 · 1499 · 72924583 · 32500127761170009153191422527529_<32> · 8042133907689848374500596451675451989411649913723669050575553_<61> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1905153368 for P32 / May 15, 2007)

2·10¹⁰⁵+3 =

2(0)₁₀₄3_<106>

= 17 · 19 · 467 · 3961175617793_<13> · 3347237247165798725331239871160802804281762325288903139153487422487976442557810503419931_<88>

2·10¹⁰⁶+3 =

2(0)₁₀₅3_<107>

= 173 · 5594493493318388089_<19> · 20909268680821569816065383_<26> · 988289716009437275446318931091762783722563293522184539500353_<60>

2·10¹⁰⁷+3 =

2(0)₁₀₆3_<108>

= 34159 · 135257 · 8581253024316133683871_<22> · 70366470719053751070081322438416837323_<38> · 71688355828884849285727325871272978657_<38> (Makoto Kamada / Msieve 1.21 for P38 x P38 / 7.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 17, 2007)

2·10¹⁰⁸+3 =

2(0)₁₀₇3_<109>

= 131 · 971 · 1663 · 211153 · 785013631 · 10956056139051043916590023409_<29> · 5206172069618515898494220381496970287426897628124942838563_<58>

2·10¹⁰⁹+3 =

2(0)₁₀₈3_<110>

= 2719 · 8543 · 430741 · 1991149621_<10> · 17549207512483876748254230582091_<32> · 57204838642635824463463028377398262905391805414776179409_<56> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=785503868 for P32 / May 15, 2007)

2·10¹¹⁰+3 =

2(0)₁₀₉3_<111>

= 7 · 26184862097599361168293556342151923_<35> · 1091142984253028074855253881145711454222019861072878061773867745555021996423_<76> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.48 hours on Core 2 Quad Q6600 / May 17, 2007)

2·10¹¹¹+3 =

2(0)₁₁₀3_<112>

= 23 · 86956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261_<110>

2·10¹¹²+3 =

2(0)₁₁₁3_<113>

= 677 · 54670303 · 1130429630033873669_<19> · 478020270900772726633696605954219944463744295928749633602720299644323342149372542277_<84>

2·10¹¹³+3 =

2(0)₁₁₂3_<114>

= 31 · 6451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451613_<112>

2·10¹¹⁴+3 =

2(0)₁₁₃3_<115>

= 29 · 79 · 269 · 46091 · 141642068744903728734080380860557_<33> · 497100539534504959831516767690043182490203130774494939527873200330969211_<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.64 hours on Core 2 Quad Q6600 / May 17, 2007)

2·10¹¹⁵+3 =

2(0)₁₁₄3_<116>

= definitely prime number

2·10¹¹⁶+3 =

2(0)₁₁₅3_<117>

= 7² · 15031 · 6544399742820969529407841_<25> · 41493132409708849993961614871982844651028070979055904408757610584660729478322747116357_<86>

2·10¹¹⁷+3 =

2(0)₁₁₆3_<118>

= 252481430303_<12> · 14233541343533_<14> · 79171895467787_<14> · 7029372274658901576417661765722869204475035431907927006123940343512211180833331_<79>

2·10¹¹⁸+3 =

2(0)₁₁₇3_<119>

= 714997972759321_<15> · 991811671612623385550841555017839892819_<39> · 28203043059484251487882072762043305121719614244673667495654922297_<65> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.96 hours on Core 2 Quad Q6600 / May 17, 2007)

2·10¹¹⁹+3 =

2(0)₁₁₈3_<120>

= 5228659514109126391498531522208323958331928046131_<49> · 38250721711810786837816564744277352704880578237524903785562032046531313_<71> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 1.03 hours on Core 2 Quad Q6600 / May 17, 2007)

2·10¹²⁰+3 =

2(0)₁₁₉3_<121>

= definitely prime number

2·10¹²¹+3 =

2(0)₁₂₀3_<122>

= 17 · 14488801 · 65881399 · 2194247719_<10> · 45230755231_<11> · 39243438138434903_<17> · 82493772245610301788337353942271_<32> · 3835995654100008613560231526090607813_<37> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3804634123 for P32 / May 15, 2007)

2·10¹²²+3 =

2(0)₁₂₁3_<123>

= 7 · 1255591 · 1846821995548619239_<19> · 873192647167017533911_<21> · 2445409000264004985346080302093575163_<37> · 5770283446250729246099452389095675049097_<40> (Makoto Kamada / Msieve 1.21 for P37 x P40 / 7.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 17, 2007)

2·10¹²³+3 =

2(0)₁₂₂3_<124>

= 19 · 252444851578307_<15> · 416974864952176659286921762537731373167739280498222726745880301034569498329218744986251818415970890775078491_<108>

2·10¹²⁴+3 =

2(0)₁₂₃3_<125>

= 107 · 241 · 807932595751_<12> · 15473661967469980997_<20> · 62038450235564933442218840576529640620666357432793040061287595166043436265300664996855027_<89>

2·10¹²⁵+3 =

2(0)₁₂₄3_<126>

= 41765060149_<11> · 323601526579_<12> · 9993023712544651881405293_<25> · 397869046237867494121907980309_<30> · 3721939007586273114581978136315755902636906895389_<49> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3873787057 for P30 / May 15, 2007)

2·10¹²⁶+3 =

2(0)₁₂₅3_<127>

= 9496596035573_<13> · 72990180616825855013_<20> · 1363935016086710284190348118562849_<34> · 2115455595883918282267614450587132366299796154935856176143403_<61> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 2.12 hours on Core 2 Quad Q6600 / May 19, 2007)

2·10¹²⁷+3 =

2(0)₁₂₆3_<128>

= 79 · 83 · 32843 · 3835231 · 1195589420583881466001_<22> · 8927757006598681262632931194240133629_<37> · 2268642375519091333458799446695979155571481664083795247_<55> (Jo Yeong Uk / Msieve v. 1.21 / 01:31:38 on Core 2 Quad Q6600 / May 19, 2007)

2·10¹²⁸+3 =

2(0)₁₂₇3_<129>

= 7 · 31 · 2963 · 193441 · 1608014948402127570106586247594522610290635832095644274448651737684348026668594835032873733512861038079830762256699673_<118>

2·10¹²⁹+3 =

2(0)₁₂₈3_<130>

= 199 · 211 · 108307883 · 439778908259318879132175124451656910736124888008620424152716208102430896908420952389976088353089547098694511271471669_<117>

2·10¹³⁰+3 =

2(0)₁₂₉3_<131>

= 12197 · 103423915189057_<15> · 15854625846360807465839312919222637107991076910585397853870551265862533057270279414491351892335733031540359985607_<113>

2·10¹³¹+3 =

2(0)₁₃₀3_<132>

= 8093 · 4567358173159_<13> · 540506822274149821_<18> · 20250623254125963298303817_<26> · 494328683079133106401078242337242213766572794591865006865231436633400917_<72>

2·10¹³²+3 =

2(0)₁₃₁3_<133>

= 463 · 275297805609606581_<18> · 81483035220514238963_<20> · 192565755118774612646331983883006930030794800546537948994802291846665356618143697402920173027_<93>

2·10¹³³+3 =

2(0)₁₃₂3_<134>

= 23 · 2739490804091120297_<19> · 202774642894094696157617_<24> · 1565375987184300132253742064897937509211101557738800048039377218390189814067798915031396989_<91>

2·10¹³⁴+3 =

2(0)₁₃₃3_<135>

= 7 · 157756740409116882389_<21> · 245627325886145161242134796623575019_<36> · 737339247296593171731659164098751163305183427019906464474193591876106604044019_<78> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 3.54 hours on Cygwin on AMD 64 3400+ / May 19, 2007)

2·10¹³⁵+3 =

2(0)₁₃₄3_<136>

= 257 · 1039 · 99257 · 7020006299581572894488170104402102406297674139_<46> · 10749361742827382298904906120880763303050229911440763032084434365062835850279407_<80> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 3.55 hours on Core 2 Quad Q6600 / May 20, 2007)

2·10¹³⁶+3 =

2(0)₁₃₅3_<137>

= 23719 · 7835404340941139_<16> · 107614850749561407878824124427790571175221117550451406518629318663620901554531941180527256812039819026153650029950983_<117>

2·10¹³⁷+3 =

2(0)₁₃₆3_<138>

= 17 · 1328613771450100770246781828785320550322299965818189662049_<58> · 8854872751704570530521108482218419399537655969341394293738394189902236177869491_<79> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 6.22 hours on Core 2 Quad Q6600 / May 20, 2007)

2·10¹³⁸+3 =

2(0)₁₃₇3_<139>

= 22082396421516652591_<20> · 90569880271293352518303498238803858248630888025984330258335249566554794436493185827628586008360528546509702442784359533_<119>

2·10¹³⁹+3 =

2(0)₁₃₈3_<140>

= 20663 · 967913662101340560422010356676184484343996515510816435173982480762715965735856361612544161060833373663069254222523350917098194841020181_<135>

2·10¹⁴⁰+3 =

2(0)₁₃₉3_<141>

= 7 · 79 · 7873 · 754242675153051504745993_<24> · 60905079120205992651499182035774058280731042907790381089516679191263999393874607733267630012429589633047391859_<110>

2·10¹⁴¹+3 =

2(0)₁₄₀3_<142>

= 19 · 167 · 511171 · 31993217 · 416824282517_<12> · 40464415611439_<14> · 40059260051938443901187811141767299_<35> · 57043556884754993123007599776067037686087494765852279033731828829_<65> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 3.69 hours on Core 2 Quad Q6600 / May 20, 2007)

2·10¹⁴²+3 =

2(0)₁₄₁3_<143>

= 29 · 18121 · 10062555889_<11> · 5499130730309_<13> · 142203315288161311512583_<24> · 1628892178337141932454034590460430447783_<40> · 2969240859409506695099012352547967144102089819518203_<52> (Jo Yeong Uk / Msieve v. 1.21 / 01:28:26 on Core 2 Quad Q6600 / May 18, 2007)

2·10¹⁴³+3 =

2(0)₁₄₂3_<144>

= 31 · 79869969541_<11> · 213191226127907995641964733297_<30> · 228969479001528543632608227557_<30> · 1654770841768982551074895703714451566312262310294250115213002864298336917_<73> (Makoto Kamada / GMP-ECM 6.1.2 B1=50000, sigma=3963908166 for P30(2289...) / May 12, 2007) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P30(2131...) x P73 / 5.26 hours on Core 2 Quad Q6600 / May 21, 2007)

2·10¹⁴⁴+3 =

2(0)₁₄₃3_<145>

= 1201 · 1168960033824751568738318599288806794044795142960334049_<55> · 1424581581949223240674405227318668880791852510435284297667922774714016704281163739428947_<88> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 9.47 hours on Cygwin on AMD 64 3200+ / May 18, 2007)

2·10¹⁴⁵+3 =

2(0)₁₄₄3_<146>

= 61 · 227 · 7911360529_<10> · 185405024863733_<15> · 1698566896904071_<16> · 511073459929064433496515670727_<30> · 1134320138268801249042282616951572493682856422065040483699499756236497921_<73> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1063430585 for P30 / May 15, 2007)

2·10¹⁴⁶+3 =

2(0)₁₄₅3_<147>

= 7 · 14243 · 106441 · 1088196679_<10> · 11297303071_<11> · 1532990132749980953389945553120218010491917071949279249377201842143209739521102656071536651055954979955117249500808887_<118>

2·10¹⁴⁷+3 =

2(0)₁₄₆3_<148>

= 1689189684351792543788723_<25> · 37217298101001103011342694765763_<32> · 31813154456124267948681707302764451170058560372489661494512147777300060017072412206709935547_<92> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 16.66 hours on Core 2 Quad Q6600 / May 22, 2007)

2·10¹⁴⁸+3 =

2(0)₁₄₇3_<149>

= 151 · 54917 · 79496880961_<11> · 360248308916767_<15> · 22142194087798266515774322687941954125664442651683_<50> · 3803413556430766247732445539023188610808389140958333384583058412229_<67> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 12.42 hours on Cygwin on AMD 64 3200+ / May 19, 2007)

2·10¹⁴⁹+3 =

2(0)₁₄₈3_<150>

= 47 · 173 · 197 · 3634354939784511165317_<22> · 228523786955320896343849_<24> · 150335330555761799982346599520277823222294967921805913894675204804052376237077781705390405123139713_<99>

2·10¹⁵⁰+3 =

2(0)₁₄₉3_<151>

= 487 · 1824453361909318934020125483109157972584403451163125882265065433_<64> · 2250962543871412830161298255938234659251521136933600855735504876723568950774217694093_<85> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 16.18 hours on Cygwin on AMD 64 3200+ / May 19, 2007)

2·10¹⁵¹+3 =

2(0)₁₅₀3_<152>

= 206127409853_<12> · 97027367754065425165181173621119251060810058720182234045762222524054645187828405948586729316796098149047845834331461971247418816223279407551_<140>

2·10¹⁵²+3 =

2(0)₁₅₁3_<153>

= 7 · 59 · 9437 · 1077079 · 3473719 · 764892666772199274490037661811796227973_<39> · 17930947920257063532703516829435538148362253000748922501535367754063948223945638948206096726431_<95> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 17.03 hours on Core 2 Quad Q6600 / May 23, 2007)

2·10¹⁵³+3 =

2(0)₁₅₂3_<154>

= 17 · 79 · 3677 · 294240857 · 1376440289607705711643874895620590896694660344209270221136185143972927196557968203597288965288158512426106493567881141417634298421288841289_<139>

2·10¹⁵⁴+3 =

2(0)₁₅₃3_<155>

= 241 · 141906841 · 32826981394635607932036482961957538515492937504121287_<53> · 17814706504328977485410892424619338104938573843248529336228689546358190125162267028033028349_<92> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 20.71 hours on Cygwin on AMD 64 3400+ / May 19, 2007)

2·10¹⁵⁵+3 =

2(0)₁₅₄3_<156>

= 23 · 1111621257288759311574554337362336029819886569891919818320899807496833211589_<76> · 7822495402005635711932598925376137473625943127630073484216479297850123896513649_<79> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 18.69 hours on Cygwin on AMD 64 3400+ / May 18, 2007)

2·10¹⁵⁶+3 =

2(0)₁₅₅3_<157>

= 97 · 125353 · 97436968800347339_<17> · 43135946585687043827750397163601212657_<38> · 39134557867852232577558454632800142255822036800416522850859882961102818904957125240913476934321_<95> (Robert Backstrom / GMP-ECM 5.0 B1=1358500, sigma=3378444485 for P38 / May 23, 2007)

2·10¹⁵⁷+3 =

2(0)₁₅₆3_<158>

= 8678368395079_<13> · 59573402681404398007654718102866364909302643_<44> · 38684724398115424654512004896712075071304442379362845270019006771965113736013768988351468162809875399_<101> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 44.23 hours on Cygwin on AMD 64 3200+ / May 21, 2007)

2·10¹⁵⁸+3 =

2(0)₁₅₇3_<159>

= 7³ · 31 · 176891153250092117_<18> · 25560955073898763070557830367_<29> · 4159977593448370364304706171478541066565887961579230858181342138794851799577442531362916884055114039300431969_<109>

2·10¹⁵⁹+3 =

2(0)₁₅₈3_<160>

= 19 · 211 · 1895315654240578217_<19> · 27027959896545436523_<20> · 9738658207678451324435719062537714360497552822646565456174754048863655310132922791044018520009793860700775434306628537_<118>

2·10¹⁶⁰+3 =

2(0)₁₅₉3_<161>

= 269741 · 300244161062830630302818080353294695395582491459143920704439_<60> · 246949676822489123478546797860086337445136656832298441810501694114885422418729064737492466489097_<96> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 32.43 hours on Cygwin on AMD 64 3200+ / May 26, 2007)

2·10¹⁶¹+3 =

2(0)₁₆₀3_<162>

= 1645747984609139286241_<22> · 23143371269685496536153160328427093498540901_<44> · 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383_<97> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.26 / Oct 6, 2007)

2·10¹⁶²+3 =

2(0)₁₆₁3_<163>

= 179397930216237714296595927956723_<33> · 11148400639791637102996387547716707811007020632209029670143600424942142750952687051685685837339502521886454403702834010533758301361_<131> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3516208220 for P33 / May 15, 2007)

2·10¹⁶³+3 =

2(0)₁₆₂3_<164>

= 166140237444137244767_<21> · 190635692847477990579123632346869310511_<39> · 631467424737264651495425260061946168071504561817690296672097889180937084893277408137330615731353547645619_<105> (Robert Backstrom / GMP-ECM 6.1.3 B1=4880000, sigma=2651749020 for P39 / Dec 29, 2007)

2·10¹⁶⁴+3 =

2(0)₁₆₃3_<165>

= 7 · 10370741 · 97689419 · 205274357 · 139874026753_<12> · 69298219423145010197_<20> · 2153254071713608720591373_<25> · 6582418788086270165044449804136959083935788871362889026363451583633652174166909560151_<85>

2·10¹⁶⁵+3 =

2(0)₁₆₄3_<166>

= 94136405394950299_<17> · 838305023383274289860418539450587157_<36> · 25343717347214324824522098723663613215893017202640604427624247481323908812513490062007103784101162836271292998421_<113> (Robert Backstrom / GMP-ECM 6.0.1 B1=1495500, sigma=1080719165 for P36 / Nov 12, 2007)

2·10¹⁶⁶+3 =

2(0)₁₆₅3_<167>

= 79 · 729941 · 1137496712761_<13> · 3151934443985899535720514258097_<31> · 29139773847805639821445881025078673003_<38> · 245334893549794309989767836564265608087_<39> · 13531387192579406360450949532177073435621_<41> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2603024962 for P31 / May 16, 2007) (honeycrack7 / GGNFS-0.77.1-20060513-pentium4 / 149.93 hours on DualCore Intel Core 2 Duo E6400, 1600 MHz, Windows XP and Cygwin / Jun 12, 2007)

2·10¹⁶⁷+3 =

2(0)₁₆₆3_<168>

= 337473788641314954387395638036113417304047480856561_<51> · 4690700023174550771994364525354487199388452766958125990189_<58> · 126343321023855007144178242728859599541361819987460022346207_<60> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 86.06 hours on Core 2 Quad Q6600 / May 21, 2007)

2·10¹⁶⁸+3 =

2(0)₁₆₇3_<169>

= 83 · 5113 · 107171503 · 57092174517726937_<17> · 17170380743133123257952990693559_<32> · 44858038464611919885751480065824250801088011690093127023208432690399488635724167714133938508092027766196393_<107> (Robert Backstrom / GMP-ECM 6.0 B1=598000, sigma=3172473091 for P32 / Feb 8, 2008)

2·10¹⁶⁹+3 =

2(0)₁₆₈3_<170>

= 17 · 4568033 · 43680967143031_<14> · 5896028798213843137237197474833906963102993131581871751699684425911935230535986344105005014558253978688551536750366043892471178185550208899868740133_<148>

2·10¹⁷⁰+3 =

2(0)₁₆₉3_<171>

= 7 · 29 · 1013 · 76541953053300386459_<20> · 12706471680112835654690980720290430949855819667071375215198272273064756284147694488613045888308212030764851003333958296721086670252760342053743103_<146>

2·10¹⁷¹+3 =

2(0)₁₇₀3_<172>

= 8627 · 41713247973026961742658321646485423054431_<41> · 5557713951456074967962531890753686473889384220379793822875068616831334165905093911472798378503095080109303609626110094430409519_<127> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 / 206.25 hours on Core 2 Duo E6300 1.86GHz, Windows Vista and Cygwin / Jun 7, 2007)

2·10¹⁷²+3 =

2(0)₁₇₁3_<173>

= 2213 · 40853 · 1531324534463359_<16> · 2439195933333443_<16> · 59225767811436665677404655299131091454174324294278314763315069306690006550853237485054095184846979975166325383100663147992888076712071_<134>

2·10¹⁷³+3 =

2(0)₁₇₂3_<174>

= 31 · 3164590541963_<13> · 1377280097548571230432695973091803101076339_<43> · 10704249832674713026912742559336870309487534796404441_<53> · 138284106376553420246923079942434034576006381033927871198757392949_<66> (suberi / GMP-ECM 6.1.2 B1=3000000, sigma=1577510330 for P43 / May 29, 2007) (JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs for P53 x P66 / Sep 18, 2007)

2·10¹⁷⁴+3 =

2(0)₁₇₃3_<175>

= 797 · 6299 · 398382328716015746459924829238394574988800476783971007327645363238035632510627346596410615056501569725970723281044988718808406584224099621078648041761622754642498669901_<168>

2·10¹⁷⁵+3 =

2(0)₁₇₄3_<176>

= 1607 · 9041761 · 65731411 · 1081691158291_<13> · 76852616085817677774513791387885482895603_<41> · 251898861882089203262483987189502786622824705946228241740108420753071099837412827838656218659332309040463_<105> (suberi / GMP-ECM 6.2.1 B1=11000000, sigma=1680173255 for P41 / Jul 5, 2008)

2·10¹⁷⁶+3 =

2(0)₁₇₅3_<177>

= 7 · 1307 · 17785019238356023897_<20> · 3214888775730183633684484492940316319_<37> · 382327974808924344375250235945475131233497457127498460037175594820337444676213458154174274593752449576287105681456329_<117> (suberi / GMP-ECM 6.2.1 B1=11000000, sigma=3437713636 for P37 / Jul 5, 2008)

2·10¹⁷⁷+3 =

2(0)₁₇₆3_<178>

= 19 · 23 · 107 · 221303620588838744540899263379_<30> · [193275258075082552732257542798544930147975742565477273667881259410088142299640908729176984976444019569373369657540183408799360677960504958362823_<144>] (matsuix / GMP-ECM 6.0 B1=5764801, sigma=1348195423 for P30 / Nov 13, 2007) SUBMIT/RESERVE

2·10¹⁷⁸+3 =

2(0)₁₇₇3_<179>

= 337 · 1297 · 1447 · 1787 · 29365373 · 113629080538653227_<18> · 5303249027172655921940588313560365248852477668638803073380969651997775203643395415597588922210937546209863336469209756209034438146229468862433_<142>

2·10¹⁷⁹+3 =

2(0)₁₇₈3_<180>

= 79 · 811 · 7219 · 1989079332932927_<16> · [217396677973103088696307064618726149413513880278211938748556249954941159094940367789320784791815107241946281840724845499241828364088651729900197748199165699_<156>] SUBMIT/RESERVE

2·10¹⁸⁰+3 =

2(0)₁₇₉3_<181>

= 1979 · 2380977433_<10> · [424452330333802442304872510104661401162841809351689152461037449522245685174777998532399690839006129089109036231723574038187792028891235957665685899677650269563100536129_<168>] SUBMIT/RESERVE

2·10¹⁸¹+3 =

2(0)₁₈₀3_<182>

= 5511837461824511266624821670808689_<34> · [3628554023684809875041241575766798527068771437488933383862974033044444603054287454851457985502624509381866036022786923582580265165248809496728968627_<148>] (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=2741714901 for P34 / May 18, 2008) SUBMIT/RESERVE

2·10¹⁸²+3 =

2(0)₁₈₁3_<183>

= 7 · 4567 · 5531 · 6976873 · [162119952559451128664297370730249211723742928665713458673949989856777959575832263109193734714140858353475737780596207284346400169562377754705897646013791039736405137649_<168>] SUBMIT/RESERVE

2·10¹⁸³+3 =

2(0)₁₈₂3_<184>

= 37441 · 107770823 · 2316040002909679_<16> · 147912404254559543507_<21> · 8754945331971863643578588567_<28> · 165263621461343967146615234240753093905509956335838533801711393326282423692813497174787331122094424554733471_<108>

2·10¹⁸⁴+3 =

2(0)₁₈₃3_<185>

= 241 · 4253 · 41715550696982867_<17> · 45046753479013599736939609_<26> · 16450357456538149478222257267964459_<35> · 56831071349735800699564104034197250430260949_<44> · 11106952378085416134328784349105056515147150726616078638907_<59> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=1916602259 for P44, Msieve 1.36 for P35 x P59 / 3.02 hours on Turion 64 X2 Mobile 1.8GHz, Gentoo Linux / Jun 24, 2008)

2·10¹⁸⁵+3 =

2(0)₁₈₄3_<186>

= 17 · 331 · 1493783 · 23793896485348836084155362360835910425178928920797710161916857648743628889915290695980051085831247984394491270349579323987469196155415850466965348776399545418511815476929867983_<176>

2·10¹⁸⁶+3 =

2(0)₁₈₅3_<187>

= 673 · 156033287693_<12> · 309740823289_<12> · 1457961196343189999407_<22> · [42174822000091876424093964203336048165117324365766001011922853285145707203506291332644631820534815664160562903177049555670641530296985671049_<140>] SUBMIT/RESERVE

2·10¹⁸⁷+3 =

2(0)₁₈₆3_<188>

= 2650288267127376709_<19> · 21691476478039441219_<20> · 4899431565604784118723228083483_<31> · 389595763391679786994327160166767_<33> · 182258522814260407226204545556975019230375927589496525253684233311399812906067616297913_<87> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=2035307540 for P33, B1=3000000, sigma=1333517547 for P31 / Jun 24, 2008)

2·10¹⁸⁸+3 =

2(0)₁₈₇3_<189>

= 7 · 31 · 38749227373442623_<17> · 23785222277923103118099188628420429739593966260699743933477349927854486154481670084027000572733631292076243413718690001102212460927078692317655609049585990575921572073733_<170>

2·10¹⁸⁹+3 =

2(0)₁₈₈3_<190>

= 211 · 617 · 186762743 · 3025939986458771807_<19> · 299721566142829669823_<21> · 6007634365195440036739_<22> · 419817276608201618522516989479656415256109781516871114787_<57> · 35960856659366982010140181518614170249139085672467809368871_<59> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P57 x P59 / 26.59 hours on Core 2 Quad Q6600 / Jul 20, 2007)

2·10¹⁹⁰+3 =

2(0)₁₈₉3_<191>

= 76949 · 1032007 · 209094547936744449194474908906729_<33> · [1204485741923092584911687923487690778909963227537014315607526677383436191113446013891831878203679688385334440434720800302150846416269081049293062249_<148>] (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=3778450102 for P33 / Jun 25, 2008) SUBMIT/RESERVE

2·10¹⁹¹+3 =

2(0)₁₉₀3_<192>

= 2221 · 283112539 · 5806007837521_<13> · 2980061483271130133454822323000539259581_<40> · 182806214988875869300773608643861228898368769920609146878022777_<63> · 100560756952935629434227230943212354457451323996998349267619421881_<66> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=134908296 for P40 / Jun 25, 2008) (Ignacio Santos / GGNFS, Msieve gnfs for P63 x P66 / 93.02 hours / May 7, 2009)

2·10¹⁹²+3 =

2(0)₁₉₁3_<193>

= 79 · 173 · 276519843869_<12> · 35108586452041_<14> · 10356144553255211560838847446569517_<35> · [1455522925575811754655315825187997365065439919940867408609722558444730235468189624497400802537194515833119641347147862725255416513_<130>] (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=1047461786 for P35 / Jun 26, 2008) SUBMIT/RESERVE

2·10¹⁹³+3 =

2(0)₁₉₂3_<194>

= 1999 · 2393 · 3728792911_<10> · [1121259765896650511089383758598218967501967808863102443564553672696080395158866492691338724906859727964961364705439128677348371183067258003530270852836665353564918996891195251739_<178>] SUBMIT/RESERVE

2·10¹⁹⁴+3 =

2(0)₁₉₃3_<195>

= 7 · 443 · 27107 · 2634001 · 383403235824016344915248750822050157_<36> · [2355998796433684043433916754819155439271356874908756261227358227215880822393080326741541660759106061961245778730432937891733785280704982173683897_<145>] (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1503835434 for P36 / May 16, 2007) SUBMIT/RESERVE

2·10¹⁹⁵+3 =

2(0)₁₉₄3_<196>

= 19 · 47 · 113 · 11071 · 126588259468129963800476691109_<30> · 14142292454874449256385710545341601030413458600321097720419472709733367544401014551310864221172502405148901436989368784462014075518851628332348975139832488253_<158> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1143283122 for P30 / May 17, 2007)

2·10¹⁹⁶+3 =

2(0)₁₉₅3_<197>

= 457661 · 1456329317141_<13> · [30007270839200086709912938162371459650880342838952925289095320179225014181778185321387602202088681120845181599333774587489369415627877656236136710817170900904569006153220567318403_<179>] SUBMIT/RESERVE

2·10¹⁹⁷+3 =

2(0)₁₉₆3_<198>

= 29836370592137497650499_<23> · 16729518439454517288281783_<26> · 400682673532747702599827593186249104211952228306848094072962577538564657735619425416018392875826151577920421751986920916957351046332971959489884265159_<150>

2·10¹⁹⁸+3 =

2(0)₁₉₇3_<199>

= 29 · 52157717415774943068631_<23> · [1322249528130632866154580775888170799409853565975777054322882862072465950040683527378460863675853050091803436737342380116080276290972007278824080281313825057944795465189759097_<175>] SUBMIT/RESERVE

2·10¹⁹⁹+3 =

2(0)₁₉₈3_<200>

= 23 · 6317 · 39503 · 20536689829_<11> · 241585002691_<12> · 2791892855273_<13> · 7002385537531_<13> · [35926592169825272295675441399620251465780531966248022891653644917427209264771561329155495410300096888239969362403968151151587601884003665919923_<143>] SUBMIT/RESERVE

2·10²⁰⁰+3 =

2(0)₁₉₉3_<201>

= 7² · 18873739043_<11> · 1737408773621_<13> · 9318870262441_<13> · [13357054371494819032060930454800021527684554278532307447210946315387890611346295668976595361114979189277165650357609403023066235492027027400297029692228361995061189_<164>] SUBMIT/RESERVE

4. References

• A081677 (On-Line Encyclopedia of Integer Sequences)