Factorizations of 299...993 2008-08-08(Fri) 00:12
Last update
Aug 8, 2008 00:12 JST
Sequence
23, 293, 2993, 29993, 299993, ...
General term
3·10n -7
Room for prime numbers
upper limit of periods: 10000
upper limit of periodical factors: 4294967296
checked terms: 100000000
terms divided by periodical factors: 77609054
room for prime numbers: 22.39%
Prime numbers
3·101 -7 = 23 is prime. (Makoto Kamada / Nov 24, 2004)
3·102 -7 = 293 is prime. (Makoto Kamada / Nov 24, 2004)
3·105 -7 = 299993 is prime. (Makoto Kamada / Nov 24, 2004)
3·1010 -7 = 29999999993<11> is prime. (Makoto Kamada / Nov 24, 2004)
3·1029 -7 = 2( 9) 28 3<30> is prime. (Makoto Kamada / PPSIQS / Nov 24, 2004)
3·1039 -7 = 2( 9) 38 3<40> is prime. (Makoto Kamada / PPSIQS / Nov 24, 2004)
3·10114 -7 = 2( 9) 113 3<115> is prime. (searched by Makoto Kamada / PFGW / Dec 23, 2004) (certified by Makoto Kamada / PPSIQS / Jan 2, 2005)
3·10484 -7 = 2( 9) 483 3<485> is prime. (searched by Makoto Kamada / PFGW / Dec 23, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 29, 2006)
3·10865 -7 = 2( 9) 864 3<866> is prime. (searched by Makoto Kamada / PFGW / Dec 23, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 29, 2006)
3·104180 -7 = 2( 9) 4179 3<4181> is PRP. (Makoto Kamada / PFGW / Dec 23, 2004)
3·105385 -7 = 2( 9) 5384 3<5386> is PRP. (Makoto Kamada / PFGW / Dec 23, 2004)
Searched:
References:
A102964 (On-Line Encyclopedia of Integer Sequences)
Condition
n≤200
Status
Completed up to n=100. (Nov 24, 2004)
Completed up to n=150. (Aug 31, 2007)
The following numbers are not factored yet. (n≤200)
n= 171 , 176 , 180 , 188 , 189 , 191 , 193 , 194 , 195 , 196 , 197 , 198 (12/200)
Factorization results
3·101 -7 =23 = definitely prime number
3·102 -7 =293 = definitely prime number
3·103 -7 =2993 = 41 · 73
3·104 -7 =29993 = 89 · 337
3·105 -7 =299993 = definitely prime number
3·106 -7 =2999993 = 173 · 17341
3·107 -7 =29999993 = 19 · 311 · 5077
3·108 -7 =299999993 = 41 · 7317073
3·109 -7 =2999999993<10> = 227 · 13215859
3·1010 -7 =29999999993<11> = definitely prime number
3·1011 -7 =299999999993<12> = 73 · 22133 · 185677
3·1012 -7 =2999999999993<13> = 59 · 50847457627<11>
3·1013 -7 =29999999999993<14> = 41 · 479 · 1527572687<10>
3·1014 -7 =299999999999993<15> = 172 · 2137 · 3023 · 160687
3·1015 -7 =2999999999999993<16> = 467 · 6423982869379<13>
3·1016 -7 =29999999999999993<17> = 43 · 21277 · 44263 · 740801
3·1017 -7 =299999999999999993<18> = 4363 · 2782159 · 24714629
3·1018 -7 =2999999999999999993<19> = 41 · 1429 · 1665023 · 30752819
3·1019 -7 =29999999999999999993<20> = 73 · 727 · 45341 · 12467313763<11>
3·1020 -7 =299999999999999999993<21> = 47 · 6382978723404255319<19>
3·1021 -7 =2999999999999999999993<22> = 29 · 14939 · 18307 · 378254887229<12>
3·1022 -7 =29999999999999999999993<23> = 64098527 · 468029475934759<15>
3·1023 -7 =299999999999999999999993<24> = 23 · 41 · 151 · 8761 · 240479984004041<15>
3·1024 -7 =2999999999999999999999993<25> = 56546197 · 53053965768909269<17>
3·1025 -7 =29999999999999999999999993<26> = 192 · 5660731 · 14680523253055523<17>
3·1026 -7 =299999999999999999999999993<27> = 5939 · 13907 · 173291 · 20960346940051<14>
3·1027 -7 =2999999999999999999999999993<28> = 73 · 83 · 8340752393<10> · 59362895149139<14>
3·1028 -7 =29999999999999999999999999993<29> = 41 · 193 · 3791229622140780993302161<25>
3·1029 -7 =299999999999999999999999999993<30> = definitely prime number
3·1030 -7 =2999999999999999999999999999993<31> = 17 · 176470588235294117647058823529<30>
3·1031 -7 =29999999999999999999999999999993<32> = 127453 · 33120937 · 7106709737797915013<19>
3·1032 -7 =299999999999999999999999999999993<33> = 67 · 4477611940298507462686567164179<31>
3·1033 -7 =2999999999999999999999999999999993<34> = 41 · 378411155279<12> · 193363040931942888287<21>
3·1034 -7 =29999999999999999999999999999999993<35> = 127 · 236220472440944881889763779527559<33>
3·1035 -7 =299999999999999999999999999999999993<36> = 73 · 139 · 64969 · 8001611909<10> · 56872186918708639<17>
3·1036 -7 =2999999999999999999999999999999999993<37> = 8291 · 15213119 · 23784612329642446512944717<26>
3·1037 -7 =29999999999999999999999999999999999993<38> = 43 · 697674418604651162790697674418604651<36>
3·1038 -7 =299999999999999999999999999999999999993<39> = 41 · 302941 · 614863 · 39282668639885187200647531<26>
3·1039 -7 =2999999999999999999999999999999999999993<40> = definitely prime number
3·1040 -7 =29999999999999999999999999999999999999993<41> = 194167 · 2676917 · 57717954094800936155245947187<29>
3·1041 -7 =299999999999999999999999999999999999999993<42> = 61 · 1699 · 1129133 · 2563615806052953325816712606539<31>
3·1042 -7 =2999999999999999999999999999999999999999993<43> = 131 · 739 · 9413 · 58706613131<11> · 56077731378430703911159<23>
3·1043 -7 =29999999999999999999999999999999999999999993<44> = 19 · 41 · 73 · 4679321 · 105566730011<12> · 1067950267835171525809<22>
3·1044 -7 =299999999999999999999999999999999999999999993<45> = 1811 · 165654334621755935946990612921038100496963<42>
3·1045 -7 =2999999999999999999999999999999999999999999993<46> = 23 · 521 · 563 · 613919983 · 9462887771<10> · 76544121199288610969<20>
3·1046 -7 =29999999999999999999999999999999999999999999993<47> = 17 · 2377 · 252381433753051<15> · 2941614437604474434732834227<28>
3·1047 -7 =299999999999999999999999999999999999999999999993<48> = 1613 · 349823429 · 531664906496470899353100146638535609<36>
3·1048 -7 =2999999999999999999999999999999999999999999999993<49> = 41 · 89 · 719 · 2957 · 1165872165481<13> · 331677676614535440225583259<27>
3·1049 -7 =29999999999999999999999999999999999999999999999993<50> = 29 · 173 · 3025369 · 3450697297<10> · 178896439009<12> · 3201770815343579417<19>
3·1050 -7 =299999999999999999999999999999999999999999999999993<51> = 5694486468763<13> · 52682538038441998362242618863241257211<38>
3·1051 -7 =2999999999999999999999999999999999999999999999999993<52> = 73 · 97 · 429570716502509<15> · 986261300021320591903991131292917<33>
3·1052 -7 =29999999999999999999999999999999999999999999999999993<53> = 38833 · 39863 · 60107 · 133789490251<12> · 2409923634153698499717890231<28>
3·1053 -7 =299999999999999999999999999999999999999999999999999993<54> = 41 · 44898546488662394786777<23> · 162969043387170361806111445049<30>
3·1054 -7 =2999999999999999999999999999999999999999999999999999993<55> = 4057290239390967318353<22> · 739409759468014964747695349027881<33>
3·1055 -7 =29999999999999999999999999999999999999999999999999999993<56> = 32665169 · 610358441181169<15> · 6976225339896877<16> · 215690436695812669<18>
3·1056 -7 =299999999999999999999999999999999999999999999999999999993<57> = 4589444731<10> · 65477631887<11> · 998316264207105833544335690930066869<36>
3·1057 -7 =2999999999999999999999999999999999999999999999999999999993<58> = 59168881 · 7682753902800453193333<22> · 6599499143290305535669023941<28>
3·1058 -7 =29999999999999999999999999999999999999999999999999999999993<59> = 41 · 43 · 3990749511865583<16> · 4263973267093125175567911209654453501117<40>
3·1059 -7 =299999999999999999999999999999999999999999999999999999999993<60> = 73 · 163 · 25127 · 6135061588459367723<19> · 163550254238434027608380315287367<33>
3·1060 -7 =2999999999999999999999999999999999999999999999999999999999993<61> = 109 · 2008225567242057245851228907<28> · 13705101771816599211970478043511<32>
3·1061 -7 =29999999999999999999999999999999999999999999999999999999999993<62> = 19 · 55977197 · 152648470361440633<18> · 184783866057050946989986973194331047<36>
3·1062 -7 =299999999999999999999999999999999999999999999999999999999999993<63> = 17 · 14124571339<11> · 20126872010957233<17> · 62075577991749361724417101512976267<35>
3·1063 -7 =2999999999999999999999999999999999999999999999999999999999999993<64> = 41 · 937 · 78090428716453653330556784756748314548246869875315615482729<59>
3·1064 -7 =29999999999999999999999999999999999999999999999999999999999999993<65> = 2762849 · 10858356718011009649821615296384275796469513896705900322457<59>
3·1065 -7 =299999999999999999999999999999999999999999999999999999999999999993<66> = 67 · 661 · 5807 · 178521407 · 17792791233404596831187<23> · 367247444439121441483719853<27>
3·1066 -7 =2999999999999999999999999999999999999999999999999999999999999999993<67> = 47 · 8941 · 7138998684044575907783174331968198140528809429189461886075859<61>
3·1067 -7 =29999999999999999999999999999999999999999999999999999999999999999993<68> = 23 · 73 · 313 · 2833 · 732889955570420529792047<24> · 27494186665736922923964291981943409<35>
3·1068 -7 =299999999999999999999999999999999999999999999999999999999999999999993<69> = 41 · 83 · 487 · 929 · 1033 · 954952261 · 197529810719025559771655747127450876142381029169<48>
3·1069 -7 =2999999999999999999999999999999999999999999999999999999999999999999993<70> = 896947 · 112842827 · 822427339 · 7344841710623<13> · 4906824622945938092484244546324901<34>
3·1070 -7 =29999999999999999999999999999999999999999999999999999999999999999999993<71> = 59 · 3169063 · 132074707 · 1214838968175389449030210093135645815191851627588101247<55>
3·1071 -7 =299999999999999999999999999999999999999999999999999999999999999999999993<72> = 149 · 77377 · 1191293 · 576763553 · 37870993660572697198300908541206230781390180477529<50>
3·1072 -7 =2999999999999999999999999999999999999999999999999999999999999999999999993<73> = 4496651918177<13> · 667163048105408665186644021277780391502794740160718246413209<60>
3·1073 -7 =29999999999999999999999999999999999999999999999999999999999999999999999993<74> = 41 · 883 · 1117 · 691437589 · 1072927892606161434458283514437101060262952971040534496587<58>
3·1074 -7 =299999999999999999999999999999999999999999999999999999999999999999999999993<75> = 7691 · 519369682548231169<18> · 1447112285977984957481<22> · 51899075057568853399874353813907<32>
3·1075 -7 =2999999999999999999999999999999999999999999999999999999999999999999999999993<76> = 73 · 22993 · 144773 · 12345684702690221215690727658471481200746127272298324605881690669<65>
3·1076 -7 =29999999999999999999999999999999999999999999999999999999999999999999999999993<77> = 127 · 754633628964966973809046907<27> · 313026697160233703777658958599629306969374056037<48>
3·1077 -7 =299999999999999999999999999999999999999999999999999999999999999999999999999993<78> = 29 · 4496509 · 47273727563<11> · 48666256610101450693770379883958247889029074363758568768851<59>
3·1078 -7 =2999999999999999999999999999999999999999999999999999999999999999999999999999993<79> = 17 · 412 · 30491 · 1917317 · 50128051 · 35822691217329452883535973372324375749278686797074020197<56>
3·1079 -7 =29999999999999999999999999999999999999999999999999999999999999999999999999999993<80> = 19 · 43 · 2072057437<10> · 524222960180108353057807908398059<33> · 33805033443334190185461635447442263<35>
3·1080 -7 =299999999999999999999999999999999999999999999999999999999999999999999999999999993<81> = 1217 · 1351099 · 9418537 · 2313020227702423<16> · 11398590629043678321871<23> · 734732868148376568253047451<27>
3·1081 -7 =2999999999999999999999999999999999999999999999999999999999999999999999999999999993<82> = 139 · 146084400680863009<18> · 147741536484100240702785606335371798030497553204677813231395243<63>
3·1082 -7 =29999999999999999999999999999999999999999999999999999999999999999999999999999999993<83> = 105041792255800663<18> · 285600610535501664630910801196245459713208417984924484364044292911<66>
3·1083 -7 =299999999999999999999999999999999999999999999999999999999999999999999999999999999993<84> = 41 · 73 · 4373 · 16706531 · 248433393185469030804567971<27> · 5522539215804046633907535836205387510458237<43>
3·1084 -7 =2999999999999999999999999999999999999999999999999999999999999999999999999999999999993<85> = 1831 · 238145213 · 799426924271<12> · 8606216821833434280793632376048651261821540928636858989221861<61>
3·1085 -7 =29999999999999999999999999999999999999999999999999999999999999999999999999999999999993<86> = 5257559 · 16292161 · 350234082530206643545873000220423449117716831546591807227963415158865007<72>
3·1086 -7 =299999999999999999999999999999999999999999999999999999999999999999999999999999999999993<87> = 534073 · 256830289 · 698096864068085227884551909064009967<36> · 3132987804392042217894882713321800607<37>
3·1087 -7 =2999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<88> = 49074331215135871662164352061620157<35> · 61131755150128619573827193417726050993904641966003949<53> (Makoto Kamada / GGNFS-0.54.5b)
3·1088 -7 =29999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<89> = 41 · 32668049842108543<17> · 1879560371784273560052702852157<31> · 11916752199520156001544300802205904815323<41>
3·1089 -7 =299999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<90> = 23 · 529956721278463<15> · 1221735429632752897111<22> · 20145397717380594702864766144334667714272774673702487<53>
3·1090 -7 =2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<91> = 27073 · 300073 · 128035463783099<15> · 7155270250560533<16> · 403089634945954657923428956224600453296801968926551<51>
3·1091 -7 =29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<92> = 73 · 1912129 · 12723947 · 16434248219657<14> · 113149242742746923725832569<27> · 9083597058727784463071328219055034579<37>
3·1092 -7 =299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<93> = 89 · 173 · 631 · 492971606256827<15> · 2081663667995930171<19> · 934932643516228947551119<24> · 32184220413324863260992821813<29>
3·1093 -7 =2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<94> = 41 · 3319 · 221212198618532822657518266919<30> · 99660043725599786755884788217021864728527174110556729974193<59> (Makoto Kamada / GGNFS-0.54.5b)
3·1094 -7 =29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<95> = 17 · 273857 · 50736806544125182727059957829623309042903<41> · 127006327579537107737996122558784534366651222399<48> (Makoto Kamada / GGNFS-0.54.5b)
3·1095 -7 =299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<96> = 3533 · 1001544527686081<16> · 42907833229284301<17> · 47794793502289827289<20> · 41341876127667250973177966751544194190969<41>
3·1096 -7 =2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<97> = 105716918560885019<18> · 84826881140613763057<20> · 334536307856845536905409704221858141814590672022973378601771<60>
3·1097 -7 =29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<98> = 19 · 521 · 14361317 · 28492109297<11> · 2370922293737<13> · 3123875664564538643409287322339749893623803998803594503291763239<64>
3·1098 -7 =299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993<99> = 41 · 672 · 151 · 46448341 · 14699350183747451<17> · 751154106800146859<18> · 21048127031018388845501130427016744996720399554603<50>
3·1099 -7 =2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 <100> = 73 · 1543 · 22657284571<11> · 33994238561<11> · 73006926117795259733621<23> · 473647476771372501389498106143899191060172913548337<51>
3·10100 -7 =29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 <101> = 43 · 520474043 · 2521284071<10> · 54259042988364807699026477681<29> · 9798504903679346799981799815998990291317699151934007<52>
3·10101 -7 =2( 9) 100 3<102> = 61 · 270538861909140599<18> · 1503944237661379360868402573256481<34> · 12087320199218433786007971497669328028718661880027<50> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs for P34 x P50 / 2.70 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 26, 2007)
3·10102 -7 =2( 9) 101 3<103> = 5503 · 3539577321355187357058316586614016942558507<43> · 154017595180034784335600556931964288371618563510589261333<57> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.35 hours on Core 2 Quad Q6600 / Aug 27, 2007)
3·10103 -7 =2( 9) 102 3<104> = 41 · 22093 · 23599 · 5635247 · 51407263 · 85935290864503<14> · 19008185993682724277<20> · 2965783485720682229873326130872834525250555929<46>
3·10104 -7 =2( 9) 103 3<105> = 14306459 · 15418327 · 2124528671<10> · 69658927796959<14> · 51317164112551327<17> · 179081126555694774392291804925465911407077526573667<51>
3·10105 -7 =2( 9) 104 3<106> = 29 · 113 · 11939 · 32843 · 26345205751<11> · 40345426547<11> · 188547589391012659<18> · 11649764616834067845518116860705408548212159084371178579<56>
3·10106 -7 =2( 9) 105 3<107> = 269 · 351599 · 85916641609<11> · 247442640229<12> · 738774190963452887<18> · 20195648113222437925515153574177134536502955251016044395929<59>
3·10107 -7 =2( 9) 106 3<108> = 732 · 31957 · 277589851523296053332037672941<30> · 1002459894818158467774433246518331<34> · 6330513515041898460559917424038309211<37> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.45 hours on Core 2 Quad Q6600 / Aug 27, 2007)
3·10108 -7 =2( 9) 107 3<109> = 41 · 140723320772963967845461<24> · 348045719063430961912708909<27> · 1493946436367187554883887397135974677940055938643149095777<58>
3·10109 -7 =2( 9) 108 3<110> = 83 · 56809 · 16216515547<11> · 1243071210473<13> · 2248059687775148500471809593908702163<37> · 140399198593424783364159287344550310097264723<45> (Sinkiti Sibata / Msieve v. 1.26 for P37 x P45 / 1.4 hours on Celeron 750MHz,Windows 2000 / Aug 26, 2007)
3·10110 -7 =2( 9) 109 3<111> = 17 · 491039 · 5146243 · 1721445263<10> · 4056699508782791903388906801562232920260501335354127930862027874602883948349825380940979<88>
3·10111 -7 =2( 9) 110 3<112> = 23 · 373003 · 27835335642957025433655367694790412609627019<44> · 12562747515193989773402390442014510943362606451247158043351463<62> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.69 hours on Core 2 Quad Q6600 / Aug 27, 2007)
3·10112 -7 =2( 9) 111 3<113> = 47 · 51329 · 23588119 · 527190145177582333444260317030062053099466733411113735957322662540237419926423245653997929202619969<99>
3·10113 -7 =2( 9) 112 3<114> = 41 · 51513642470265587<17> · 23701595572502442779<20> · 50132733817468641778099964125202773<35> · 119540802551021556641486044708047824109037<42> (Makoto Kamada / Msieve 1.26 for P35 x P42 / 4.9 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Aug 26, 2007)
3·10114 -7 =2( 9) 113 3<115> = definitely prime number
3·10115 -7 =2( 9) 114 3<116> = 19 · 73 · 183978391 · 52741576847<11> · 148097434733<12> · 15051415032624839272796239307797611365954407544272847296283005945190961524544515279<83>
3·10116 -7 =2( 9) 115 3<117> = 5711 · 3219174617934997967729103654362313099113789<43> · 16317910987225509303709497983754427492567247926719168101616013003489667<71> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.83 hours on Core 2 Quad Q6600 / Aug 27, 2007)
3·10117 -7 =2( 9) 116 3<118> = 65663146013<11> · 1115445346207<13> · 218367804382939724096025924452209<33> · 187569691815535808504272490616328250324358050799297959129311747<63> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs for P33 x P63 / 10.53 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 27, 2007)
3·10118 -7 =2( 9) 117 3<119> = 41 · 127 · 167 · 1213 · 9897661 · 14329261617626323<17> · 200539541744802669558099610471711696723801947641295708137598305473137079551362983266923<87>
3·10119 -7 =2( 9) 118 3<120> = 78368605499<11> · 53095903456340370936693577<26> · 188290868464416554619696945024940247957<39> · 382903082208360177830892669855412560821185463<45> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs for P39 x P45 / 2.71 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 26, 2007)
3·10120 -7 =2( 9) 119 3<121> = 5839 · 40493 · 7873580993<10> · 1611500804618018920416277327603751960929318129969962351751472775272740456386711094959536999325299568563 <103>
3·10121 -7 =2( 9) 120 3<122> = 43 · 4337 · 7031670871<10> · 21125729592553<14> · 169087047557767<15> · 11849991123529165669<20> · 540461496936340133701144762007986592828319113259134309253127<60>
3·10122 -7 =2( 9) 121 3<123> = 227 · 541 · 5821 · 2440113394861<13> · 83874866130091704225931620360708407017715883677<47> · 2050494856118000514981197734640153342657783824277403827<55> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 2.62 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 27, 2007)
3·10123 -7 =2( 9) 122 3<124> = 41 · 73 · 25229 · 80436896303091941<17> · 25717660438571745381489038333885826323571075209<47> · 19205593766110280619993552722286434599284651570080801<53> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 2.60 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 27, 2007)
3·10124 -7 =2( 9) 123 3<125> = 499 · 50123 · 4979165454103<13> · 32069277584934255341895947641<29> · 7511694512964920660213222237541918019312926923461518825741959466812334839383<76> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 3.48 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 27, 2007)
3·10125 -7 =2( 9) 124 3<126> = 8929 · 105642398249<12> · 318038854042474590841624434519546128113364597743750708667591053125474563140439565756732101437336647209578296433 <111>
3·10126 -7 =2( 9) 125 3<127> = 17 · 1947761627248864935777984869025486217<37> · 90601737793013067707297429917950567899839201443202358104654069381901149336940160966925537<89> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 1.98 hours on Core 2 Quad Q6600 / Aug 27, 2007)
3·10127 -7 =2( 9) 126 3<128> = 139 · 181 · 491 · 52314763871<11> · 46421815166515942054629056212512630972121829637426324358911515355441565203529703724844328748618857947465260707 <110>
3·10128 -7 =2( 9) 127 3<129> = 41 · 59 · 54773 · 7537788328018616405984189140699812345322214029<46> · 300382702420089950889070923665817867552296755414839069498484220494663049491<75> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 2.00 hours on Core 2 Quad Q6600 / Aug 27, 2007)
3·10129 -7 =2( 9) 128 3<130> = 13634014563100632163485094139<29> · 139215960043020963366563162682325387847822463557<48> · 1580550856695477889083277991070258583743421455170186591<55> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 2.83 hours on Core 2 Quad Q6600 / Aug 27, 2007)
3·10130 -7 =2( 9) 129 3<131> = 1171 · 278757858367742941463<21> · 91904598132686346780820614473422413139780712486439835126506806791746850203603242336943654784374659215916341 <107>
3·10131 -7 =2( 9) 130 3<132> = 67 · 73 · 1019 · 116345861 · 977792987 · 556928995904051921<18> · 59726562069597109314324525106720499<35> · 15906850721045874492067807848099118867247459356850020189<56> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs for P35 x P56 / 4.36 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 27, 2007)
3·10132 -7 =2( 9) 131 3<133> = 2521 · 12924559 · 92073080921359787437475420014943909736351050261133039298638936043529890608166831533180614686946553381372373890860885463887 <122>
3·10133 -7 =2( 9) 132 3<134> = 19 · 23 · 29 · 41 · 4133 · 845895553 · 15285736889<11> · 63642234051349873089290850183434749198604956677859<50> · 16976338245683764819391125937000990768709124738416339799<56> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 6.23 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 28, 2007)
3·10134 -7 =2( 9) 133 3<135> = 593 · 1974304861<10> · 3113816399009399331502040880885247<34> · 82292327352237237759282275303994140450126197932685043092723845873827586615938532821406403<89> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=916588648 for P34 / Aug 20, 2007)
3·10135 -7 =2( 9) 134 3<136> = 173 · 3767 · 4603408670673678169561954975594261697645049571039035371057755899651828857541380807775464138679220673601446084110414291435665062123 <130>
3·10136 -7 =2( 9) 135 3<137> = 89 · 1259 · 19246037 · 50843011 · 273610613173572184314688065898806371900333711622405918497593770818128895110745150711625752461204761515171765221862749 <117>
3·10137 -7 =2( 9) 136 3<138> = 233 · 701 · 5477 · 21661 · 488603 · 6476427849686591970532300943502577690100886356016287<52> · 4892540299472487410211328047955667103685004673915706548024083374513<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 4.06 hours on Core 2 Quad Q6600 / Aug 28, 2007)
3·10138 -7 =2( 9) 137 3<139> = 41 · 119617 · 904286291 · 676454429502225918046520757179306967939933913900456238419488571312244894562861677438863361825076381458797189851296464088459 <123>
3·10139 -7 =2( 9) 138 3<140> = 73 · 743 · 1447 · 8089 · 44357 · 808196944503758129<18> · 836617817977783013624277121<27> · 1575577370354228377776494151421374328316543300862879300850332723907996910985253<79>
3·10140 -7 =2( 9) 139 3<141> = 163 · 257 · 22303 · 277717378709055933498757<24> · 37093886403445655363232597242736014387<38> · 31169644391610806846824618395203670558943768245441618617177544108945299<71> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 11.33 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 28, 2007)
3·10141 -7 =2( 9) 140 3<142> = 6397202872201<13> · 468954957335569090511649262700943541094113100410688877527511298162402599051005534156014161127050959282671746600219899815826225393 <129>
3·10142 -7 =2( 9) 141 3<143> = 17 · 43 · 373 · 971 · 3350911 · 9620632886332129154929892341<28> · 3514870106914108345406517412425465775454616884446672411785268027905576643346816691885052515554485991 <100>
3·10143 -7 =2( 9) 142 3<144> = 41 · 5461117 · 10069687 · 22362475732852823<17> · 2637453503735239381<19> · 2255980031085937390123230461692929651446696232854796074224525926167886189121112417153968514849<94>
3·10144 -7 =2( 9) 143 3<145> = 18599213 · 17212516823<11> · 9370921697067736101509915668666524834479967418197513761679217340038627790407423975555652928877627886519362752811613681741052107 <127>
3·10145 -7 =2( 9) 144 3<146> = 881 · 69669013 · 123399738089<12> · 3960877860017655387557299413351438582955602298745046582859124671697045089229849463136903602045141855351929003254850928494429 <124>
3·10146 -7 =2( 9) 145 3<147> = 1854775915575395694657042218355139211068315081<46> · 161744606170893075229127752358828695970725053902533763048339214947771986894331414501673269180172824753 <102> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 11.47 hours on Core 2 Quad Q6600 / Aug 28, 2007)
3·10147 -7 =2( 9) 146 3<148> = 73 · 97 · 1657063033<10> · 255674627260153646516206521906177265384354530316168720276398635139260630866908792603402370413630743079266622475357304138872093365346841 <135>
3·10148 -7 =2( 9) 147 3<149> = 41 · 293 · 23176583 · 420246714641792212696158791990420325985853003<45> · 256398832799819491996337343700283603386076585422635350041027234530711778924253071751054434289<93> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 25.94 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 31, 2007)
3·10149 -7 =2( 9) 148 3<150> = 179 · 521 · 3463 · 5282612227<10> · 35419352915554933199557<23> · 21272798033221076607577777047006013<35> · 233380215802854007300467394780726271343697166092228509059711875575719508047<75> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=2894591195 for P35 / Aug 27, 2007)
3·10150 -7 =2( 9) 149 3<151> = 83 · 189651047 · 16655019752526043619345197086882937152885261185068417<53> · 11443075559040216743203773330203910152796400883206795006697965100458043235549364132362629<89> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 32.25 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 30, 2007)
3·10151 -7 =2( 9) 150 3<152> = 19 · 156901 · 2776542823659779412773229802771285257042021400690501832194379669<64> · 3624412053738393293775064001860434687254067055643958807515278373333482272091019563<82> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 37.52 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Sep 2, 2007)
3·10152 -7 =2( 9) 151 3<153> = 21419 · 39111724098589<14> · 6256881900772855177774283<25> · 57234401466004564622314659495068850297923427270981654934536130156776665032786481422195112907293155615384079381 <110>
3·10153 -7 =2( 9) 152 3<154> = 41 · 1367 · 152729 · 350467197066908065138673900838897476819510509047630610421954277466994169648620804342420534240926520184963180073402277323673646790483330973857711 <144>
3·10154 -7 =2( 9) 153 3<155> = 34019 · 609903171398591373643<21> · 3638448521596708316295882652136033250258553<43> · 397395170759107781009516079528422156485067127226121794287339983126117723660641650772993<87> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 57.07 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Sep 18, 2007)
3·10155 -7 =2( 9) 154 3<156> = 23 · 73 · 10333 · 12641093 · 18943129103597<14> · 72211735649817090988968245723900684844204410757785843620258795826399357717876433788968295437619330193896011121330668926863924419 <128>
3·10156 -7 =2( 9) 155 3<157> = 20326576471807<14> · 755863572447083289435283827464011678816063064420816854967<57> · 195260141964162497840754186283403004144880025879973776465137141067044484471377181806897<87> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 45.23 hours on Cygwin on AMD XP 2700+ / Sep 20, 2007)
3·10157 -7 =2( 9) 156 3<158> = 1475129 · 1737809617<10> · 1216200005067323<16> · 14727583118035831<17> · 727011729433678369<18> · 6006402632184905734339<22> · 149622433904500682887740394139684660311996484164146297871579604342815847<72>
3·10158 -7 =2( 9) 157 3<159> = 17 · 41 · 47 · 3041 · 841123744137979613<18> · 263885431718243596975433066048441779693678318105769<51> · 13567470651611743221749122292261888185172901056388384006891037144978168857382893251<83> (suberi / GGNFS-0.77.1-20060722-k8 snfs / 49.54 hours on Turion 64 X2 Mobile 1.79GHz, Windows XP and Cygwin / Nov 3, 2007)
3·10159 -7 =2( 9) 158 3<160> = 2659 · 629501473 · 3776223670753814722104781857341<31> · 2429003868169712771564765938483840128221281<43> · 195398061142744316558324686703766895073805079591953321661587802348156465519<75> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2566452289 for P31 / Aug 22, 2007) (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 gnfs for P43 x P75 / 56.60 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Sep 21, 2007)
3·10160 -7 =2( 9) 159 3<161> = 127 · 40829 · 1767818010311<13> · 16453710424472833724720213<26> · 156576499347676290337540161614647420749481<42> · 1270342440851204099715174694929205958381506676212657967303937958146615630937<76> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=3734854031 for P42 / Aug 28, 2007)
3·10161 -7 =2( 9) 160 3<162> = 29 · 61 · 3257 · 53717 · 241313 · 32371309 · 103528123293945208277<21> · 1198573279750995653400341941182039366354667310712305043897588264383401423275498691870653282350121116813509672488529957 <118>
3·10162 -7 =2( 9) 161 3<163> = 311 · 839 · 4051197719261188815701375854427236740369079486103<49> · 20165397378055339711076080733916793276540156689149<50> · 140737126881900958635390331620494185432391996158454693370011<60> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 45.25 hours on Cygwin on AMD 64 3400+ / Sep 20, 2007)
3·10163 -7 =2( 9) 162 3<164> = 41 · 43 · 73 · 433163734125755498123<21> · 984803325251956195887249668731139<33> · 546442521935781460110773913223987286991730594097092602213887622250012599971203648826978554376441175284731 <105> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=4192204273 for P33 / Oct 24, 2007)
3·10164 -7 =2( 9) 163 3<165> = 67 · 2552597274973289<16> · 1754139591152451686804312012432644493744524845024710249172627207544961301144157951346848542805329436820183510885167494526068893153304139532530922011 <148>
3·10165 -7 =2( 9) 164 3<166> = 389 · 72612871 · 4893118907011<13> · 9586550427068758139277418251508130186850823<43> · 763966565598162182661254838642609221002481461<45> · 2963709019423440832352969589339376348532317934047934059<55> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.33 / Jan 24, 2008)
3·10166 -7 =2( 9) 165 3<167> = 25411 · 4718927 · 954512749 · 611255532829942634147397320551746694935812453256656449<54> · 428796965068732802120208918501494985696065115728677764830252574676814510715480757019757325969<93> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.33 / Jan 26, 2008)
3·10167 -7 =2( 9) 166 3<168> = 655467036657994741996643867126553366964783<42> · 457688919841947776110399176672643492197644369408954631966772160173721908536961345672536829147905758344010973197701056308278871 <126> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=3265550511 for P42 / Aug 27, 2007)
3·10168 -7 =2( 9) 167 3<169> = 41 · 109 · 12707934241218043<17> · 52824566435319229836793818203408945538558827619501267406240061485986182898660755947267906681573590490007191531323540884030414758595806839731210102479 <149>
3·10169 -7 =2( 9) 168 3<170> = 19 · 43055561 · 10073117473<11> · 310792818964334717<18> · 275860320126853307413096987739888963147811740022702997<54> · 42463353702343919630941476770580199897205148009535304984674887647746788420522251<80> (matsui / GGNFS-0.77.1-20060513-prescott snfs / Mar 7, 2008)
3·10170 -7 =2( 9) 169 3<171> = 571 · 19364771 · 6500447580664317282363738571189216214014916119<46> · 4173779680365580296879466841090799172626675464658891545229584269857535434533778203229820960806843647214822728845567 <115> (matsui / GGNFS-0.77.1-20060513-prescott snfs / Mar 31, 2008)
3·10171 -7 =2( 9) 170 3<172> = 73 · 26103770121167<14> · [1574327777949404635376174768673852196943179488710897574632998700132319413715457346172529249449492909562247276388632517481561461992754350763645351691241306623 <157> ] SUBMIT/RESERVE
3·10172 -7 =2( 9) 171 3<173> = 131 · 461 · 1481339 · 19066031 · 12697821007221211<17> · 907781215359903216323<21> · 2441028438556608761871741655549673371<37> · 625102233126823174647422983194808336324391991485377318806731843475223989628620169<81> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3296257244 for P37 / Aug 23, 2007)
3·10173 -7 =2( 9) 172 3<174> = 41 · 139 · 151 · 1093 · 1685407 · 6821392519<10> · 22138926149<11> · 77680027519201<14> · 3426211144509826462542397<25> · 715354854868831667492444551<27> · 335733348651970999890000899829539707<36> · 19604311645442277565086098446148222093<38> (Makoto Kamada / Msieve 1.26 for P36 x P38 / 4.2 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Aug 26, 2007)
3·10174 -7 =2( 9) 173 3<175> = 17 · 13707838783<11> · 37843367550258766630487<23> · 2335652610416605452519508897978433<34> · 145648266590335890831386445560195486299154390924262334577765318323875048848015754190501837612604655871004353 <108> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=4118715206 for P34 / Aug 7, 2008)
3·10175 -7 =2( 9) 174 3<176> = 773 · 4729 · 149615293 · 1357303109276593<16> · 40412862702780788089192628849723087500346075023752264918482149803781630513952722107404046737066773881468287242932636884334880874995308989642226721 <146>
3·10176 -7 =2( 9) 175 3<177> = 3983827881785093<16> · 6361621691528742703<19> · [11837305297500476833272061812632709569273438156977425706603207959380043080856984547345584022048778543024109119089522487518143570839379652439467 <143> ] SUBMIT/RESERVE
3·10177 -7 =2( 9) 176 3<178> = 23 · 1753 · 925915713899395469251986786287599<33> · 80360022181039925458264011703983589381427749270077492993109687046726845066099393288440521768615672663893061938919668184954131153418567467753 <140> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1307875811 for P33 / Aug 24, 2007)
3·10178 -7 =2( 9) 177 3<179> = 41 · 173 · 1277 · 3421157 · 968115988973227449763674672832386626010442244448659914206517852033181576471116631855105487651414173092600480303557739651720198680759948394513876215754799069497891109 <165>
3·10179 -7 =2( 9) 178 3<180> = 73 · 3683111 · 16927973 · 584455519 · 482923793970269<15> · 75814253468842025360202563<26> · 666955264597468844867283661741291944087841<42> · 4618500484221053916134988602864131972644643376658791905760135103112512419<73> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P42 x P73 / 25.35 hours on Core 2 Quad Q6600 / Sep 18, 2007)
3·10180 -7 =2( 9) 179 3<181> = 89 · 379 · 7669 · [11597204098100919558162450689316356763537171835993468439189010764636950163555176108782300180105739363917090830218675450151952173408632330162164207449256075888299735028240487 <173> ] SUBMIT/RESERVE
3·10181 -7 =2( 9) 180 3<182> = 1936760724982998289<19> · 68808646991249141025719<23> · 1724512309637715528857993530467193207<37> · 130537703533059377398780785440600547165396660129485394210598345885209061956376547057033455498259978403289 <105> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=4240482263 for P37 / Aug 3, 2008)
3·10182 -7 =2( 9) 181 3<183> = 419 · 4657 · 149394995916071445497<21> · 1029117451889188198907257077051657562342164186763426363823483311211748925087377127130025159687821783849827109878279047192103969504565570579345811841061026043 <157>
3·10183 -7 =2( 9) 182 3<184> = 41 · 1151 · 54986573 · 11349541095622322797<20> · 101865499526035948449977571645560665716712455648930126519740714243444955908259088083826485783758803608012602912655869192906249511905548209295610839024183 <153>
3·10184 -7 =2( 9) 183 3<185> = 43 · 436988932087<12> · 1596549402916574016883694745270397851459235778990999918228926214112346987261629259980744612543824954064232287399971026376854119964045474194708452102759525007064875700732973 <172>
3·10185 -7 =2( 9) 184 3<186> = 229 · 4679 · 38576168540177<14> · 3156872466842098507811557111<28> · 2299093318610349359260445136357948350931575621414831473913776195298914528490153824765167995755012801405339136452353580268760527144132086709 <139>
3·10186 -7 =2( 9) 185 3<187> = 59 · 18149 · 2801667178749167671375646601437628818322156237771890126084361934308375770808682553364755587224771220527628640883234916991270938960077176591883943738787494478380935215182047663829823 <181>
3·10187 -7 =2( 9) 186 3<188> = 19 · 73 · 1471 · 8087 · 2684475081689940476726062783<28> · 677306589355946429738517894949420454571084119778696051252547689181773844742676115175168648255986594277487583912011488270257527279428358527016188630029 <150>
3·10188 -7 =2( 9) 187 3<189> = 41 · 797 · 16300343009<11> · [563225531107067631860010730837416411659680240167133813031633518755964288240206350514851318183551932448042433036109401457622408019328888441845942073520779158876980505242419301 <174> ] SUBMIT/RESERVE
3·10189 -7 =2( 9) 188 3<190> = 29 · 4139 · 116881 · 184949 · [1156197229316160396762315730175930111081283203778573999467088600070417101990118265692270415871328771104272033008565072588817320507710785715366738566584516960163137868646008187 <175> ] SUBMIT/RESERVE
3·10190 -7 =2( 9) 189 3<191> = 17 · 8677 · 203377421038716281718403622829793436332698343829868008053745873133164756048783464059820078774854415662773118928336576073324339531825176768875119484234860245815509562128412503643845460277 <186>
3·10191 -7 =2( 9) 190 3<192> = 83 · 49033 · 2586047 · 337445182074243533<18> · [84472442371853755570598610642670278068996299561350872616834134266116465590055271388113540351841293220600893956637689213302570537404174146409794186156823212514537 <161> ] SUBMIT/RESERVE
3·10192 -7 =2( 9) 191 3<193> = 12648047 · 135631362211<12> · 2333106755322571<16> · 749554212448962449640869342236440428456031602228118119314157107776761347998286353324804275619138551461703244358095110448988070177519306688883700997316121619799 <159>
3·10193 -7 =2( 9) 192 3<194> = 41 · 364541 · [2007201705907348505949446216394676339059456057704640402789180727839439385887271136352490311739166011705598908510475016995980444770473474126935837321921900985944168614042610617387812980453 <187> ] SUBMIT/RESERVE
3·10194 -7 =2( 9) 193 3<195> = 1971621683<10> · 204338781059399207261<21> · [744640872852904611291755255231823307308468548198988147991712895923330197484924929112939701419349803255698181873510387775922617840793203753606810847110672127348771711 <165> ] SUBMIT/RESERVE
3·10195 -7 =2( 9) 194 3<196> = 73 · 367 · 1013 · 919621 · [120202639669058973888268402090971402561363544532247161895386154452471510366259104194772554978811683839054088817399849252798657635273332700636799211174747179998589745178664132032947751 <183> ] SUBMIT/RESERVE
3·10196 -7 =2( 9) 195 3<197> = 26358873989007219801079<23> · [1138136629527926185494163100278909144228558660475166767396335709851632501516920808886668131717636797745150831060574461448133565709914093606153528200547329751721513549069076367 <175> ] SUBMIT/RESERVE
3·10197 -7 =2( 9) 196 3<198> = 67 · 25681669240470105277<20> · 21451079937695822139779<23> · 1876671100474280819361703093<28> · [4330976988588861597642516703502643572946498675819236690760299247042532595697073682060977818571773462597312462576121850836567441 <127> ] SUBMIT/RESERVE
3·10198 -7 =2( 9) 197 3<199> = 41 · 383 · 10834836709<11> · 134241485743<12> · 197835467070393370849<21> · [663934674734524533577996759184873846633846078885387284258843492877172942404263750983806183796095674083008373566479125782070300190573884171493939694285837 <153> ] SUBMIT/RESERVE
3·10199 -7 =2( 9) 198 3<200> = 23 · 152170079 · 430353680327<12> · 652471876769<12> · 30526487399392689651774263149155078397800384026240819127615231748059649647496871761812017238455192441281727869964822415945908995001717358864083535426067788205120876583 <167>
3·10200 -7 =2( 9) 199 3<201> = 15732113 · 863755526189<12> · 418832359443925351<18> · 44951452064325790309<20> · 1172625691123156425388693186951653980645423936681982313045099032078087799518542737600953819175328745280211938295747161126993519127664881504854511 <145>