Table of contents 目次

  1. About 244...447 244...447 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 244...447 244...447 の形の素数
    1. Last updated 最終更新日
    2. Known (probable) prime numbers 既知の (おそらく) 素数
    3. Range of search 捜索範囲
    4. Prime factors that appear periodically 周期的に現れる素因数
    5. Difficulty of search 捜索難易度
  3. Factor table of 244...447 244...447 の素因数分解表
    1. Last updated 最終更新日
    2. Range of factorization 分解範囲
    3. Terms that have not been factored yet まだ分解されていない項
    4. Factor table 素因数分解表
  4. Related links 関連リンク

1. About 244...447 244...447 について

1.1. Classification 分類

Quasi-repdigit of the form ABB...BBC ABB...BBC の形のクワージレプディジット (Quasi-repdigit)

1.2. Sequence 数列

24w7 = { 27, 247, 2447, 24447, 244447, 2444447, 24444447, 244444447, 2444444447, 24444444447, … }

1.3. General term 一般項

22×10n+239 (1≤n)

2. Prime numbers of the form 244...447 244...447 の形の素数

2.1. Last updated 最終更新日

March 17, 2015 2015 年 3 月 17 日

2.2. Known (probable) prime numbers 既知の (おそらく) 素数

  1. 22×103+239 = 2447 is prime. は素数です。
  2. 22×109+239 = 2444444447<10> is prime. は素数です。
  3. 22×1015+239 = 2(4)147<16> is prime. は素数です。
  4. 22×1021+239 = 2(4)207<22> is prime. は素数です。
  5. 22×1027+239 = 2(4)267<28> is prime. は素数です。
  6. 22×1087+239 = 2(4)867<88> is prime. は素数です。
  7. 22×10180+239 = 2(4)1797<181> is prime. は素数です。 (Makoto Kamada / PPSIQS / October 9, 2004 2004 年 10 月 9 日)
  8. 22×101941+239 = 2(4)19407<1942> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / October 9, 2004 2004 年 10 月 9 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 12, 2006 2006 年 6 月 12 日)
  9. 22×103960+239 = 2(4)39597<3961> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / October 9, 2004 2004 年 10 月 9 日) (certified by: (証明: Ray Chandler / 4.0.2 - LX64 / May 12, 2013 2013 年 5 月 12 日)
  10. 22×104995+239 = 2(4)49947<4996> is PRP. はおそらく素数です。 (Makoto Kamada / October 9, 2004 2004 年 10 月 9 日)
  11. 22×108577+239 = 2(4)85767<8578> is PRP. はおそらく素数です。 (Makoto Kamada / October 9, 2004 2004 年 10 月 9 日)
  12. 22×1023481+239 = 2(4)234807<23482> is PRP. はおそらく素数です。 (Erik Branger / PFGW / April 29, 2010 2010 年 4 月 29 日)
  13. 22×1027855+239 = 2(4)278547<27856> is PRP. はおそらく素数です。 (Erik Branger / PFGW / April 29, 2010 2010 年 4 月 29 日)
  14. 22×1080595+239 = 2(4)805947<80596> is PRP. はおそらく素数です。 (Bob Price / PFGW / March 16, 2015 2015 年 3 月 16 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了
  2. n≤50000 / Completed 終了 / Erik Branger / May 1, 2013 2013 年 5 月 1 日
  3. n≤100000 / Completed 終了 / Bob Price / March 16, 2015 2015 年 3 月 16 日

2.4. Prime factors that appear periodically 周期的に現れる素因数

  1. 22×103k+1+239 = 3×(22×101+239×3+22×10×103-19×3×k-1Σm=0103m)
  2. 22×106k+2+239 = 13×(22×102+239×13+22×102×106-19×13×k-1Σm=0106m)
  3. 22×106k+5+239 = 7×(22×105+239×7+22×105×106-19×7×k-1Σm=0106m)
  4. 22×1016k+6+239 = 17×(22×106+239×17+22×106×1016-19×17×k-1Σm=01016m)
  5. 22×1018k+2+239 = 19×(22×102+239×19+22×102×1018-19×19×k-1Σm=01018m)
  6. 22×1021k+19+239 = 43×(22×1019+239×43+22×1019×1021-19×43×k-1Σm=01021m)
  7. 22×1028k+4+239 = 29×(22×104+239×29+22×104×1028-19×29×k-1Σm=01028m)
  8. 22×1028k+4+239 = 281×(22×104+239×281+22×104×1028-19×281×k-1Σm=01028m)
  9. 22×1034k+22+239 = 103×(22×1022+239×103+22×1022×1034-19×103×k-1Σm=01034m)
  10. 22×1041k+32+239 = 83×(22×1032+239×83+22×1032×1041-19×83×k-1Σm=01041m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 13.60%. 捜索難易度 (周期的に現れる素因数で割り切れない項の割合) は 13.60% です。

3. Factor table of 244...447 244...447 の素因数分解表

3.1. Last updated 最終更新日

March 29, 2016 2016 年 3 月 29 日

3.2. Range of factorization 分解範囲

3.3. Terms that have not been factored yet まだ分解されていない項

n=189, 193, 196, 198, 200, 201, 203, 209, 211, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 228, 229, 231, 232, 234, 236, 237, 239, 240, 241, 245, 247, 248, 249, 251, 253, 254, 255, 256, 259, 260, 261, 262, 263, 265, 266, 267, 269, 270, 271, 272, 274, 275, 277, 281, 282, 283, 285, 287, 288, 289, 291, 296, 297, 298, 299, 300 (66/300)

3.4. Factor table 素因数分解表

22×101+239 = 27 = 33
22×102+239 = 247 = 13 × 19
22×103+239 = 2447 = definitely prime number 素数
22×104+239 = 24447 = 3 × 29 × 281
22×105+239 = 244447 = 7 × 47 × 743
22×106+239 = 2444447 = 17 × 143791
22×107+239 = 24444447 = 3 × 2357 × 3457
22×108+239 = 244444447 = 13 × 157 × 229 × 523
22×109+239 = 2444444447<10> = definitely prime number 素数
22×1010+239 = 24444444447<11> = 32 × 2716049383<10>
22×1011+239 = 244444444447<12> = 7 × 2011 × 17364811
22×1012+239 = 2444444444447<13> = 374893 × 6520379
22×1013+239 = 24444444444447<14> = 3 × 379 × 21499071631<11>
22×1014+239 = 244444444444447<15> = 13 × 1579 × 11908434961<11>
22×1015+239 = 2444444444444447<16> = definitely prime number 素数
22×1016+239 = 24444444444444447<17> = 3 × 1217 × 6695273745397<13>
22×1017+239 = 244444444444444447<18> = 7 × 587 × 242173 × 245650871
22×1018+239 = 2444444444444444447<19> = 11847467 × 206326334941<12>
22×1019+239 = 24444444444444444447<20> = 32 × 43 × 27791 × 2272819946491<13>
22×1020+239 = 244444444444444444447<21> = 13 × 192 × 181 × 192323 × 1496303933<10>
22×1021+239 = 2444444444444444444447<22> = definitely prime number 素数
22×1022+239 = 24444444444444444444447<23> = 3 × 17 × 103 × 2239 × 6733 × 308681116577<12>
22×1023+239 = 244444444444444444444447<24> = 7 × 899939 × 38803335471220739<17>
22×1024+239 = 2444444444444444444444447<25> = 107 × 257 × 88892121329664513053<20>
22×1025+239 = 24444444444444444444444447<26> = 3 × 283 × 28792042926318544693103<23>
22×1026+239 = 244444444444444444444444447<27> = 132 × 3229290887<10> × 447905401416449<15>
22×1027+239 = 2444444444444444444444444447<28> = definitely prime number 素数
22×1028+239 = 24444444444444444444444444447<29> = 33 × 31177 × 142231 × 3503483 × 58275741241<11>
22×1029+239 = 244444444444444444444444444447<30> = 7 × 701 × 3069175309<10> × 16230893110417169<17>
22×1030+239 = 2444444444444444444444444444447<31> = 188551829 × 12964310436068188150243<23>
22×1031+239 = 24444444444444444444444444444447<32> = 3 × 769 × 10595771323989789529451428021<29>
22×1032+239 = 244444444444444444444444444444447<33> = 13 × 29 × 83 × 281 × 349 × 119851 × 2977399 × 223228829357<12>
22×1033+239 = 2444444444444444444444444444444447<34> = 163 × 277 × 327463482523<12> × 165329336085555539<18>
22×1034+239 = 24444444444444444444444444444444447<35> = 3 × 7151 × 12147853214183<14> × 93797789372734253<17>
22×1035+239 = 244444444444444444444444444444444447<36> = 72 × 269 × 224733913 × 18530632811<11> × 4453207657609<13>
22×1036+239 = 2444444444444444444444444444444444447<37> = 2039 × 42932468134811<14> × 27923965280553367643<20>
22×1037+239 = 24444444444444444444444444444444444447<38> = 32 × 61 × 44525399716656547257640153815017203<35>
22×1038+239 = 244444444444444444444444444444444444447<39> = 13 × 172 × 19 × 122323 × 46363897 × 18356305309<11> × 32893648471<11>
22×1039+239 = 2444444444444444444444444444444444444447<40> = 563 × 416398237 × 10427084534295115048604434537<29>
22×1040+239 = 24444444444444444444444444444444444444447<41> = 3 × 43 × 1223 × 9084926393<10> × 80936674157<11> × 210715865664341<15>
22×1041+239 = 244444444444444444444444444444444444444447<42> = 7 × 150646543 × 7209341047<10> × 32153436065753108756401<23>
22×1042+239 = 2444444444444444444444444444444444444444447<43> = 7202053 × 339409394022016284029629391014540499<36>
22×1043+239 = 24444444444444444444444444444444444444444447<44> = 3 × 151 × 2145083 × 10272006809<11> × 28898388539<11> × 84743996987203<14>
22×1044+239 = 244444444444444444444444444444444444444444447<45> = 13 × 592 × 5401729044360472111118477105262511754899<40>
22×1045+239 = 2444444444444444444444444444444444444444444447<46> = 44939 × 79367 × 717812988689<12> × 954784785829515576827371<24>
22×1046+239 = 24444444444444444444444444444444444444444444447<47> = 32 × 48073 × 948053 × 8973667 × 6641005967659856762908947121<28>
22×1047+239 = 244444444444444444444444444444444444444444444447<48> = 7 × 21924751 × 1592749441972450251996961558224078377671<40>
22×1048+239 = 2444444444444444444444444444444444444444444444447<49> = 383 × 589921 × 11960587 × 212570047181<12> × 4255327378282868117807<22>
22×1049+239 = 24444444444444444444444444444444444444444444444447<50> = 3 × 839 × 29234497 × 458480303 × 724570498633620791485567010701<30>
22×1050+239 = 244444444444444444444444444444444444444444444444447<51> = 13 × 197 × 10133 × 912839 × 10319017850449035817324042546121174021<38>
22×1051+239 = 2(4)507<52> = 47 × 5233 × 14361877813<11> × 25734457042951<14> × 26890900231261252235419<23>
22×1052+239 = 2(4)517<53> = 3 × 26203 × 170207 × 1826966073888506107150805347787934943566769<43>
22×1053+239 = 2(4)527<54> = 7 × 2939 × 26777 × 5024861 × 88307293433503001744507640821370881087<38>
22×1054+239 = 2(4)537<55> = 17 × 179 × 28631 × 223303 × 1038232890957443<16> × 121018665970223629217532071<27>
22×1055+239 = 2(4)547<56> = 36 × 97 × 15972240917005586886919<23> × 21642880252629861271416319601<29>
22×1056+239 = 2(4)557<57> = 13 × 19 × 103 × 5669 × 417839 × 580096371557<12> × 6992466815097184037953713601241<31>
22×1057+239 = 2(4)567<58> = 26206837 × 13061826191<11> × 239502104657<12> × 29816202494018551862179423613<29>
22×1058+239 = 2(4)577<59> = 3 × 5081 × 29311 × 901070261945457965299<21> × 60718415451808894526402696561<29>
22×1059+239 = 2(4)587<60> = 7 × 1043753 × 2273267599889609759<19> × 14717492815501903620098323954291423<35>
22×1060+239 = 2(4)597<61> = 292 × 281 × 15264209 × 163202739523<12> × 4152179379226535125950262844228037701<37>
22×1061+239 = 2(4)607<62> = 3 × 43 × 274951 × 537127957 × 2510694503<10> × 65496913689433<14> × 7802660168015249659051<22>
22×1062+239 = 2(4)617<63> = 13 × 406483907 × 2527269972086731<16> × 18303823762413173153266507019836966907<38>
22×1063+239 = 2(4)627<64> = 107260091 × 218858558631843866881<21> × 104130625127134801458265142227083757<36>
22×1064+239 = 2(4)637<65> = 32 × 17477 × 155407071163017072879558813452883754804374285215772122373179<60>
22×1065+239 = 2(4)647<66> = 7 × 487 × 1979 × 36233257126558765015123514479690674707551088192587798822877<59>
22×1066+239 = 2(4)657<67> = 1363081 × 2158903 × 2288440657<10> × 681797683527744193<18> × 532390382034364696376292929<27>
22×1067+239 = 2(4)667<68> = 3 × 109 × 193 × 1567 × 5641 × 2858441 × 28860751 × 531145067926808516779775885018130686561801<42>
22×1068+239 = 2(4)677<69> = 13 × 7057 × 1548149 × 5200831017546443<16> × 1052012358974763679<19> × 314564971528245141197539<24>
22×1069+239 = 2(4)687<70> = 22481 × 103152476073610612236786197669<30> × 1054107463984906046364112480988894723<37>
22×1070+239 = 2(4)697<71> = 3 × 17 × 194827 × 2460145833195649035282326839029180382399029772159296723925554511<64>
22×1071+239 = 2(4)707<72> = 7 × 12541 × 263869 × 148071242775771626461<21> × 71267392751842953046430467905239686516309<41>
22×1072+239 = 2(4)717<73> = 127962641 × 19102797702060904201285158255247673767880771110721639798325547567<65>
22×1073+239 = 2(4)727<74> = 32 × 83 × 313 × 476030332862484190849<21> × 219624408568286159266021196758370537134880115973<48>
22×1074+239 = 2(4)737<75> = 13 × 19 × 806233 × 2315247373<10> × 530182327911101043865546866107781641929217115190187360389<57>
22×1075+239 = 2(4)747<76> = 439 × 45779 × 260399 × 1504691009<10> × 106580902503637<15> × 16848020634447721<17> × 172875891314478383414641<24>
22×1076+239 = 2(4)757<77> = 3 × 5333 × 77167 × 2602447 × 7608058138270737834912966406162642983250675722020117533038497<61>
22×1077+239 = 2(4)767<78> = 72 × 107 × 156811441 × 297318934623823076144211198658690787785283859751675668432485281469<66>
22×1078+239 = 2(4)777<79> = 389 × 22557811 × 278569533201599596589560883507166191510670864830026000133788260492193<69>
22×1079+239 = 2(4)787<80> = 3 × 16657 × 26489 × 1340039 × 13780949126819037828827215538807071673870489673837586267985955467<65>
22×1080+239 = 2(4)797<81> = 13 × 18803418803418803418803418803418803418803418803418803418803418803418803418803419<80>
22×1081+239 = 2(4)807<82> = 68399 × 378243739 × 67646645403647<14> × 2438087810854979407474703<25> × 572879211601901251127819413747<30>
22×1082+239 = 2(4)817<83> = 33 × 43 × 1291 × 15550837751<11> × 593243849123<12> × 1767806291218188697285044407463899316072270025868252689<55>
22×1083+239 = 2(4)827<84> = 7 × 7723 × 2157517 × 2095761558925902520439560686227178343447113873225880104162590249977811431<73>
22×1084+239 = 2(4)837<85> = 571 × 31729 × 275285341 × 490122446530248943957023658779002623465851143001151803004818200943713<69>
22×1085+239 = 2(4)847<86> = 3 × 113 × 387493 × 5355136160856296579<19> × 144830662364851133717939<24> × 239930565203194500500643558149987081<36>
22×1086+239 = 2(4)857<87> = 13 × 17 × 157 × 360778813 × 3266252771<10> × 39627705871529<14> × 18140656450666801<17> × 8316593973153890446333825967974553<34>
22×1087+239 = 2(4)867<88> = definitely prime number 素数
22×1088+239 = 2(4)877<89> = 3 × 29 × 281 × 273527 × 203809875827297239<18> × 17936147727270231050437264987126606776972489484206253459925617<62>
22×1089+239 = 2(4)887<90> = 7 × 164879129450352186390443979229791453354390383<45> × 211795362075526346678187653710472372077965287<45> (Makoto Kamada / GGNFS-0.54.5b for P45(1648...) x P45(2117...))
22×1090+239 = 2(4)897<91> = 103 × 191 × 71079469 × 335905676215927347758559835204308397<36> × 5204129103654708585545406753630481903733023<43> (Makoto Kamada / GGNFS-0.54.5b for P36 x P43)
22×1091+239 = 2(4)907<92> = 32 × 4967 × 16451 × 33239248748334954811121212080651996603099261064500989280647928662967444384240459499<83>
22×1092+239 = 2(4)917<93> = 13 × 19 × 17509 × 453763537 × 124563924029861910349775932509086106445911468346245433261981764945176011970197<78>
22×1093+239 = 2(4)927<94> = 199 × 10798342117<11> × 923315890279<12> × 1596508071517661499408046160609<31> × 771700148367678425047984932335736258019<39>
22×1094+239 = 2(4)937<95> = 3 × 13408545433<11> × 47407462826656287729435731<26> × 12818303069279498784290701315107928539795926240985532276463<59>
22×1095+239 = 2(4)947<96> = 7 × 1492 × 3067473411058909<16> × 17638405214875401457<20> × 29071635979813777829872890527392120041070135235219180917<56>
22×1096+239 = 2(4)957<97> = 929 × 2631264202846549455806721684009089821791651716301877765817485946657098433201770123191005860543<94>
22×1097+239 = 2(4)967<98> = 3 × 47 × 61 × 857 × 3071659 × 132935213 × 1186114327764083<16> × 3595974744032311<16> × 73714661667936959<17> × 25830945535489836844332557539<29>
22×1098+239 = 2(4)977<99> = 13 × 3007506121<10> × 2667033852802817251920131995196461243727839<43> × 2344238374394885885161290578455254416298971101<46> (Makoto Kamada / GGNFS-0.54.5b for P43 x P46)
22×1099+239 = 2(4)987<100> = 30381719 × 80566188492686355971<20> × 998653919050199146827412204219566670001715608715839839525344466302938003<72>
22×10100+239 = 2(4)997<101> = 32 × 57977 × 313211 × 149570145676760006519748155343124009089735723085539577113062927636778422250303695225274989<90>
22×10101+239 = 2(4)1007<102> = 7 × 569 × 520309 × 201543343 × 867085223828407432063<21> × 674960384536936659492772237687440107142007867614093957839912189<63>
22×10102+239 = 2(4)1017<103> = 17 × 59 × 277 × 10618264544595981314549183771879838048526138753<47> × 828601906275618561461709775254426181373901654948329<51> (Serge Batalov / Msieve-1.36 for P47 x P51 / 22 min on Opteron-2.8GHz; Linux x86_64 / July 9, 2008 2008 年 7 月 9 日)
22×10103+239 = 2(4)1027<104> = 3 × 43 × 131 × 2333 × 193577 × 13665516021204565111685281<26> × 268717541520088824947961269927959<33> × 872225176827859486467165019886327<33> (Makoto Kamada / Msieve 1.36 for P33(2687...) x P33(8722...) / 52 seconds on Pentium 4 3.06GHz, Windows XP and Cygwin / July 9, 2008 2008 年 7 月 9 日)
22×10104+239 = 2(4)1037<105> = 133 × 167 × 227 × 7808204801<10> × 11048650854030818839<20> × 34021020800767482367872204416117855571356154056484509112723293516801<68>
22×10105+239 = 2(4)1047<106> = 46769521747639502141065669<26> × 52265756695872513411378515678589143684351235310758798527224369720260132932431763<80>
22×10106+239 = 2(4)1057<107> = 3 × 9689 × 11057 × 76057605962995960555310008760449884210263684145227585862329369951089334560116243070761869395019213<98>
22×10107+239 = 2(4)1067<108> = 7 × 1087 × 381591330607017206412657428815125306888619<42> × 84188755147859735744695342070485785175230396419321883226185157<62> (Serge Batalov / Msieve-1.36 for P42 x P62 / 41 min on Opteron-2.8GHz; Linux x86_64 / July 9, 2008 2008 年 7 月 9 日)
22×10108+239 = 2(4)1077<109> = 443 × 7529 × 769844223455726196788224292250471499171<39> × 951998562560586340256760402450547611450431456341933895606371031<63> (Serge Batalov / Msieve-1.36 for P39 x P63 / 42 minutes on Opteron-2.8GHz; Linux x86_64 / July 9, 2008 2008 年 7 月 9 日)
22×10109+239 = 2(4)1087<110> = 33 × 113608441459662824962269148437092967080552227087<48> × 7969036302290367567268621003851406845020368538649090611909603<61> (Serge Batalov / Msieve 1.36 for P48 x P61 / 1.00 hours on Opteron-2.8GHz; Linux x86_64 / July 10, 2008 2008 年 7 月 10 日)
22×10110+239 = 2(4)1097<111> = 13 × 19 × 45763 × 3465941099<10> × 6239467878060538658162141620504756949518077353179951391464535757823997435475484489368107429273<94>
22×10111+239 = 2(4)1107<112> = 3557 × 149007630641314672182841<24> × 4611984054679255355233746536283220444674047797428181629566853987211715345327594630731<85>
22×10112+239 = 2(4)1117<113> = 3 × 236919800068739<15> × 34392010063253792078205982507516666469260737227186728723764580260515561238953303962538111998521191<98>
22×10113+239 = 2(4)1127<114> = 7 × 108271571 × 322528200136995524290680467919274216820227305288060525462594746322050879218522052484441374134311165768851<105>
22×10114+239 = 2(4)1137<115> = 83 × 163 × 78191 × 3416683 × 33319373 × 4616751856764010560641603977181<31> × 4396627454638834962965514259782807864624263415930800244963587<61> (Sinkiti Sibata / Msieve v. 1.36 for P31 x P61 / 3.66 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / July 9, 2008 2008 年 7 月 9 日)
22×10115+239 = 2(4)1147<116> = 3 × 49991 × 4661063579273<13> × 98836609636823<14> × 353805211642100192879796743977420536496984263893253873605426737733846135287979687341<84>
22×10116+239 = 2(4)1157<117> = 13 × 29 × 281 × 1249 × 13127 × 278489 × 5066433148979327314463<22> × 99745707556106066147658453173646360368267263279361834037369015612756417209471<77>
22×10117+239 = 2(4)1167<118> = 911 × 954962039576383<15> × 153350347540615171531355729586920964045930299<45> × 18322761197418823300515221966963200845626965065189219581<56> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 snfs for P45 x P56 / 2.93 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / July 10, 2008 2008 年 7 月 10 日)
22×10118+239 = 2(4)1177<119> = 32 × 17 × 151 × 23549 × 12484115843<11> × 8189904828434741<16> × 34335021462117365417<20> × 2125479414153033633621633514867<31> × 6021552155789139413364130881246593<34> (Makoto Kamada / GMP-ECM 6.2 B1=250000, sigma=697105309 for P31 x P34 / July 2, 2008 2008 年 7 月 2 日)
22×10119+239 = 2(4)1187<120> = 72 × 6841 × 2408657 × 10041935068223963639989<23> × 30148945901898927162352706417112629383674510712428728241264827314332318118232022479771<86>
22×10120+239 = 2(4)1197<121> = 1319 × 1853255833543930587145143627327099654620503748631117850223233089040518911633392300564400640215651587903293741049616713<118>
22×10121+239 = 2(4)1207<122> = 3 × 2664153049273<13> × 96142154551769<14> × 2339695940797013917<19> × 1163017618481092932615047<25> × 11690690962834769562455754284153470860939042354054223<53>
22×10122+239 = 2(4)1217<123> = 13 × 6121 × 257451703 × 1913707933<10> × 6235094117316947525669978871745262205804845131339906616521244428158263819044714351845407670830063161<100>
22×10123+239 = 2(4)1227<124> = 22142383 × 4261412657<10> × 26763002716631911281029424155030335139<38> × 967982226653429397489275031441447420090456022581392764391905774301483<69> (Serge Batalov / Msieve-1.36 for P38 x P69 / 1.20 hours on Opteron-2.8GHz; Linux x86_64 / July 9, 2008 2008 年 7 月 9 日)
22×10124+239 = 2(4)1237<125> = 3 × 43 × 103 × 31127363639203918155230106265371550433065849027<47> × 59103186631439869309748970750979721507029739430928737715066147860616020803<74> (Serge Batalov / Msieve-1.36 for P47 x P74 / 49min on Opteron-2.8GHz; Linux x86_64 / July 9, 2008 2008 年 7 月 9 日)
22×10125+239 = 2(4)1247<126> = 7 × 221980461661184390672131213<27> × 157314002589720532603282560613947125229637324639240433975103060803282447026889398737354430629391117<99>
22×10126+239 = 2(4)1257<127> = 499 × 1103 × 87797 × 448607 × 6732252439515400559819<22> × 5244805083985130173131426609173<31> × 3193512685867020820044526963651820924786832284035313015287<58> (Sinkiti Sibata / Msieve v. 1.36 for P31 x P58 / 1.66 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / July 9, 2008 2008 年 7 月 9 日)
22×10127+239 = 2(4)1267<128> = 32 × 1055851411540761761126901338111649728911<40> × 2572378417103811115329524052621719508567986338053396769025584246379410302932317285466153<88> (Serge Batalov / Msieve-1.36 for P40 x P88 / 1.50 hours on Opteron-2.8GHz; Linux x86_64 / July 9, 2008 2008 年 7 月 9 日)
22×10128+239 = 2(4)1277<129> = 13 × 19 × 8194776089<10> × 3934292331971<13> × 668426865130797987405649315345219<33> × 1388343975982515290269796897309261<34> × 33077183561244911430284006767620500381<38> (Serge Batalov / Msieve 1.36 for P33 x P34 x P38 / 2.00 hours on Opteron-2.8GHz; Linux x86_64 / July 10, 2008 2008 年 7 月 10 日)
22×10129+239 = 2(4)1287<130> = 767747 × 9294347693<10> × 145463583266265491036564533866890587<36> × 2354988803953860722933036576440462288212379685460602193096133727602333545086411<79> (Robert Backstrom / GMP-ECM 6.2.1 B1=1400000, sigma=3304658584 for P36 x P79 / July 9, 2008 2008 年 7 月 9 日)
22×10130+239 = 2(4)1297<131> = 3 × 107 × 1801 × 2063 × 6917 × 2927360538429619027<19> × 1012204370959080121500134584543329507268243859522341941215407367707505176942939739699285504153626871<100>
22×10131+239 = 2(4)1307<132> = 7 × 233 × 674318596793<12> × 127599449770529340523<21> × 1485468538436582264497629280992342831383<40> × 1172597093940178493433708438105100250038657021267386646301<58> (Serge Batalov / Msieve 1.36 for P40 x P58 / 2.00 hours on Opteron-2.8GHz; Linux x86_64 / July 10, 2008 2008 年 7 月 10 日)
22×10132+239 = 2(4)1317<133> = 2687 × 778785229 × 31870902618307355072948857<26> × 1066310319098017272671211681952031856865065671<46> × 34372951380569981263498111038130737929995501699787<50> (Serge Batalov / Msieve 1.36 for P26 x P46 x P50 / 2.50 hours on Opteron-2.8GHz; Linux x86_64 / July 10, 2008 2008 年 7 月 10 日)
22×10133+239 = 2(4)1327<134> = 3 × 3611555331037538552357<22> × 2256132718810464264200619767995180052866650069000416313044098384249881331501362750024152231142853562612316453457<112>
22×10134+239 = 2(4)1337<135> = 13 × 17 × 8171 × 3865943 × 1273577761<10> × 927635160731<12> × 3922695262964501<16> × 376420044120693463721<21> × 20072305577929007542286878651593589570978107847404540425698990729<65>
22×10135+239 = 2(4)1347<136> = 521510884511581<15> × 7749840687559835663<19> × 604817041472739958778986033717154240316212327170610228546987201938156490724454843930483245899210032549<102>
22×10136+239 = 2(4)1357<137> = 34 × 17597 × 474430838713204111<18> × 160942727758616147304759991172660468836593226620551349083<57> × 224601291731175620982413630782755053499706451971227086767<57> (Serge Batalov / Msieve 1.36 for P57(1609...) x P57(2246...) / 4 hours on Opteron-2.8GHz; Linux x86_64 / July 10, 2008 2008 年 7 月 10 日)
22×10137+239 = 2(4)1367<138> = 7 × 1741 × 6477307 × 56495077137950327<17> × 5838733377978851433090143474291042027<37> × 9387709216450097303503200248806037900230421287622289557752517186938865827<73> (Serge Batalov / Msieve 1.36 for P37 x P73 / 4.00 hours on Opteron-2.8GHz; Linux x86_64 / July 10, 2008 2008 年 7 月 10 日)
22×10138+239 = 2(4)1377<139> = 2799078671<10> × 155810637693047503621475661225318370708471397541118401055253<60> × 5604901198936834141789322417044567348370536055675412409260801606914669<70> (Serge Batalov / Msieve 1.36 for P60 x P70 / 5.80 hours on Opteron-2.8GHz; Linux x86_64 / July 10, 2008 2008 年 7 月 10 日)
22×10139+239 = 2(4)1387<140> = 3 × 4349 × 384822306832803106175504740480258261<36> × 29820580306445179468434784370467918075513<41> × 163265032757307485732791583648752186409635917475529565664157<60> (Robert Backstrom / GMP-ECM 6.2.1 B1=1158000, sigma=2850817191 for P36, GGNFS-0.77.1-20051202-athlon snfs for P41 x P60 / 3.87 hours on Cygwin on AMD 64 X2 6000+ / July 10, 2008 2008 年 7 月 10 日)
22×10140+239 = 2(4)1397<141> = 13 × 4931 × 185599 × 489682697282794027121192851<27> × 41957676090985293373541212235703332957326015093281437003072973517190792976741712466470653972751492069901<104>
22×10141+239 = 2(4)1407<142> = 773 × 32993 × 320867 × 6647461757<10> × 44936368171834209127358685470592037604549261388531444976170158565433360478942479229936378843856324233561010316370685317<119>
22×10142+239 = 2(4)1417<143> = 3 × 9936191 × 820047455624408603673998230121396433316161912361401682812674207666514074472617137507536655459637213913072740665728763481715291921033739<135>
22×10143+239 = 2(4)1427<144> = 7 × 47 × 22277 × 7533054917<10> × 24899585554378077503177286185969857<35> × 177813330540874967071390044687145423961622216372486528405096995740758978152899220369615973311<93> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P35 x P93 / 17.00 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / July 10, 2008 2008 年 7 月 10 日)
22×10144+239 = 2(4)1437<145> = 29 × 281 × 6690491558713094261<19> × 24491557737939074393638448434527023<35> × 1830633552595663753669826211681350715915526535694694172275334022433701837826737468955001<88> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P35 x P88 / 13.14 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / July 10, 2008 2008 年 7 月 10 日)
22×10145+239 = 2(4)1447<146> = 32 × 43 × 10671352823<11> × 26172017367152437248707175326456702997166050893<47> × 226158298190510848206744669030862864131241436076272580498188671436573372939791504234879<87> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P47 x P87 / 15.40 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / July 10, 2008 2008 年 7 月 10 日)
22×10146+239 = 2(4)1457<147> = 13 × 19 × 691 × 827 × 225508344619<12> × 877528400546131797964133967369485080367167411<45> × 8751366321326903185967256414898843569806199348466925509478330018011501491730031177<82> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P45 x P82 / 22.11 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / July 11, 2008 2008 年 7 月 11 日)
22×10147+239 = 2(4)1467<148> = 65203 × 128552809986493<15> × 1719658046526775063872329620833713151617719446440944978655437<61> × 169585580715031070644678516951803468114192521983834826364569163297389<69> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P61 x P69 / 26.74 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / July 11, 2008 2008 年 7 月 11 日)
22×10148+239 = 2(4)1477<149> = 3 × 197 × 349 × 3391 × 1066781793815242607<19> × 32761507591849376690982616501691866255884031809751048485711641545453095617982528994970611198337567827674050835631040212309<122>
22×10149+239 = 2(4)1487<150> = 7 × 811 × 5849 × 33289 × 221145907423479387891021473166432244805040939309593357541261382664843178707973607898595912685552886225390644928996119120591367813457434651<138>
22×10150+239 = 2(4)1497<151> = 17 × 144950542221999492574472267<27> × 991999391440559448512413856936297787970201454642554506205558738505636188596902879615219728834183055968841546077320502684973<123>
22×10151+239 = 2(4)1507<152> = 3 × 97 × 8834843 × 18558168955073395708146667411<29> × 70985983835086576997852624750687510213827313422930409<53> × 7217397353726318978026298518599642790594988964775374257181581<61> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 gnfs for P53 x P61 / 59.21 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / July 14, 2008 2008 年 7 月 14 日)
22×10152+239 = 2(4)1517<153> = 13 × 150329 × 769837 × 87625711531<11> × 769556122625057200022794067<27> × 10813062888571622922756770354132923<35> × 222830526301659720606359045665497825172567913566370741154408463204093<69> (Serge Batalov / Msieve-1.36 gnfs for P35 x P69 / 4.20 hours on Opteron-2.8GHz; Linux x86_64 / July 9, 2008 2008 年 7 月 9 日)
22×10153+239 = 2(4)1527<154> = 56481795945430483380410900923<29> × 58070127730633005462504324727<29> × 745279014540102949022878635907058589821872804105863051589829523214608979330997468189508441637307<96>
22×10154+239 = 2(4)1537<155> = 32 × 1613 × 6144493 × 85808033 × 26756289861065329<17> × 1798409594124660216759258210120687655281031358400703839301<58> × 66370454423809885762078346386195882275783383739027815254557491<62> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona gnfs for P58 x P62 / 70.89 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / July 13, 2008 2008 年 7 月 13 日)
22×10155+239 = 2(4)1547<156> = 7 × 83 × 4197485769504263<16> × 100233941058044038717631765525788192419333956232823916502744651014664325221677311723592706008392903375311552398829205471124944463472473749<138>
22×10156+239 = 2(4)1557<157> = 4547 × 10601 × 817603 × 2219635954465259223327708947<28> × 140350244666350609226894618859195516341027638500563633<54> × 199099872181567014671579008715002480094143366187033872354713317<63> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp gnfs, Msieve 1.36 for P54 x P63 / 42.90 hours on Cygwin on AMD 64 3200+ / July 15, 2008 2008 年 7 月 15 日)
22×10157+239 = 2(4)1567<158> = 3 × 61 × 16281316836123124752133540501<29> × 8204262621657606932107392435599837200715023014565960185279419103195264347791513436894798532631118767565774169679945518590637109<127>
22×10158+239 = 2(4)1577<159> = 13 × 103 × 100591 × 14065771 × 77006431 × 41970499708599475548745693906469796007<38> × 39921402516784417137477507774986630829373202203626798195388657530740030186361497142025588004796529<98> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=4012819776 for P38 x P98 / July 11, 2008 2008 年 7 月 11 日)
22×10159+239 = 2(4)1587<160> = 977 × 1878199 × 106656572640070259039999<24> × 12489825736914381176801370209778058360515231280679425880328031261512409364144378481895783058882902893586701444282840163049928311<128>
22×10160+239 = 2(4)1597<161> = 3 × 59 × 1185889 × 111246536441<12> × 18275254618976078978614739674353667489<38> × 57281308395505724725642726213432671439294032138257996320630107178666862119375122137370004294231648428551<104> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3597465798 for P38 x P104 / July 11, 2008 2008 年 7 月 11 日)
22×10161+239 = 2(4)1607<162> = 72 × 73795848330403<14> × 107546926227583<15> × 1502437621398893305826089711439184886680078009309919<52> × 418367277957308925333921233455513317862150641697102827631297773846327424699635013<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.36 for P52 x P81 / 47.99 hours on Cygwin on AMD 64 3400+ / July 15, 2008 2008 年 7 月 15 日)
22×10162+239 = 2(4)1617<163> = 1978727 × 1171413239<10> × 1087986601832676187<19> × 1030690545220291183793531315683239605395413174248632823<55> × 940442666446536063195756357805894289825335687502835965056411741932351986299<75> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs for P55 x P75 / 95.03 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / July 27, 2008 2008 年 7 月 27 日)
22×10163+239 = 2(4)1627<164> = 33 × 443567 × 2488363 × 18057001737479<14> × 73151581097461<14> × 9341132069122380143<19> × 249102491687358608662848197534804232352965847<45> × 266868000887712185768043059435968943896537652150789168406059<60> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 gnfs, for P45 x P60 / 13.82 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / July 11, 2008 2008 年 7 月 11 日)
22×10164+239 = 2(4)1637<165> = 13 × 19 × 157 × 877 × 370824437303<12> × 3897947297568115721<19> × 1995019063063025398231422514593900200743<40> × 2492485343226881663435258057593521762659123549921057652169671101365172576804392184453401<88> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3167058222 for P40 x P88 / July 11, 2008 2008 年 7 月 11 日)
22×10165+239 = 2(4)1647<166> = 3630210973012969<16> × 184423336707533618359111<24> × 519065104826878486825033434428939<33> × 13564038936664591900573721755613575846723<41> × 518586933045876452658110256298142053169804574677366689<54> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=226623195 for P33, pol51+Msieve 1.36 gnfs for P41 x P54 / 1.70 hours on Opteron-2.8GHz; Linux x86_64 / July 11, 2008 2008 年 7 月 11 日)
22×10166+239 = 2(4)1657<167> = 3 × 17 × 43 × 283 × 4703080575754659158607561533<28> × 8374766069000778361294252005547473440499393911476092766234684664404648236471570509512957247387318061240884733706764828941029958093761<133>
22×10167+239 = 2(4)1667<168> = 7 × 9603193 × 154772603 × 61131652319577338269<20> × 384331740817903149442071297309946974787467939565910479189911419019920853502296437061681402032977511236749847189035472692442719845471<132>
22×10168+239 = 2(4)1677<169> = 4543813 × 1878087349<10> × 157077838092449523332749097610339671<36> × 12314963809991883286233006440538730997310281149<47> × 148079820454272076138749463653539263120184911826609262340495505792576389<72> (Robert Backstrom / GMP-ECM 6.2.1 B1=624000, sigma=472445585 for P36, GGNFS-0.77.1-20051202-athlon gnfs, Msieve 1.36 for P47 x P72 / 51.39 hours on Cygwin on AMD 64 3200+ / July 16, 2008 2008 年 7 月 16 日)
22×10169+239 = 2(4)1687<170> = 3 × 508951 × 5476421 × 43209020731<11> × 12949020669240185407690493<26> × 5224861342729530411824877306071494409155702531417728581321227880594650089363191230493064860889494411419271907879542997593<121>
22×10170+239 = 2(4)1697<171> = 13 × 30269 × 1305013 × 15705883 × 576536873321293<15> × 4800627597251347<16> × 10950562895921486663683452122543943680151906087769502884108136745120232328458492769713361739979289580269328717213128369639<122>
22×10171+239 = 2(4)1707<172> = 277 × 4433581 × 190700753733277<15> × 976818085474159<15> × 10685126144085653197582273989428205530277396278740375668446637774397363963796968280462027827249640866388014497032265740920592317522517<134>
22×10172+239 = 2(4)1717<173> = 32 × 29 × 281 × 44693696266745446969<20> × 2549704685907509370463<22> × 27967758598179240323264057652458400413978392639<47> × 104577806027991375625889373792165848207081915249081381035000999574807400010045699<81> (Sinkiti Sibata / Msieve 1.40 snfs for P47 x P81 / March 8, 2010 2010 年 3 月 8 日)
22×10173+239 = 2(4)1727<174> = 7 × 26557 × 624738918926696617026480583427783554414155170496779<51> × 2104769569075983439269108367771371408243333338166694269946412434388897100049518126394608775065678536993872431454145207<118> (Dmitry Domanov / GGNFS/msieve snfs for P51 x P118 / 94.38 hours / December 18, 2009 2009 年 12 月 18 日)
22×10174+239 = 2(4)1737<175> = 947 × 13793496764933613173998444708639348503342167<44> × 110540140507371818048930699460533646011671649<45> × 1692917532546119710378264581159890068911580941102272929764210993817970269701152940547<85> (Robert Backstrom / GMP-ECM 6.2.1 B1=4606000, sigma=970024370 for P44, GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.36 for P45 x P85 / 48.99 hours on Athlon 64 X2 6000+ / August 22, 2008 2008 年 8 月 22 日)
22×10175+239 = 2(4)1747<176> = 3 × 109 × 87359443 × 30652695389564890841853593<26> × 27916045207768849165975948945863215949198646180664344879575713613815340450059960624602119609926083039703917841579003481178577525941052065739<140>
22×10176+239 = 2(4)1757<177> = 13 × 1109 × 2083 × 12637 × 2201791629722900115084517<25> × 98202646709372914952284004731<29> × 263918040926244833932442223532777<33> × 11287649866483430593118539466784682520308464734220950406084876622638519492533399<80> (Serge Batalov / Msieve 1.36 gnfs for P33 x P80 / 15.00 hours on Opteron-2.2GHz; Linux x86_64 / July 15, 2008 2008 年 7 月 15 日)
22×10177+239 = 2(4)1767<178> = 593 × 9868967 × 3130315679<10> × 768567622797661091189<21> × 173613526857259157898969410352389509386430313271051046184749107136843945777383650367971752008103691012927967518344762076752191568153403627<138>
22×10178+239 = 2(4)1777<179> = 3 × 9511 × 7058628672138574632984994873<28> × 407818136912747014681334981443<30> × 75160945043175857866901963484673054341461063508311<50> × 3959621107875479961537988501024588458702472685250586541345053347871<67> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=430382 for P30, pol51+Msieve 1.36 gnfs for P50 x P67 / 17.00 hours on Opteron-2.8GHz; Linux x86_64 / July 12, 2008 2008 年 7 月 12 日)
22×10179+239 = 2(4)1787<180> = 7 × 9811 × 41179 × 349759 × 5073160483<10> × 247602662246059366508164925346498863298457<42> × 196738905205468855813624539871972321101788083183648699443213584629087351285163889112862059428260985455190747938821<114> (Dmitry Domanov / Msieve 1.50 snfs for P42 x P114 / May 20, 2013 2013 年 5 月 20 日)
22×10180+239 = 2(4)1797<181> = definitely prime number 素数
22×10181+239 = 2(4)1807<182> = 32 × 1858573 × 19707749 × 23468960719226551<17> × 785195612198167577972729<24> × 17785632801658181817419234383456954573<38> × 828838352497750545369169782925386115193<39> × 272966991471668803728822291820565994032634354475909<51> (Serge Batalov / GMP-ECM 6.2.1 B1=11000000, sigma=1242344107 for P39, Msieve-1.39/QS for P38 x P51 / 0.77 hours / December 9, 2008 2008 年 12 月 9 日)
22×10182+239 = 2(4)1817<183> = 132 × 17 × 19 × 3673990757<10> × 44982980583091433538219963671317681<35> × 77327863248332345626114301120437434763<38> × 350403670508377822985021815952709043625410159334533841827120698248297040897287405805206946065611<96> (Serge Batalov / GMP-ECM 6.2 B1=3000000, sigma=970377937 for P35 / July 11, 2008 2008 年 7 月 11 日) (Ignacio Santos / GMP-ECM 6.3 B1=3000000, sigma=2425072536 for P38 x P96 / July 13, 2011 2011 年 7 月 13 日)
22×10183+239 = 2(4)1827<184> = 107 × 69833 × 122544613669<12> × 2669570946254135604343368832918241651075402476018687919834641956186322455801962280420283134964616916017418962019658088157616970819679526411138151394010103142741224273<166>
22×10184+239 = 2(4)1837<185> = 3 × 8741 × 883727969 × 428463058069<12> × 103877743860680497<18> × 218460649344400193524021<24> × 144099946999744771890872989<27> × 14478093885479986710222592427921863391<38> × 51998985992916577835802224283132907761310866802294639523<56> (Serge Batalov / Msieve v. 1.36 for P27 x P38 x P56 / 2.5 hours on Opteron-2.8GHz; Linux x86_64 / July 10, 2008 2008 年 7 月 10 日)
22×10185+239 = 2(4)1847<186> = 7 × 191 × 1061 × 1913 × 34318699957<11> × 4270547367391<13> × 175924971977510966840247067595429695724452241532105435171464881847<66> × 3493627107144071633071853352966316601457287725309994260064270894707733734943935153351903<88> (Dmitry Domanov / Msieve 1.50 snfs for P66 x P88 / August 12, 2013 2013 年 8 月 12 日)
22×10186+239 = 2(4)1857<187> = 539113 × 25086631755540164279<20> × 83314723134026924024720227<26> × 22324664477631905214930348612756314848637941436444386880985263893619<68> × 97174276574553833926724915569250140017366581891220342088925742957497<68> (Robert Backstrom / Msieve 1.44 gnfs for P68(2232...) x P68(9717...) / May 23, 2012 2012 年 5 月 23 日)
22×10187+239 = 2(4)1867<188> = 3 × 43 × 8609 × 132059731 × 18072992123460676488892269169324885372988318924969<50> × 264188721525790105445261352357554635458898704888161<51> × 34907842870827207098328506292909322120323730516791771559746930434232169213<74> (matsui / Msieve 1.48 snfs for P50 x P51 x P74 / October 23, 2010 2010 年 10 月 23 日)
22×10188+239 = 2(4)1877<189> = 13 × 6189273399288534095811470799393323<34> × 3038065632321280803476378108253243566314611187787592040202073700106715272161599074003370726703208829303229285374974719559646659679887499093314088198875153<154> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1373200339 for P34 x P154 / July 11, 2008 2008 年 7 月 11 日)
22×10189+239 = 2(4)1887<190> = 47 × 673 × 3134039 × 59395355863<11> × [415155087155130635569665237755239818292988007773226810698977764189610049474845456321847338415541323856805629014825619786381491269119892593330566177264436621303112620641<168>] Free to factor
22×10190+239 = 2(4)1897<191> = 33 × 11731008189844231<17> × 109647439924942065555485001670822001095967<42> × 703853983906629398788846783850218685030521755317637767209409128174498576168845084399262752381777888153444601808985530818903634534293<132> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3085433674 for P42 x P132 / June 21, 2013 2013 年 6 月 21 日)
22×10191+239 = 2(4)1907<192> = 7 × 96163291176200475289<20> × 22299958700382149786204092003<29> × 16284287229324626554297251167567189007351975533302036333333004216104763320962870254991596879304770483130467580951018652897222873944190257043963<143>
22×10192+239 = 2(4)1917<193> = 103 × 199 × 1091 × 57328900950613879<17> × 19797658140088379562199<23> × 3911348087270340711987300409919305907096835197<46> × 24623581174713823818990279328066558820004880452453040646765620554030358755308767168991242029741224153<101> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3824859 for P46 x P101 / June 21, 2013 2013 年 6 月 21 日)
22×10193+239 = 2(4)1927<194> = 3 × 151 × 853 × 883 × 2074622894844739<16> × [34532901375296696830449952880510069476914612322303724549062612192997458357353988088560452423453898802116465681057963024476294277970758009154821206878781682898903131057759<170>] Free to factor
22×10194+239 = 2(4)1937<195> = 13 × 338269 × 1134183969957757<16> × 49010723614189683618045629560238194326776633364266905013298690111472427397216961671151604608500843799208073649763500397671933121394741234837653481813794393383498277514689443<173>
22×10195+239 = 2(4)1947<196> = 163 × 39421685286020176622030291<26> × 213144221823434271208809084238966307<36> × 1784776408370790219693552793941553367252865242660235982974711386470861046642725912037082622886790599649727113544193747182804438147037<133> (Ignacio Santos / GMP-ECM 6.3 B1=3000000, sigma=3243762290 for P36 x P133 / October 16, 2010 2010 年 10 月 16 日)
22×10196+239 = 2(4)1957<197> = 3 × 83 × 5305087578004374091<19> × [18504964936539603036179136447081951736257154376533743806967375792094594004455642530714159162632795940016007120728661822663954336200980666272873579605829230246808847899377399333<176>] Free to factor
22×10197+239 = 2(4)1967<198> = 7 × 113 × 695297672042072244900952876381872976120480443321416660609207<60> × 15289769744936237230919203210804611301606749732361166218939120705391<68> × 29069125530481941095166355250055849161785796071989116662232205007841<68> (Wataru Sakai / Msieve for P60 x P68(1528...) x P68(2906...) / 843.82 hours / October 1, 2009 2009 年 10 月 1 日)
22×10198+239 = 2(4)1977<199> = 17 × 790056373279<12> × 1128907190558561861<19> × [161218519972830790758343186946204641556893408349174294893020021916989737610792382410702763318842248300901992208181565222108880638438436422581947957033249404731911737789<168>] Free to factor
22×10199+239 = 2(4)1987<200> = 32 × 619 × 128173 × 742789 × 149620828199987785329497659<27> × 43482312117488028224282836493909<32> × 7084028770911422344248461958410720572198835237947535379552273443567806999719918274887993804124122573096734631865106103730841651<127> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=329097599 for P32 x P127 / October 21, 2008 2008 年 10 月 21 日)
22×10200+239 = 2(4)1997<201> = 13 × 19 × 29 × 181 × 281 × 11702296387<11> × 4465102616530714372076129<25> × [12840968712497450919524752296800378540941132236667548291827633406545096197596703651594870363690753013859548008689664276384395211838449267164143857366931954123<158>] Free to factor
22×10201+239 = 2(4)2007<202> = 7937 × 32723172113<11> × 71024700391<11> × [132513151917055425591773506946109240009647421045497801854744926758570356606079861201437758641912230526716087461966765871635220219345575463262623969626003211472661169788870017657<177>] Free to factor
22×10202+239 = 2(4)2017<203> = 3 × 57899357 × 1783497481<10> × 59915321243806561104403817<26> × 924380389875849630551796484751<30> × 1424702084941307307073141403508167959039841863919396047541613245225136112154095214129671714229010697728436505338313677744319413991<130> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=1683189631 for P30 x P130 / July 10, 2008 2008 年 7 月 10 日)
22×10203+239 = 2(4)2027<204> = 72 × 1571 × 7127 × 5161243 × 37288817 × 28825811450921<14> × 476746906234018668659<21> × [168460781145260058965872978374747987484505224810272234495589311796968555061101747921180637534410357310041163492114899214173847649793500212666699451<147>] Free to factor
22×10204+239 = 2(4)2037<205> = 720023 × 50715854861597509<17> × 1888715261066607592247<22> × 192419819014657626660048413404243<33> × 184193270944572775718293604852340692637144385757769845962737152831321614464484501568395567703368265474703829715890241313565646801<129> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3657586577 for P33 x P129 / July 11, 2008 2008 年 7 月 11 日)
22×10205+239 = 2(4)2047<206> = 3 × 24457891344177158596038382209821843<35> × 333150067333504127041200418927446510324243550214699309048573280958283536566982470734295682777969804513514684898269450709698370283985337599954540181538237184334875077992343<171> (Serge Batalov / GMP-ECM B1=1000000, sigma=1994628425 for P35 x P171 / July 9, 2008 2008 年 7 月 9 日)
22×10206+239 = 2(4)2057<207> = 13 × 631 × 662539 × 2328446353<10> × 19316559477285652472235786720636788484079001641264936231128451886452678735847063647027443066150978990859892021949200849088186454342970444997898290130102701164191580505767320018134920435047<188>
22×10207+239 = 2(4)2067<208> = 16538563 × 234949921 × 2672511229<10> × 235389755315997536398278551257036366901908579348129910711177065818490157953197329900613462940573397321894619547256747842761038995576512335891585942375665330878809300354553018312282041<183>
22×10208+239 = 2(4)2077<209> = 32 × 43 × 8289247 × 469995020213<12> × 13905135538621497534078647<26> × 1165965345665929323025392959358641244574508020473755287555182851277023731906466447625645557222871639734103547541605011595065058299290641823310929871700709059816793<163>
22×10209+239 = 2(4)2087<210> = 7 × 86743 × 616884423557182357022598053879<30> × [652595220686468604854846531476779078239326534361758413208472337192046186838089083437491645550897643197796659247339583213820862166685267354917434862948399256181647880449620793<174>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=980036650 for P30 / April 10, 2013 2013 年 4 月 10 日) Free to factor
22×10210+239 = 2(4)2097<211> = 787 × 2682096709<10> × 10139690211074731<17> × 132491741936478659147097568006441<33> × 862020331495079583135408796939549608208187904182138659838824463103361760007183618552863650258937763026680081423707432207357364112222059470099215995979<150> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=911299686 for P33 x P150 / April 6, 2013 2013 年 4 月 6 日)
22×10211+239 = 2(4)2107<212> = 3 × 739 × 367309 × 146610975311<12> × 12565306613742542713159<23> × [16294586163560915672419621247627212466174133686789576106123522212002253928161576012154985709214044185729808288360149273285608510517470247338139858073767123846488443905451<170>] Free to factor
22×10212+239 = 2(4)2117<213> = 13 × 3847 × 113989 × 8282003 × 63815579 × 81131516088436081798525712860729991328508031309126588828153693951815270582078408636248279183675299848755661320528068881934778769577089105523839444636853648630234330051212933231474959832489<188>
22×10213+239 = 2(4)2127<214> = 27701 × 110378310643<12> × 38143350508985068492843858929614211757<38> × [20959559089662334144095322758124437564362175609870989263096375070591879423935602214048996318326745572857907521446817718417395394890901128131492411333104196331797<161>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2646637073 for P38 / April 11, 2013 2013 年 4 月 11 日) Free to factor
22×10214+239 = 2(4)2137<215> = 3 × 17 × 644569 × 2500741 × [297352686201307835357558063734025769290732925860780792771396360591130693707990333324178963080924081152317670403994032983761212123077761551980466819001654097431547857014681641938511301298180501079585993<201>] Free to factor
22×10215+239 = 2(4)2147<216> = 7 × 263 × 1120267969617256919<19> × [118523498972754198988672380006370409219758636069059581000276644559397922614839754608207017593202126037485332601882636565801201366340594294220321475717460824589602991139103416038361368454870552393<195>] Free to factor
22×10216+239 = 2(4)2157<217> = 245755953879231539671<21> × 604511595764758820354300326682085911327<39> × [16453999783563931887904185838407171173221428111662076366983359477482448082066125078909189715824637658329359106272944312039042524060536894521767879715129775591<158>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3307780888 for P39 / April 12, 2013 2013 年 4 月 12 日) Free to factor
22×10217+239 = 2(4)2167<218> = 34 × 61 × 223 × 227 × 150474063137<12> × [649490718496891967642968599209701636486079144333939460273818808164065448313073637905094163859455274959752912503321678092283887893658502976779213590874518650127375807851477787427522029209183763642071<198>] Free to factor
22×10218+239 = 2(4)2177<219> = 13 × 19 × 59 × 46046777619631<14> × [364277177633194323390055182451721375168619254220650776669289129627656725067065242557310983353979539649208709678097941477173023732213619519356397407613077778418620482905317941430350554925468285245945269<201>] Free to factor
22×10219+239 = 2(4)2187<220> = 4275380697718854421<19> × 6605707936633737409148789941080396440521<40> × [86553774415422159998630601907293291667383476625121486260427497084651763453567108936396159378917986094202312632845888726084376583293571937776189957803734264446667<161>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1620135259 for P40 / June 28, 2013 2013 年 6 月 28 日) Free to factor
22×10220+239 = 2(4)2197<221> = 3 × 760262571281<12> × 37381472318713319<17> × [286707401014367784516435033957736557668075500744477760176015628370153639558618796158927989697305053109707544505243246857241243593432003845181772917948909184041243990983794488631240465477531091<192>] Free to factor
22×10221+239 = 2(4)2207<222> = 7 × 141998999 × 1017720431311602191599305017295142101923<40> × [241639737435233960880153372375154889834076765360072272291935711209375482046156018230073402778394601227643972316824929416799065770915646143147400257941542613459197575425505973<174>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3662742991 for P40 / April 16, 2013 2013 年 4 月 16 日) Free to factor
22×10222+239 = 2(4)2217<223> = 367 × [6660611565243717832273690584317287314562518922191946715107478050257341810475325461701483499848622464426279140175597941265516197396306388132001211020284589766878595216469875870420829548894943990311837723281864971238268241<220>] Free to factor
22×10223+239 = 2(4)2227<224> = 3 × 769 × 8266092679378845597916942446213836583887069<43> × 1281835534027185298164222988174354746885516306886562046039498253934417467295027821332120160459500067761036811782912374712706483898499973920385517148249133962060702914268986887609<178> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3993469879 for P43 x P178 / June 26, 2013 2013 年 6 月 26 日)
22×10224+239 = 2(4)2237<225> = 13 × 27527 × 1285481 × 867839870189<12> × 193622472834040589192282021<27> × 81718711866339497807284678785426349<35> × 38698613123631291568155145563162841917672333559030991081134770273718861924037314730232731999526744584956859764876690098733605808020909104377<140> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=418917746 for P35 x P140 / April 10, 2013 2013 年 4 月 10 日)
22×10225+239 = 2(4)2247<226> = 53171 × 18039291927353872529<20> × 133959877048311403439858551<27> × 19024406457449834041512851346249398890409521160683884565511657970900943082219676739642848006825914713067099932382350611440820575999930547390640810867798260388155748638460560083<176>
22×10226+239 = 2(4)2257<227> = 32 × 103 × 34660227293<11> × 3666633039174407573621107<25> × 785044362771625092061608289363<30> × 19507021121005104154972076092633<32> × 1506069285612858083861553033812913008292836648948723844477499<61> × 8996456370242463071695349131012779231082519074692509084032403585391<67> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=1679752494 for P30 / April 6, 2013 2013 年 4 月 6 日) (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3845394295 for P32, Msieve 1.49 gnfs for P61 x P67 / April 13, 2013 2013 年 4 月 13 日)
22×10227+239 = 2(4)2267<228> = 7 × 2341 × 4703 × 82997 × 253203252919101180473<21> × 81663041496466091412967227527<29> × 59109402829730138996953332686827<32> × 20270941104035013663045491349458302822683661683623<50> × 1542474627164374892770407941804744637236092479243228824080698651692046996688094312501<85> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2396722826 for P29 / April 10, 2013 2013 年 4 月 10 日) (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3895543164 for P32 / April 13, 2013 2013 年 4 月 13 日) (Erik Branger / GGNFS, Msieve gnfs for P50 x P85 / June 28, 2013 2013 年 6 月 28 日)
22×10228+239 = 2(4)2277<229> = 29 × 281 × 2069 × 2521 × 161573 × 345614943737606606316651575775431<33> × [1029867175172446797730811548930239921729724760143281838350415585256086607881279730793260744817162178879469446946058004706673579638539727482450031330710717755356356656454587458370469<181>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3259057020 for P33 / April 11, 2013 2013 年 4 月 11 日) Free to factor
22×10229+239 = 2(4)2287<230> = 3 × 43 × 14627 × 288203 × 1042335304541486844767<22> × [43125014552871667193211385497906740139017957813853908664713755121184677190867953721269070171008154691653365348657092052389168013417479140027826647277048526346909429975426610438643853929336158494209<197>] Free to factor
22×10230+239 = 2(4)2297<231> = 13 × 17 × 319955914033156631229465241<27> × 3456987073881726873315446796913107311595281510348313448474684417856678114209634316826337480280842316719582418816808209104283575220002299631120480923079625953459114455759933179319693953797345257105027427<202>
22×10231+239 = 2(4)2307<232> = 2619333098337853488149302391<28> × 1115450310305625852579894672128851<34> × [836641131712649095070174633691707279873343375583010934987105371095114657132527303463137491673181796403624084296861859626765867988563143665293591420007670407125057117488867<171>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=235015927 for P34 / April 7, 2013 2013 年 4 月 7 日) Free to factor
22×10232+239 = 2(4)2317<233> = 3 × 179 × 508987 × 14591321911<11> × [6129210777981867432610880531412163478742137322345642863543861155216534044579058476657037965679050550023358804436906713760731232114478946937297671151469700005844885807976979628232207378300573793060335091183737199283<214>] Free to factor
22×10233+239 = 2(4)2327<234> = 7 × 131 × 1051 × 3082786798004445011<19> × 82274382081540001324932775326455028553080561727978512148526982020749697893219691348411580818004250801157237119962159310645157861578050392211510219863819828265079116088480298221917589778962251341921675970317731<209>
22×10234+239 = 2(4)2337<235> = 2753 × 11274449 × 91520230566682111<17> × 9509804501943180148210986087432511655540323<43> × [90487781146665442090879415395336688418063126553809432939876715975328393332397945517454525705644334300117124532285673022021470750094787398856371858154878059564871867<164>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2287367625 for P43 / June 24, 2013 2013 年 6 月 24 日) Free to factor
22×10235+239 = 2(4)2347<236> = 32 × 47 × 419 × 23369 × 78342463 × 6381885770745025939<19> × 90747038610866174856961<23> × 130078926267140061346074069035049881771113690591015452576638357273883807611825143269321307699312225304686893699551456148181428219120661310894924509457309173119703783395336078487<177>
22×10236+239 = 2(4)2357<237> = 13 × 19 × 107 × 229 × 77880763 × 62386711754219<14> × 49673178860786439391055544614983095779<38> × [167347685788402126206457761040212252069931628888765109455367295698029746447639362989662231622909165557562944598423547727276447622487678820210275329212712648671055432434109<171>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1764853846 for P38 / April 16, 2013 2013 年 4 月 16 日) Free to factor
22×10237+239 = 2(4)2367<238> = 83 × 503 × 5202469299795748159431913<25> × 314992085815408069326309719713<30> × [35729334381401106040497161210702705872074410763330535489708929690892826069149567511635868198856394858903168487190065905868716670191064618179225348544202458924138772737096287848587<179>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3293660699 for P30 / April 11, 2013 2013 年 4 月 11 日) Free to factor
22×10238+239 = 2(4)2377<239> = 3 × 6097057 × 22896244012056686779<20> × 133526230980569614469<21> × 437127195131140577840098531295642893281213612473789712815327916150846757252541134399695247490064533950827647720438466210910123934803533850395673788267329769247343588515272787719081772118926307<192>
22×10239+239 = 2(4)2387<240> = 7 × 1559 × 5867 × 1791762619951<13> × 2785122856553831<16> × [765059299580968460464044429989990003978204720275350975150104590865341657962083627085741097989382030193953611690929340300029102250827974729246828441535295629979718707580150375795394305324345823918100999797<204>] Free to factor
22×10240+239 = 2(4)2397<241> = 277 × 937 × 1154415025587959533<19> × 4974913011552990213072318830022801041<37> × [1639884833502918944354627458161843720269116457938934188373066131142683216017609752029492943817802164805620404827008256301486007378203940686524884058930355558199520685967523055170951<181>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2680348356 for P37 / April 16, 2013 2013 年 4 月 16 日) Free to factor
22×10241+239 = 2(4)2407<242> = 3 × 8753 × 4574987 × 235987712395563346475798291982149<33> × [862229213991549144374429533778155689228759168708919360581473491414615522195920327364287157902528454504036627472311600903206400164160920891204900904508936662571574337851895544365148947445196525145891<198>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1050178161 for P33 / April 11, 2013 2013 年 4 月 11 日) Free to factor
22×10242+239 = 2(4)2417<243> = 13 × 157 × 470453 × 167279620607119581195468792101573549113<39> × 1521871168628728165859121469301246672385303493704842129838518202492572335174270143014000165025358129115163892044721621026355948196586281193095633144527522037079594059952827117659934836046818746803<196> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=20409698 for P39 x P196 / June 25, 2013 2013 年 6 月 25 日)
22×10243+239 = 2(4)2427<244> = 149 × 23629 × 173590363 × 709806299793746942606453<24> × 5634859603916583495313251044705169385233321355037289311963914497677918878781723455014191138061843745639829210912256687490148086106525670953036806241910367199208064098425282216337378828261791328582941182313<205>
22×10244+239 = 2(4)2437<245> = 33 × 673395351864275467776499<24> × 1344455068975823080680062104462839980298693471971714843432575694820318534850984713222317277054306555928867906014655393150085362945554304294667187387056325033920629922038772197232705465044655037269293933084483919246767039<220>
22×10245+239 = 2(4)2447<246> = 72 × 1087591 × [4586891700574273211544811937659196285962098793261558360886009922143121900331050777180933514649826335797572096091353002137610374661671650022181478531206639343928873855893427457685397612132150076232784845541978376971363436732442964696502233<238>] Free to factor
22×10246+239 = 2(4)2457<247> = 17 × 197 × 158794551427134949373<21> × 4596522888596895492646182402830546923114264562838868843934700972754004963096328009191915595017977010270665823697003887705150061448883811379881107944359683743599948189637858174512209940699516118325023002182204378219852652511<223>
22×10247+239 = 2(4)2467<248> = 3 × 97 × 12157 × [6909725039112969701515268152452278690693790729492022455475694838023953064373542499504462787251796002428831166930382604352630530751998253221510112241259456940211060063946992609703584416723255744344947544665326368456125271807382745970585991481<241>] Free to factor
22×10248+239 = 2(4)2477<249> = 13 × 2153647 × 4397779 × 2128790467<10> × 2675126986293269<16> × 1625984040838642594564966030337159653<37> × [214405192838514887507281708034305246952166119706173285137020283369463107567011625850392986001966144928783299410069349460509050301066591392238848196174172570941628981724865877<174>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=4022012745 for P37 / April 11, 2013 2013 年 4 月 11 日) Free to factor
22×10249+239 = 2(4)2487<250> = 1451 × 1723 × 1152060017<10> × [848696433408412235525531742550147621334533088272786390434311396671070165701352866107236966210241123203922268758071259750316844008446407241289178524265798204867584743945004314550481742496358257253521299819413806764840579393836505469367<234>] Free to factor
22×10250+239 = 2(4)2497<251> = 3 × 43 × 2669801718167<13> × 798874847637504863010663611919045360668717<42> × 88844941378032914952751487546643820049950528181838858110051490706917443774485168351134788709752708962536126536621698298725537235792867688086715170687835701077485830149290484830998552208376898237<194> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=262312977 for P42 x P194 / July 5, 2013 2013 年 7 月 5 日)
22×10251+239 = 2(4)2507<252> = 7 × 2980759 × 2991647184586971538865641<25> × [3916019927178618193239448486364239810399752677442160292345492373841110584530556455615622587036331822567466447381828493615032416558964487548925149585157147610341904389956768524594975264277881785435929774011567617637878759<220>] Free to factor
22×10252+239 = 2(4)2517<253> = 1151 × 86939 × 4561594357<10> × 174332238043<12> × 4237440823512311<16> × 7249235235404144084855020906861576732699111599796535721606143700463252054516966874147188327509018593661313747508601596655129428788532832994942327187820044725804832276419920744282250732364238739586173462567843<208>
22×10253+239 = 2(4)2527<254> = 32 × 7883 × 128717 × 36681643 × 7754954834920456468339288017955525969<37> × [9409838583690084745530234935939986669559010513397066061635443057571053877438647301828377859283716589217391040489550250397817061322526644990688916354376666722406955645930646910588041317661225055310859<199>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=167558699 for P37 / March 22, 2016 2016 年 3 月 22 日) Free to factor
22×10254+239 = 2(4)2537<255> = 13 × 19 × 3371 × 1147453 × 20725537614828203<17> × 23051219878244641858467401376577111<35> × [535537444237715810210977329039726899268099647322824083796255280509423758113917849358867162992281581197024151235730443379364777872915662482828974458295128121767362143061410603299911901184726419<192>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=967666690 for P35 / February 26, 2016 2016 年 2 月 26 日) Free to factor
22×10255+239 = 2(4)2547<256> = 3863 × 34630979 × 508957205773309<15> × [35901238161836970601206485256586982541211986859585136166410651965796577984463361813429621125421148015952858782605177955188194889418511013874745032126738892679327143870783657531593419818125745605259320866839514578950588346200472079<230>] Free to factor
22×10256+239 = 2(4)2557<257> = 3 × 29 × 281 × 443437 × 10803319019<11> × [208720674971193950742407970550720187578024551783825393866006302010263334021857313939804230695253652348411522227208747017066771419294307333770652266044539172055009790971854517767989354225466690583772987039469594347752419576727162046597967<237>] Free to factor
22×10257+239 = 2(4)2567<258> = 7 × 4339802573<10> × 8046595284747051242167332325012408032166175435979889363257593266705250334649413306533592083503434274920164815276410252645592095905841779552979825131007156678535070982510088629997370832158110855823172240106167759286370403429621782225860466725641677<247>
22×10258+239 = 2(4)2577<259> = 337 × 982043071 × 85133716757704969799<20> × 17999781738396742040576211892709273<35> × 4820042877772450362297710383024233163877514201208933646266514637872983289766894704612603957460516478971367585287450262698286123598809359635892524011736903642398883473816991743057439491917754943<193> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=79412550 for P35 x P193 / February 26, 2016 2016 年 2 月 26 日)
22×10259+239 = 2(4)2587<260> = 3 × 193 × [42218384187296104394549990404912684705430819420456726156208021492995586259834964498176933410094031855689886777969679524083669161389368643254653617347917866052581078487814239109575897140663980042218384187296104394549990404912684705430819420456726156208021493<257>] Free to factor
22×10260+239 = 2(4)2597<261> = 132 × 103 × 461 × 5342452680857<13> × 468138738471429201249676053742071087384949<42> × [12179797055599129580298590151513020095375386767147168290398076075196563565803090978828090875601277311203162806056069543705518657677032057764665142146584547321435911609204472703620628992064608735698777<200>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1422400949 for P42 / March 22, 2016 2016 年 3 月 22 日) Free to factor
22×10261+239 = 2(4)2607<262> = 2207 × 97649 × 1510219 × 6892489 × [1089667571788592490283828064546797022307905579061745737576121068771824892779944530742863981416799426469728596383822723863065174750577943068065072470667684857340456184677829562560201875887957134433385401395794203882692252481143714824111069819<241>] Free to factor
22×10262+239 = 2(4)2617<263> = 32 × 17 × 40531691 × 320503181 × 728506532969<12> × 2125066354471360807545391<25> × [7944301668251671979035709186884064142996832901844747066243285909199084918897826794961602578269080242350996112947972142087628277841930452501427367476358713008148895284366236919715796366935193955213049223157311<208>] Free to factor
22×10263+239 = 2(4)2627<264> = 7 × 3321343063<10> × 90356936939593<14> × [116360852633596783422546479802699103351598377389538587438025103098103516597882990980806864504898304101397411917769557920332094896329169346112368492265355015855474286354287417421838113295504995969151182537985870046199248643095473992916182919<240>] Free to factor
22×10264+239 = 2(4)2637<265> = 349 × 35839 × 69771971015552235413<20> × 2801030704268198467377013723103583666874533568621544997556201833371418620312339674438724094115475022878364743332895735575153246021706281153762698764520963754555033724528800919074001286377043309498212598651256241227578704730315284179969729<238>
22×10265+239 = 2(4)2647<266> = 3 × 35111 × 3956279 × 141916849501886909<18> × 198634521802150649<18> × [2080846845402329377338135395641134471636624217575693935909970652571500856383553894194905026815008488823523494858721125084101463656468720548319485847253645727934033738883381141337519611707027554967799281689411207028398081<220>] Free to factor
22×10266+239 = 2(4)2657<267> = 13 × 3724537 × 18509778899<11> × 5061322091167<13> × [53888900073509647553310699249716882598395416412120623933133950548194634483717787264167759836169819228580629518622747973356957425876470405319294355703794025926092370707385292742155141307004296484343298392363434845958409982644488933575039<236>] Free to factor
22×10267+239 = 2(4)2667<268> = 58657 × [41673533328408279394521445768526253378871139752194016817164949527668384752790706044367158982635396362658241035928268483632719785267648267801702174411313985448359862325799895058466073008241888341450201074798309569948078565975833139172553053249304336131142820881471<263>] Free to factor
22×10268+239 = 2(4)2677<269> = 3 × 151 × 1667 × 48109 × 11569153 × 42474569 × 1460214883<10> × 131390238383<12> × 3661556412217961<16> × 1949143858690174834892920520494945028209650230854657357564980686649001558818471099714283860939477433070265899635503820098412806014440918009458113637172211809973614601471399573799886370090674214812379143423961<208>
22×10269+239 = 2(4)2687<270> = 7 × 523 × 4232931589<10> × 29995331123684357<17> × 27724552954290414695956344990608494943<38> × [18967975509848952299356220835816215318790772852683797671420322154871039041905904762281411625371079358586009046036178281742535386248664807732680214260330528056986828776788139383891369010886955764801553293<203>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=52773524 for P38 / February 27, 2016 2016 年 2 月 27 日) Free to factor
22×10270+239 = 2(4)2697<271> = 167 × 4729 × 6863 × 13469 × 142810477 × 4521394604621<13> × 7385125405235900116682194510199<31> × [7021900618511288015928433517664699202006304901613891781906531556362995163741738944518802177731559013033490607333469841882211815517449617792913339345262795227436818412631956076624865161555711265293651873029<205>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=1227080167 for P31 / February 27, 2016 2016 年 2 月 27 日) Free to factor
22×10271+239 = 2(4)2707<272> = 33 × 43 × 3257 × 1459641058560876767852774932087<31> × [4428780149329370338817421614612451317445269059257158185914988050045171596293231653879170668520401759934426957293511552986382610602487858729719285633941143408029365644444561965204515949638313177223377207676938493966469118608957517996953<235>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=1028619801 for P31 / February 27, 2016 2016 年 2 月 27 日) Free to factor
22×10272+239 = 2(4)2717<273> = 13 × 19 × 1787 × 761711 × 159984403 × 1517839909433<13> × [2994089825474825957842533261394384704930885448772329795668809849360405052677944042157300071857044083884931141123118221360295930684164518616409908815080678617624448329357592085277923056136356078621640743811196086566481292239820708498519645007<241>] Free to factor
22×10273+239 = 2(4)2727<274> = 2629784558816083<16> × 6991570855564927<16> × 1616975076915457474771<22> × 82220840309941135335840843214625483534349187265169565919002215084190751826427325699567641844715235608912531305309350066972514393541182307748844558037007095549579844991072750529807778397133724120590548157043477026159461177<221>
22×10274+239 = 2(4)2737<275> = 3 × 2579 × 112674663133<12> × 599495373900705310981244014286211287<36> × 154860506711678460665638397914391103993627469<45> × [302033276589639982652129222227789908516259005538472517173932966506347610724853370936824896160486259122174067167762377618505661340893895240047117604472869036098030583484711474392969<180>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2558822500 for P36 / February 27, 2016 2016 年 2 月 27 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3684797615 for P45 / March 28, 2016 2016 年 3 月 28 日) Free to factor
22×10275+239 = 2(4)2747<276> = 7 × 70022117610510893758001<23> × 21964166203932685419320193552412233169<38> × [22705557480103473322398712370072951560483903643903628009391834454715400008988199706092834017426067308369600399368554303259071564733731755063067787021333464497409560421964356904306593383367118032577486731704617293609<215>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=326526564 for P38 / February 27, 2016 2016 年 2 月 27 日) Free to factor
22×10276+239 = 2(4)2757<277> = 59 × 163 × 3168563 × 952011163 × 11048693281<11> × 34942615805329<14> × 53090491895377<14> × 90805259334619<14> × 1733977957249127<16> × 370223381838698903054862625650197<33> × 63514820639945253557350397355428597<35> × 14857203090469562320988101081348994806570521871<47> × 74734740895898747194311076811570192723733625310631166248210768098927429738749<77> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1791529885 for P33, B1=1e6, sigma=1822543652 for P35 / February 27, 2016 2016 年 2 月 27 日) (Dmitry Domanov / Msieve 1.50 gnfs for P47 x P77 / March 16, 2016 2016 年 3 月 16 日)
22×10277+239 = 2(4)2767<278> = 3 × 61 × 7344991172863<13> × 1822379992289650921365050689<28> × 44714052172927934988594190588017709<35> × [223179775071002626545548632104333673125035579689428128058307173018123783563153719084694651449470466757091164930128641371767900129756046553596110847227603886943823670997155160774057473615428139610835043<201>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3745337492 for P35 / March 16, 2016 2016 年 3 月 16 日) Free to factor
22×10278+239 = 2(4)2777<279> = 13 × 17 × 83 × 24971 × 78962557 × 374809486874700786046842753604837703<36> × 830909964516429133487833395476853765073807<42> × 21701418652005359215225252344917044055217070925568633584712919262177110806838170883795952863307437264316563901432524669709856375363972942197294904130903843755580504708629117710270490367<185> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4092231854 for P36 / March 16, 2016 2016 年 3 月 16 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3847054608 for P42 x P185 / March 28, 2016 2016 年 3 月 28 日)
22×10279+239 = 2(4)2787<280> = 2082464463508795290693700279058690443980211<43> × 1173822884989710812872193834651843160943107972704841829143110348024595731382590929994709188290460284759272550699214330961905953515246458667375324008343593372909842763461678285061613825887359626639329957956931775162895999780520908288066277<238> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=625705490 for P43 x P238 / March 14, 2016 2016 年 3 月 14 日)
22×10280+239 = 2(4)2797<281> = 32 × 191 × 257 × 176623169 × 389948867770605053<18> × 4016340541089739999<19> × 200025472948689236153419602605062799432051583992815357717606218292974087413422736517363986984840972806219895532718287618643110777912225979853999867842861081315655322197604626692867537197388836460255509732055360753134633080106807763<231>
22×10281+239 = 2(4)2807<282> = 7 × 47 × [742992232353934481594056062141168524147247551502870651806822019587977034785545423843296183721715636609253630530226274907125970955758189800742992232353934481594056062141168524147247551502870651806822019587977034785545423843296183721715636609253630530226274907125970955758189800743<279>] Free to factor
22×10282+239 = 2(4)2817<283> = 49263255063331265557<20> × [49620035080953234328201398151767949639465346672404455751763288347866326719218174126973820211197956770462950917848388338048942798095760437168417033796833200399262229918111779958927134308434949106467795063946802723071702928856400079629839576828025836762922719100771<263>] Free to factor
22×10283+239 = 2(4)2827<284> = 3 × 109 × 922627 × [81022615569785093489460466392301330358091555026000579022229615609549888357262311389290034620709516583974303889603981603946244203671084551102232564508666166255524953792424848819929229684211030206678074673035969381407735470187557164608721509821115282556790875334386457188247843<275>] Free to factor
22×10284+239 = 2(4)2837<285> = 13 × 29 × 281 × 1833749 × 962586281 × 29018371043<11> × 697302017103860920585033594659883<33> × 64603938127222050801079047631330973536295414910649462965100080170809652582283440507381707622213288043489799504428397034427191049763774419328083865055870214636666474924153126567664187146884785546341381887565369282244836571<221> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1646731226 for P33 x P221 / March 16, 2016 2016 年 3 月 16 日)
22×10285+239 = 2(4)2847<286> = 25409 × 569480708576004571<18> × 404776491301436492291<21> × 4077507777449037027845430007<28> × [102353689429515243063426976875637961871574722283605821723369499798908803881712500513392042781789306749056385781470788282761640235930334841360151304099342888672975092308914763071967901396757312697124106903409018166729<216>] Free to factor
22×10286+239 = 2(4)2857<287> = 3 × 46302023 × 207687367 × 847322755340362310152261458583477656759472139222692905079859704306027913285660020847871484710771305255472590848541939024055427661455779507128639799637213277496486821969909922350424845057850054918133314253510472709590831822989314624499082219239103309086416530173060385989<270>
22×10287+239 = 2(4)2867<288> = 73 × 6449 × 2774805836533691609194153262929<31> × [39825485153823303685639384488036069546759447146318259174816549584104798898605286337479372206126092127378404028302990072449422513113603908932205577713758722548370212691712783676083627645916303251944411262808651486692864950039278708322118544774408902649<251>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=2125933128 for P31 / February 28, 2016 2016 年 2 月 28 日) Free to factor
22×10288+239 = 2(4)2877<289> = 3277427914889<13> × 31025654220853031221967<23> × [24039535674138271416486300257412763008386573743064706278870734090285623760707054917252915499901739709043344592370911032612976066060536015128764791452795615901694112553316592825072212655463340755296576211938814028952645530498979877088924184924206150196969<254>] Free to factor
22×10289+239 = 2(4)2887<290> = 32 × 107 × 75767 × 74317027 × [4508016167238886278936996902410847891967376397832718255096769784178526087032836641413552875642466546857030773338515717850175057030489980875667073978693694751031749645271167200123993294864580479342353606819977419802450910761339640871327472771812476136953535223304077553637041<274>] Free to factor
22×10290+239 = 2(4)2897<291> = 13 × 19 × 989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568600989653621232568601<288>
22×10291+239 = 2(4)2907<292> = 199 × 310620689 × 186133930206593<15> × [212457060665161878906020399971252038660830720102013976208562380165030155230617045805695360883611711032030639786930746389828919529425464216092721264485163984114629345633453760699379176472579314861145313788845199573845737568231181664689432904911004610762634787066838489<267>] Free to factor
22×10292+239 = 2(4)2917<293> = 3 × 43 × 3493506853<10> × 739785696847517<15> × 1561950527581663<16> × 1302008274606422889959363<25> × 10905634042935810123506517767<29> × 26688653423380340699083310531<29> × 71374647519473141352078700973<29> × 1735482961215413433028878667693078825116274561468712094871240308587821921466010772859949137604884056168328343754816345921867477567470061125707<142>
22×10293+239 = 2(4)2927<294> = 7 × 15233 × 6881002964609<13> × 1245199869475170531325343<25> × 267550568330877098664770523882109661695612526579069484747451314988005765277837967492947018579984630681177478508664254638210062651329383727597840882532909336806464672787928589457499888587786794008137385484055530841359011471937295807948841514349727165751<252>
22×10294+239 = 2(4)2937<295> = 17 × 103 × 439 × 241448852411833357<18> × 13170563588571753926369863096823597127541376392010759799244469699557671374921324480697274259891696314229694584767269631033535998430064671735432627966306700780922010289757064286313279898354760218712536733502286958383220487425797645419738637894784805342710088377518460446539<272>
22×10295+239 = 2(4)2947<296> = 3 × 17359 × 469390411207336145408615020919877190399685935143046727815435690313275427625332573774304288734843490301754026622970686568820101857719231991943553669459539613350316731847926041139935949544797980767794697168509024030655461037395480623777184638985433962103125073342251751146272720096097018730811<291>
22×10296+239 = 2(4)2957<297> = 13 × 4909 × 5841045057374201726106151<25> × [655772545529329725976031854795829412655549820889554088096888505600117697898951009632034278959534400700705819749653756747143894578516269483022781733521347252416091785605173646090755227215946182622230961589620208751769959520430098196173569167886690076130559464823594241<267>] Free to factor
22×10297+239 = 2(4)2967<298> = 627546433 × 1018411501<10> × [3824820080983628606750923012770526343871488172714758154921873222906346161837767941967324139676237993174300008500290650221655398787495225037665056502511791444351971295644664390460775368925387117789854150635060949752019071849984449526065884547897932310834703890201976196169892196859<280>] Free to factor
22×10298+239 = 2(4)2977<299> = 35 × 75738811 × 1116351422286897188257841<25> × 1440740084390827533933934397687500195471<40> × [825788528323048803774068653328153615470614968912600126197619111376809219535759320015560087255130314502058363357674126005279732810109554391714669071496031460923899870199444745221652000796527390037310044757134949312403051910849<225>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1604880123 for P40 / March 23, 2016 2016 年 3 月 23 日) Free to factor
22×10299+239 = 2(4)2987<300> = 7 × [34920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634920634921<299>] Free to factor
22×10300+239 = 2(4)2997<301> = 302183159 × 38326820596327<14> × 11516397017092192369<20> × 246223702106284355769630918015343291<36> × [74432162241064593492392341672869129512505266099718689517611717424840610409553564804114143882611816394360886678044810834359853551835247856224021360578771352300666131914360774482758115299095592574004597006540170669468676446301<224>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4115332969 for P36 / March 15, 2016 2016 年 3 月 15 日) Free to factor
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