Numerator of partial sum of log 2 (n = 1 to 100)

(Complete : June 15, 2003)

Numerator of partial sum of log 2 =

1 - 1/2 + 1/3 - ...


  n : N = factors

  1 : 1 (1) = 1
  2 : 1 (1) = 1
  3 : 5 (1) = prime
  4 : 7 (1) = prime
  5 : 47 (2) = prime

  6 : 37 (2) = prime
  7 : 319 (3) = 11 * 29
  8 : 533 (3) = 13 * 41
  9 : 1879 (4) = prime
 10 : 1627 (4) = prime

 11 : 20417 (5) = 17 * 1201
 12 : 18107 (5) = 19 * 953
 13 : 263111 (6) = prime
 14 : 237371 (6) = 17 * 13963
 15 : 52279 (5) = 23 * 2273

 16 : 95549 (5) = prime
 17 : 1768477 (7) = prime
 18 : 1632341 (7) = prime
 19 : 33464927 (8) = 29 * 71 * 16253
 20 : 155685007 (9) = 31 * 5022097

 21 : 166770367 (9) = 1747 * 95461
 22 : 156188887 (9) = 797 * 195971
 23 : 3825136961 (10) = 263 * 14544247
 24 : 3602044091 (10) = 37 * 359 * 271177
 25 : 19081066231 (11) = 97 * 97 * 2027959

 26 : 18051406831 (11) = 103 * 1597 * 109741
 27 : 57128792093 (11) = 41 * 79 * 17637787
 28 : 7751493599 (10) = 37 * 43 * 139 * 35051
 29 : 236266661971 (12) = 271 * 16339 * 53359
 30 : 225175759291 (12) = 7 * 7 * 919 * 1831 * 2731

 31 : 7313175618421 (13) = 47 * 18793 * 8279651
 32 : 13981692518567 (14) = 223 * 62698172729
 33 : 14606816124167 (14) = 151 * 15791 * 6125887
 34 : 14000078506967 (14) = 7 * 2153 * 928941577
 35 : 102126365345729 (15) = 53 * 107741 * 17884673

 36 : 98115155543129 (14) = 71 * 1381903599199
 37 : 3774664307989373 (16) = prime
 38 : 3634060848592973 (16) = 10864471 * 334490363
 39 : 3771059091081773 (16) = 59 * 9601 * 6657249847
 40 : 3637485804655193 (16) = 61 * 757 * 3217 * 24486377

 41 : 154479849447926113 (18) = 507961 * 304117539433
 42 : 149264130644602513 (18) = 99053 * 1506911760821
 43 : 6637417807457499259 (19) = prime
 44 : 6423336258393807859 (19) = 67 * 1021 * 71861 * 1306672817
 45 : 6632660439700528339 (19) = 1013 * 8136967 * 804666209

 46 : 6427886784074388739 (19) = 2177105257 * 2952492427
 47 : 311530267010298692333 (21) = 71 * 307 * 13187 * 1083820888547
 48 : 302306920271471321183 (21) = 73 * 6857 * 105509 * 5724025667
 49 : 2179394248109401221881 (22) = 883 * 66293 * 37231233409399
 50 : 2117413358024481287753 (22) = 573995603 * 3688901704051

 51 : 2178178936539108674153 (22) = 12509720567 * 174118912159
 52 : 2118581926842070275953 (22) = 79 * 26817492744836332607
 53 : 115383886626875721331909 (24) = 41534561 * 2778021094935269
 54 : 112342231835671317157109 (24) = 1319 * 85172275842055585411
 55 : 115328583812490186710549 (24) = 83 * 22531 * 61670632008745213

 56 : 112395559549543082684849 (24) = 219070937 * 513055547617177
 57 : 115277127246473570850449 (24) = 61 * 1889788971253665095909
 58 : 112445241751214297998049 (24) = prime
 59 : 6798518622046681407324091 (25) = 89 * 5323 * 32353 * 443560905021401
 60 : 6637006752633727545642211 (25) = 3474551 * 1910176812092764661

 61 : 414548124075434611985087671 (27) = 3253 * 31699 * 4020178429965324793
 62 : 405013713719766690472899271 (27) = 983 * 412018020060800295496337
 63 : 414396784228519248151560871 (27) = 2137 * 337283 * 574933218856710101
 64 : 810320648392931898373256717 (27) = 97 * 8353821117452906168796461
 65 : 828509369686821471719585357 (27) = 2377 * 15643 * 22281693567242162687

 66 : 810596235079202952514867757 (27) = 151849 * 5338173021088074024293
 67 : 55492214634409420086007501319 (29) = 101 * 549427867667420000851559419
 68 : 54327334028013992263606600919 (29) = 103 * 5011 * 11197 * 45863 * 204971098461313
 69 : 55475332306780500842204589719 (29) = 95890799 * 578526124355064565081
 70 : 54343734003424942386158000759 (29) = 565907 * 96029443006403777274637

 71 : 3937616995478060001340479281089 (31) = 107 * 727905616813 * 50556223205648879
 72 : 3859505279260322146805041126489 (31) = 109 * 937 * 37789013142278422711611733
 73 : 287367928953680642243319549364897 (33) = 2141681 * 25558969 * 5249768866513798073
 74 : 281819885974755910304964644762497 (33) = 1009361 * 279206236395854318033849777
 75 : 57458791009458995830161630127373 (32) = 113 * 173 * 433 * 1361 * 3169 * 590092417 * 2667126673

 76 : 56378382639878916452692517125853 (32) = 634717 * 152856331 * 581097559358594339
 77 : 5222250884721089255661129169783 (31) = 271 * 373 * 16447 * 799474259 * 3929057928137
 78 : 5126550376459916723391137808343 (31) = 2339 * 2191770148123093939029986237
 79 : 412462119384704878664959213051417 (33) = 249049294166149 * 1656146510134406533
 80 : 405090787735888064366863128436501 (33) = 1326839 * 264465499 * 1154423382423758441

 81 : 1237113345870825124354207413798143 (34) = 157 * 50821097259467 * 155047869189280897
 82 : 1215538716654775911774413995413023 (34) = 181615693019 * 6692916765334868354317
 83 : 102658833078062436108819421926860749 (36) = 134227 * 8758903 * 87318591728322519050329
 84 : 100910774429914448718128064718180669 (36) = 127 * 4127 * 58396181 * 3296969300825549488681
 85 : 102638267682201871551281876547935101 (36) = 8350969726777 * 12290580739754928231013

 86 : 100930861560755000146420550902247581 (36) = 338573 * 31752313 * 8562689027 * 1096443152947
 87 : 102618642324484091420191516483042141 (36) = 131 * 587 * 369913 * 374792161 * 9625577047582021
 88 : 1110450449763771138019847430622322711 (37) = 126460717 * 9733187632397 * 902170140364639
 89 : 100445296219864371632765235386207115199 (39) = 35509847711508353 * 2828660292657666072383
 90 : 98848036764429950620977519259395836767 (38) = 17011 * 5810830448793718806711981615389797

 91 : 100427743918156301072196139604593804447 (39) = 137 * 1523 * 14989339 * 32110772543526495723820423
 92 : 98865207494361758778055982524017553807 (38) = 139 * 2521 * 4708875217 * 59915426378710367213509
 93 : 100410942451233779112044094904802661967 (39) = 97 * 1035164355167358547546846339224769711
 94 : 98881651483264652611396281591898246447 (38) = 6273504563299 * 15761788404799774731328453
 95 : 100394844651570946201510960027824720751 (39) = 5021 * 142007 * 345109 * 163136032537 * 2500951424401

 96 : 98897413912101176502959976158939147221 (38) = 6869399 * 104261287371203 * 138083920679144593
 97 : 9736802500462912011848012138830112339317 (40) = 1531 * 3821 * 356693 * 6779616497 * 688278840246617327
 98 : 9594516020402274303348963549166209678997 (40) = 179 * 367 * 3323843 * 232509227 * 188983236722672827289
 99 : 9735365263290582338024789425803204231637 (40) = 149 * 20177 * 3546409 * 165715301 * 5510080676834909141
100 : 47979622564155786918478609039662898122617 (41) = 151 * 2471555704454041 * 128561069541389422646087

What's new index Numbers still not completely factored

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima