Cullen numbers (n = 1 to 100)


Cn = n.2n+1


  n : Cn (alen) = factors

  1 : 3 (1) = prime
  2 : 9 (1) = 3 * 3
  3 : 25 (2) = 5 * 5
  4 : 65 (2) = 5 * 13
  5 : 161 (3) = 7 * 23

  6 : 385 (3) = 5 * 7 * 11
  7 : 897 (3) = 3 * 13 * 23
  8 : 2049 (4) = 3 * 683
  9 : 4609 (4) = 11 * 419
 10 : 10241 (5) = 7 * 7 * 11 * 19

 11 : 22529 (5) = 13 * 1733
 12 : 49153 (5) = 13 * 19 * 199
 13 : 106497 (6) = 3 * 3 * 11833
 14 : 229377 (6) = 3 * 157 * 487
 15 : 491521 (6) = 17 * 29 * 997

 16 : 1048577 (7) = 17 * 61681
 17 : 2228225 (7) = 5 * 5 * 19 * 4691
 18 : 4718593 (7) = 11 * 19 * 107 * 211
 19 : 9961473 (7) = 3 * 17 * 37 * 5279
 20 : 20971521 (8) = 3 * 3 * 3 * 103 * 7541

 21 : 44040193 (8) = 23 * 1914791
 22 : 92274689 (8) = 13 * 23 * 43 * 7177
 23 : 192937985 (9) = 5 * 151 * 421 * 607
 24 : 402653185 (9) = 5 * 11 * 1399 * 5233
 25 : 838860801 (9) = 3 * 17 * 2459 * 6689

 26 : 1744830465 (10) = 3 * 5 * 7 * 7 * 2373919
 27 : 3623878657 (10) = 7 * 29 * 53 * 336823
 28 : 7516192769 (10) = 29 * 29 * 8937209
 29 : 15569256449 (11) = 31 * 83 * 6051013
 30 : 32212254721 (11) = 17 * 17 * 31 * 59 * 149 * 409

 31 : 66571993089 (11) = 3 * 3 * 7 * 61 * 1483 * 11681
 32 : 137438953473 (12) = 3 * 1777 * 25781083
 33 : 283467841537 (12) = 47 * 6031230671
 34 : 584115552257 (12) = 19 * 23 * 67 * 1061 * 18803
 35 : 1202590842881 (13) = 37 * 32502455213

 36 : 2473901162497 (13) = 37 * 37 * 1933 * 934861
 37 : 5085241278465 (13) = 3 * 5 * 339016085231
 38 : 10445360463873 (14) = 3 * 3 * 20879 * 55586743
 39 : 21440476741633 (14) = 41 * 3433 * 152326961
 40 : 43980465111041 (14) = 41 * 131611 * 8150491

 41 : 90159953477633 (14) = 13 * 43 * 1291 * 124932557
 42 : 184717953466369 (15) = 23 * 43 * 83 * 2250270487
 43 : 378231999954945 (15) = 3 * 5 * 163 * 2633 * 58752797
 44 : 774056185954305 (15) = 3 * 5 * 28909 * 1785040843
 45 : 1583296743997441 (16) = 11 * 47 * 2437 * 1256655529

 46 : 3236962232172545 (16) = 5 * 31 * 47 * 139297 * 3189821
 47 : 6614661952700417 (16) = 7 * 11 * 43 * 3593 * 556021079
 48 : 13510798882111489 (17) = 7 * 379 * 997 * 5107973329
 49 : 27584547717644289 (17) = 3 * 3 * 3 * 3 * 340549971822769
 50 : 56294995342131201 (17) = 3 * 163 * 211 * 563 * 857 * 1130809

 51 : 114841790497947649 (18) = 53 * 101 * 21453725107033
 52 : 234187180623265793 (18) = 7 * 11 * 17 * 53 * 1433 * 2355599273
 53 : 477381560501272577 (18) = 5591 * 16747 * 5098461301
 54 : 972777519512027137 (18) = 29 * 107 * 7187 * 110503 * 394739
 55 : 1981583836043018241 (19) = 3 * 109 * 2185637 * 2772596459

 56 : 4035225266123964417 (19) = 3 * 3 * 1021 * 439136496476653
 57 : 8214565720323784705 (19) = 5 * 13 * 59 * 10740337 * 199434979
 58 : 16717361816799281153 (20) = 31 * 59 * 101 * 7002713 * 12923089
 59 : 34011184385901985793 (20) = 37 * 43 * 61 * 350446511482643
 60 : 69175290276410818561 (20) = 61 * 2267 * 1529093 * 327141571

 61 : 140656423562035331073 (21) = 3 * 19 * 37 * 41 * 21557 * 110359 * 683759
 62 : 285924533142498050049 (21) = 3 * 5104570123 * 18671146721
 63 : 581072438321850875905 (21) = 5 * 313993 * 370118084366117
 64 : 1180591620717411303425 (22) = 5 * 5 * 29 * 41 * 113 * 7416361 * 47392381
 65 : 2398076729582241710081 (22) = 67 * 149 * 2357 * 367019 * 277685929

 66 : 4869940435459321626625 (22) = 5 * 5 * 5 * 13 * 67 * 107 * 131 * 8353 * 382030403
 67 : 9887454823508319666177 (22) = 3 * 3 * 413009 * 7451263 * 356987159
 68 : 20070057552195992158209 (23) = 3 * 7 * 4841894819 * 197384920991
 69 : 40730410914750689968129 (23) = 7 * 71 * 193 * 135979 * 3122721481331
 70 : 82641413450218791239681 (23) = 37 * 47 * 71 * 139 * 4815318361753391

 71 : 167644010141872405086209 (24) = 11 * 11 * 73 * 173 * 5113 * 21456452254477
 72 : 340010386766614455386113 (24) = 41 * 73 * 6011 * 40163 * 470557385537
 73 : 689465506498968201199617 (24) = 3 * 7 * 89 * 277 * 1331752354101535409
 74 : 1397820478929414983254017 (25) = 3 * 3 * 3 * 130860199 * 395621657653429
 75 : 2833419889721787128217601 (25) = 149 * 367 * 298013 * 663557 * 262026467

 76 : 5742397643169488579854337 (25) = 47 * 47 * 79939 * 27729643 * 1172720609
 77 : 11635911013790805806546945 (26) = 5 * 17 * 79 * 1732823680385823649523
 78 : 23574053482485268906770433 (26) = 41 * 79 * 78094529 * 93197166057943
 79 : 47752569874777852400893953 (26) = 3 * 59 * 157 * 3533 * 36930529 * 13170269561
 80 : 96714065569170333976494081 (26) = 3 * 67 * 1960787 * 245393561523640963

 81 : 195845982777569926302400513 (27) = 83 * 13633 * 984666689 * 175774509403
 82 : 396527668833598369303625729 (27) = 43 * 83 * 163 * 681615322182320440507
 83 : 802726744224113772004900865 (27) = 5 * 23 * 15373 * 2205616169 * 205864436623
 84 : 1624796301562061610805100545 (28) = 5 * 2971 * 22637 * 4831782703823228467
 85 : 3288278229351791355200798721 (28) = 3 * 3 * 15607 * 24763 * 132157 * 144163 * 49620299

 86 : 6653927711158918977582792705 (28) = 3 * 5 * 3989 * 6687383 * 69261971 * 240088711
 87 : 13462597927228510489527975937 (29) = 19 * 89 * 173 * 22853 * 2013705447963047603
 88 : 27234680864278366047780732929 (29) = 89 * 2137 * 13607459 * 10523270337143867
 89 : 55088331748199422233011027969 (29) = 7 * 79867 * 372067 * 264833583219205703
 90 : 111414603535684224740921180161 (30) = 7 * 47 * 179 * 1891878275724375961367971

 91 : 225305087149939210031640608769 (30) = 3 * 181 * 9157 * 74609 * 607332797678367491
 92 : 455561934457019941162877714433 (30) = 3 * 3 * 94957781 * 533057872502798481877
 93 : 921027389228322924524948422657 (30) = 71 * 79 * 887 * 127703 * 1449647415604834793
 94 : 1861861819085211933448282832897 (31) = 7 * 62869 * 4230706069276050048396059
 95 : 3763337719427556035693337640961 (31) = 29 * 97 * 769973 * 1737512608551063059489

 96 : 7605903601369376408980219232257 (31) = 97 * 57735121 * 1358122681230804234961
 97 : 15370263527767281493147526365185 (32) = 3 * 5 * 13 * 283583 * 1806689 * 153844901960056309
 98 : 31057439705591620336669228531713 (32) = 3 * 929 * 260171 * 42832142214886804432769
 99 : 62748704711297355374086808666113 (32) = 13 * 101 * 197 * 35461 * 6841051101464703338953
100 : 126765060022822940149670320537601 (33) = 101 * 12006189421 * 104537714688315156481

What's new index Numbers still not completely factored

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