# Least Carmichael Numbers withGiven Divisors (up to 2999)

 home   |   indexmodular arithmeticCarmichael numbersconjecture It is conjectured that every odd number coprime to its Euler totient divides some Carmichael number.  Only numbers satisfying this necessary condition are listed here; a question mark indicates those for which the Carmichael multiple given need not be the least one:  885, 2391, 2571, 2589, 2595, 2685, 2949.  The list on this page dates back to 2003  (see footnotes).  It was updated in 2007, shortly before we published (jointly with Joe Crump) a similar list extended to all divisors below 10000. See also our list of Carmichael multiples of primes up to 10000.
```   1:                      561 = 3.11.17
3:                      561 = 3.11.17
5:                     1105 = 5.13.17
7:                     1729 = 7.13.19
11:                      561 = 3.11.17
13:                     1105 = 5.13.17
15:                    62745 = 3.5.47.89
17:                      561 = 3.11.17
19:                     1729 = 7.13.19
23:                     6601 = 7.23.41
29:                     2465 = 5.17.29
31:                     2821 = 7.13.31
33:                      561 = 3.11.17
35:                   825265 = 5.7.17.19.73
37:                    29341 = 13.37.61
41:                     6601 = 7.23.41
43:                   334153 = 19.43.409
47:                    62745 = 3.5.47.89
51:                      561 = 3.11.17
53:                  2433601 = 17.37.53.73
59:                 74165065 = 5.13.59.83.233
61:                    29341 = 13.37.61
65:                     1105 = 5.13.17
67:                     8911 = 7.19.67
69:             116150434401 = 3.23.101.2081.8009
71:                 10024561 = 71.271.521
73:                    10585 = 5.29.73
77:                    41041 = 7.11.13.41
79:                  2508013 = 53.79.599
83:                 55462177 = 17.23.83.1709
85:                     1105 = 5.13.17
87:                 11921001 = 3.29.263.521
89:                    62745 = 3.5.47.89
91:                     1729 = 7.13.19
95:                   449065 = 5.19.29.163
97:                    46657 = 13.37.97
101:                   101101 = 7.11.13.101
103:                    52633 = 7.73.103
107:                 84350561 = 107.743.1061
109:                   188461 = 7.13.19.109
113:                   278545 = 5.17.29.113
115:                  1050985 = 5.13.19.23.37
119:                   825265 = 5.7.17.19.73
123:                689880801 = 3.41.71.197.401
127:                  1152271 = 43.127.211
131:                 18307381 = 29.61.79.131
133:                     1729 = 7.13.19
137:                   410041 = 41.73.137
139:                  2628073 = 7.37.73.139
141:                    62745 = 3.5.47.89
143:                    41041 = 7.11.13.41
145:                     2465 = 5.17.29
149:                 12261061 = 19.61.71.149
151:                   838201 = 7.13.61.151
157:                  4335241 = 53.157.521
159:                230996949 = 3.53.317.4583
161:                     6601 = 7.23.41
163:                   449065 = 5.19.29.163
167:              18633869185 = 5.43.167.193.2689
173:                 45318561 = 3.29.173.3011
177:             939161538561 = 3.59.233.281.81041
179:                851703301 = 179.1069.4451
181:                   488881 = 37.73.181
185:                  1050985 = 5.13.19.23.37
187:                      561 = 3.11.17
191:                 34657141 = 191.421.431
193:                  3224065 = 5.13.193.257
197:                   656601 = 3.11.101.197
199:                   670033 = 7.13.37.199
209:                  6313681 = 11.17.19.1777
211:                   399001 = 31.61.211
213:                174352641 = 3.71.641.1277
215:                115542505 = 5.13.43.67.617
217:                     2821 = 7.13.31
221:                     1105 = 5.13.17
223:                977892241 = 17.31.53.157.223
227:               2436691321 = 227.1583.6781
229:                  6840001 = 7.17.229.251
233:                   162401 = 17.41.233
235:                    62745 = 3.5.47.89
239:                  9613297 = 19.29.73.239
241:                   115921 = 13.37.241
247:                     1729 = 7.13.19
249:            1070730898161 = 3.29.83.89.239.6971
251:                  3828001 = 101.151.251
255:            1886616373665 = 3.5.17.23.83.353.10979
257:                  3224065 = 5.13.193.257
259:                    63973 = 7.13.19.37
263:                 11921001 = 3.29.263.521
265:                  6054985 = 5.53.73.313
267:                    62745 = 3.5.47.89
269:                962500561 = 11.239.269.1361
271:                   512461 = 31.61.271
277:                 35703361 = 61.277.2113
281:                 29111881 = 211.281.491
283:                182356993 = 7.13.73.97.283
287:                     6601 = 7.23.41
293:                790623289 = 37.233.293.313
295:                 74165065 = 5.13.59.83.233
299:                   340561 = 13.17.23.67
303:                   656601 = 3.11.101.197
307:                  1033669 = 7.13.37.307
311:                181154701 = 7.13.37.173.311
313:                  6054985 = 5.53.73.313
317:                230996949 = 3.53.317.4583
319:                  2704801 = 11.29.61.139
321:              17544679041 = 3.41.107.449.2969
323:                   825265 = 5.7.17.19.73
329:               2574243721 = 7.47.139.181.311
331:                  1857241 = 31.181.331
335:                 40280065 = 5.7.67.89.193
337:                  3057601 = 43.211.337
339:              42887804961 = 3.71.89.113.20021
341:                    75361 = 11.13.17.31
345:            1886616373665 = 3.5.17.23.83.353.10979
347:              34087042891 = 11.19.307.347.1531
349:                413058601 = 31.73.349.523
353:                  1615681 = 23.199.353
359:                325546585 = 5.7.13.359.1993
365:                    10585 = 5.29.73
367:                257495641 = 13.31.367.1741
371:                 13992265 = 5.7.19.53.397
373:                 46483633 = 7.19.373.937
377:                 10402561 = 13.29.41.673
379:                  6733693 = 109.163.379
383:               1678569121 = 31.37.383.3821
389:               1955324449 = 13.29.67.199.389
391:                   340561 = 13.17.23.67
393:               1848112761 = 3.11.41.131.10427
395:               1074363265 = 5.19.37.53.73.79
397:                   314821 = 13.61.397
401:                  8341201 = 11.31.61.401
403:                     2821 = 7.13.31
407:                 29020321 = 11.37.113.631
409:                   334153 = 19.43.409
411:              58856010081 = 3.11.29.41.137.10949
413:                544101481 = 7.11.59.229.523
415:                 74165065 = 5.13.59.83.233
419:                426821473 = 13.127.419.617
421:                   530881 = 13.97.421
427:                   172081 = 7.13.31.61
431:                 34657141 = 191.421.431
433:                   748657 = 7.13.19.433
435:           62267183533185 = 3.5.29.449.3137.101627
437:                  1050985 = 5.13.19.23.37
439:               4382684065 = 5.17.67.439.1753
443:                 60112885 = 5.7.443.3877
445:                    62745 = 3.5.47.89
447:            4173049274241 = 3.23.149.281.1444481
449:                  5632705 = 5.13.193.449
451:                    41041 = 7.11.13.41
455:                 41298985 = 5.7.13.139.653
457:                 16046641 = 13.37.73.457
461:                  1909001 = 41.101.461
463:                 10267951 = 67.331.463
467:              14005499521 = 13.17.97.467.1399
469:                     8911 = 7.19.67
473:                 10877581 = 11.13.29.43.61
479:               1441316269 = 19.29.43.127.479
481:                    29341 = 13.37.61
485:                  9582145 = 5.23.97.859
487:                 64377991 = 163.487.811
491:                 14676481 = 71.421.491
493:                     2465 = 5.17.29
499:               2230305949 = 499.997.4483
501:             236359158267 = 3.47.167.239.41999
503:                175997185 = 5.7.13.503.769
509:                 11119105 = 5.17.257.509
511:                    15841 = 7.31.73
515:                130032865 = 5.19.97.103.137
517:                 26932081 = 11.47.113.461
519:                 45318561 = 3.29.173.3011
521:                  4335241 = 53.157.521
523:                 14469841 = 73.379.523
527:                    75361 = 11.13.17.31
533:                    41041 = 7.11.13.41
535:                413631505 = 5.7.17.73.89.107
537:          675961912209921 = 3.17.179.281.13217.19937
541:                  1461241 = 37.73.541
545:                 67371265 = 5.13.37.109.257
547:                 15829633 = 43.547.673
551:                   449065 = 5.19.29.163
553:                 72286501 = 7.67.79.1951
557:               8270944801 = 7.31.41.557.1669
559:                 10877581 = 11.13.29.43.61
561:                      561 = 3.11.17
563:              80414269057 = 17.67.89.563.1409
565:                   278545 = 5.17.29.113
569:               6879465481 = 7.41.103.409.569
571:                  9439201 = 61.271.571
573:             304044043521 = 3.191.257.641.3221
577:                   997633 = 7.13.19.577
581:               3034203361 = 7.83.821.6361
583:                173085121 = 11.31.53.61.157
587:             114919915021 = 587.5861.33403
589:                  2113921 = 19.31.37.97
591:                   656601 = 3.11.101.197
593:                 28787185 = 5.7.19.73.593
595:                   825265 = 5.7.17.19.73
599:                  2508013 = 53.79.599
601:                  5049001 = 31.271.601
607:                 94536001 = 7.19.607.1171
611:                945959365 = 5.13.19.43.47.379
613:                 36765901 = 37.613.1621
617:                 19384289 = 89.353.617
619:                 38637361 = 7.37.241.619
623:                 40280065 = 5.7.67.89.193
629:                  2433601 = 17.37.53.73
631:                  1193221 = 31.61.631
635:                  3664585 = 5.29.127.199
641:                 70561921 = 31.53.67.641
643:                 11972017 = 43.433.643
647:                 90698401 = 103.647.1361
649:                544101481 = 7.11.59.229.523
653:                 41298985 = 5.7.13.139.653
659:                114910489 = 127.659.1373
661:                 34901461 = 7.19.397.661
665:                   825265 = 5.7.17.19.73
667:                  5031181 = 19.23.29.397
671:                   852841 = 11.31.41.61
673:                 10402561 = 13.29.41.673
677:               2642025673 = 7.53.67.157.677
679:                182356993 = 7.13.73.97.283
681:              77403893505 = 3.5.197.227.257.449
683:                 84311569 = 19.73.89.683
685:                130032865 = 5.19.97.103.137
691:                 79624621 = 139.691.829
695:                 15403285 = 5.37.139.599
697:                   162401 = 17.41.233
699:             939161538561 = 3.59.233.281.81041
701:                 31405501 = 71.631.701
703:                    63973 = 7.13.19.37
705:                    62745 = 3.5.47.89
707:                   101101 = 7.11.13.101
709:                547652161 = 7.17.709.6491
713:                683379841 = 23.31.41.97.241
717:             101536702401 = 3.197.239.449.1601
719:             110765400481 = 17.719.757.11971
721:                    52633 = 7.73.103
727:                278152381 = 13.19.727.1549
731:                  1569457 = 17.19.43.113
733:                295643089 = 7.157.367.733
739:                  4909177 = 7.13.73.739
743:                 84350561 = 107.743.1061
745:                745864945 = 5.7.89.149.1607
749:                413631505 = 5.7.17.73.89.107
751:                 68154001 = 151.601.751
753:               7281824001 = 3.251.2417.4001
757:                  6868261 = 43.211.757
761:                  7519441 = 41.241.761
763:                   188461 = 7.13.19.109
767:                 74165065 = 5.13.59.83.233
769:                 50201089 = 97.673.769
771:              77403893505 = 3.5.197.227.257.449
773:                419520241 = 7.31.41.61.773
779:                 16778881 = 7.17.19.41.181
781:                 67994641 = 11.13.37.71.181
785:                 31692805 = 5.47.157.859
787:                542497201 = 263.787.2621
789:                 11921001 = 3.29.263.521
793:                    29341 = 13.37.61
795:          294628486347105 = 3.5.53.113.11699.280337
797:               5685601141 = 11.181.797.3583
799:                 20964961 = 17.19.47.1381
803:                  4903921 = 11.31.73.197
805:                225745345 = 5.7.23.193.1453
807:           60580578044001 = 3.17.269.20369.216791
809:              44378446561 = 809.5657.9697
811:                 64377991 = 163.487.811
815:                   449065 = 5.19.29.163
817:                   334153 = 19.43.409
821:               2438403661 = 739.821.4019
823:               8346731851 = 823.2467.4111
827:               1746692641 = 113.827.18691
829:                 79624621 = 139.691.829
835:              18633869185 = 5.43.167.193.2689
839:             330983586241 = 7.11.839.1553.3299
843:               6097778961 = 3.131.281.55217
851:                  1050985 = 5.13.19.23.37
853:                  7995169 = 7.13.103.853
857:             148689562561 = 71.673.857.3631
859:                  9582145 = 5.23.97.859
863:                255160621 = 37.61.131.863
865:              92429188345 = 5.13.73.109.173.1033
869:                105869401 = 11.29.79.4201
871:                   340561 = 13.17.23.67
877:               1200778753 = 293.877.4673
879:          836229561461841 = 3.53.113.293.509.521.599
881:                128697361 = 13.17.661.881
883:               1349671681 = 37.109.379.883
885:     24354644805191195265 = 3.5.59.449.1373.205553.217169 [?]
887:                981567505 = 5.17.47.277.887
893:                 20964961 = 17.19.47.1381
895:              75150127585 = 5.13.179.1303.4957
899:                765245881 = 19.29.31.71.631
901:                  2433601 = 17.37.53.73
907:                 18900973 = 7.13.229.907
911:                 40622401 = 17.43.61.911
913:               4375257601 = 11.13.83.449.821
917:                393716701 = 7.53.131.8101
919:                  2531845 = 5.19.29.919
923:                 67994641 = 11.13.37.71.181
929:                600892993 = 19.59.577.929
933:         7357194781706001 = 3.41.89.113.311.701.27281
937:                 46483633 = 7.19.373.937
941:                507726901 = 11.181.271.941
943:                     6601 = 7.23.41
947:               7558388641 = 331.947.24113
949:                   126217 = 7.13.19.73
951:                230996949 = 3.53.317.4583
953:                  5444489 = 29.197.953
957:               1534274841 = 3.11.29.479.3347
959:                302751505 = 5.7.103.137.613
965:                  3224065 = 5.13.193.257
967:                 53245921 = 17.41.79.967
971:               6155121421 = 19.37.71.127.971
973:                  2628073 = 7.37.73.139
977:               3222053185 = 5.13.113.449.977
983:              34138047673 = 983.3929.8839
985:                 21584305 = 5.17.197.1289
989:                111291181 = 23.43.131.859
991:                  8830801 = 7.19.67.991
995:                  3664585 = 5.29.127.199
997:               1950276565 = 5.19.59.349.997
1001:                    41041 = 7.11.13.41
1003:               2709611521 = 17.59.61.67.661
1007:                 13992265 = 5.7.19.53.397
1009:                 84417985 = 5.29.577.1009
1013:                413138881 = 617.661.1013
1019:              12760344961 = 7.13.23.31.193.1019
1021:                473847121 = 11.31.1021.1361
1031:                434330401 = 43.97.101.1031
1033:               4210922233 = 7.37.1033.15739
1037:                   552721 = 13.17.41.61
1039:                130497361 = 29.61.71.1039
1041:         3776882591682201 = 3.53.89.137.347.701.8009
1043:                745864945 = 5.7.89.149.1607
1049:                939947009 = 263.1049.3407
1051:                 58489201 = 19.29.101.1051
1057:                   838201 = 7.13.61.151
1059:              28173681537 = 3.353.2699.9857
1061:                 84350561 = 107.743.1061
1063:               3102234751 = 7.11.151.251.1063
1067:                172430401 = 11.13.31.97.401
1069:                851703301 = 179.1069.4451
1073:                 12945745 = 5.19.29.37.127
1077:          480656935630257 = 3.197.359.419.1163.4649
1079:                 74165065 = 5.13.59.83.233
1087:              18152272801 = 13.17.19.41.97.1087
1091:               3347570941 = 11.13.43.499.1091
1093:                  3581761 = 29.113.1093
1097:              13657063105 = 5.7.19.97.193.1097
1099:                 43620409 = 7.19.157.2089
1103:              29465082049 = 13.269.1103.7639
1105:                     1105 = 5.13.17
1109:               8885251441 = 11.47.1109.15497
1111:                   101101 = 7.11.13.101
1115:              10967410945 = 5.19.223.449.1153
1117:                775368901 = 373.1117.1861
1121:                338740417 = 19.59.449.673
1123:                743404663 = 103.1123.6427
1129:                529782121 = 11.29.1129.1471
1133:                557795161 = 7.11.53.103.1327
1135:              77403893505 = 3.5.197.227.257.449
1139:                   340561 = 13.17.23.67
1141:                  1082809 = 7.13.73.163
1145:                231194965 = 5.23.229.8779
1147:                  2113921 = 19.31.37.97
1149:         5949649907586561 = 3.11.83.257.383.1373.16073
1151:                104569501 = 47.1151.1933
1153:                176659201 = 37.41.101.1153
1157:                226509361 = 13.89.137.1429
1159:                  2455921 = 13.19.61.163
1163:              56549585233 = 1163.4649.10459
1165:                 74165065 = 5.13.59.83.233
1167:          655510549443465 = 3.5.23.53.389.2663.34607
1169:              18660149641 = 7.19.31.41.167.661
1171:                  5481451 = 31.151.1171
1173:            1886616373665 = 3.5.17.23.83.353.10979
1177:               4752717761 = 11.17.107.173.1373
1181:                193708801 = 11.13.31.37.1181
1187:              27968406181 = 31.53.1187.14341
1189:                 10402561 = 13.29.41.673
1193:                957044881 = 13.23.1193.2683
1195:               1999004365 = 5.29.37.239.1559
1199:                100427041 = 11.13.17.109.379
1201:                  7207201 = 17.353.1201
1203:                684106401 = 3.11.17.401.3041
1207:                 75151441 = 17.19.29.71.113
1211:                181154701 = 7.13.37.173.311
1213:               6693621481 = 607.1213.9091
1217:               1337805505 = 5.109.1217.2017
1219:               2140538401 = 23.29.53.151.401
1223:              15039215101 = 31.37.71.151.1223
1229:              10550902321 = 17.41.109.113.1229
1231:                897880321 = 13.19.1231.2953
1235:                  1050985 = 5.13.19.23.37
1237:               1420379065 = 5.7.53.619.1237
1241:                   825265 = 5.7.17.19.73
1243:                  6049681 = 11.31.113.157
1245:            1886616373665 = 3.5.17.23.83.353.10979
1247:                 10877581 = 11.13.29.43.61
1249:                 23382529 = 97.193.1249
1253:               1362132541 = 7.11.37.179.2671
1257:               5860426881 = 3.17.41.419.6689
1259:             106339394161 = 7.11.13.19.1259.4441
1261:                    46657 = 13.37.97
1267:                  4463641 = 7.13.181.271
1271:                   852841 = 11.31.41.61
1273:                     8911 = 7.19.67
1277:                174352641 = 3.71.641.1277
1279:               1194866101 = 11.13.47.139.1279
1283:              63280622521 = 1283.3847.12821
1285:                  3224065 = 5.13.193.257
1289:                 21584305 = 5.17.197.1289
1291:                517937581 = 7.37.1291.1549
1293:             199438988001 = 3.11.41.71.431.4817
1295:               1615335085 = 5.7.13.37.229.419
1297:                171454321 = 163.811.1297
1301:                 27062101 = 11.31.61.1301
1303:                955134181 = 311.1303.2357
1307:               2111488561 = 7.13.41.433.1307
1309:               2313774001 = 7.11.17.19.31.3001
1313:                   101101 = 7.11.13.101
1315:             959694999145 = 5.29.47.263.277.1933
1319:             144377609419 = 1319.9227.11863
1321:                  8719921 = 7.23.41.1321
1327:                557795161 = 7.11.53.103.1327
1329:              55086689841 = 3.29.41.71.443.491
1333:                  8927101 = 31.37.43.181
1335:                    62745 = 3.5.47.89
1337:                 72108421 = 7.11.191.4903
1339:                  7995169 = 7.13.103.853
1343:                 53245921 = 17.41.79.967
1345:              12782849065 = 5.7.269.317.4283
1347:              10031651841 = 3.29.71.449.3617
1349:                 12261061 = 19.61.71.149
1351:                 37167361 = 7.11.41.61.193
1353:               1848112761 = 3.11.41.131.10427
1357:               3284630713 = 7.13.23.59.67.397
1361:                 90698401 = 103.647.1361
1363:              13402361281 = 17.29.47.67.89.97
1367:             157596376201 = 11.31.233.1367.1451
1373:                 13187665 = 5.17.113.1373
1381:                 15247621 = 61.181.1381
1383:             180481509681 = 3.11.17.41.461.17021
1385:                334783585 = 5.37.47.139.277
1387:                   126217 = 7.13.19.73
1391:               4521794641 = 7.13.23.61.107.331
1393:                   670033 = 7.13.37.199
1397:                631071001 = 11.29.37.127.421
1399:              14005499521 = 13.17.97.467.1399
1401:         2220232577722881 = 3.197.449.467.1373.13049
1403:                  9494101 = 23.61.67.101
1409:               5447713921 = 13.23.67.193.1409
1411:                 55462177 = 17.23.83.1709
1415:               1332521065 = 5.283.659.1429
1417:                   188461 = 7.13.19.109
1423:               1442761201 = 7.241.601.1423
1427:            4310730293521 = 311.373.1427.26041
1429:                226509361 = 13.89.137.1429
1433:              88183003921 = 1433.4297.14321
1437:               1534274841 = 3.11.29.479.3347
1439:            2803378414477 = 1439.8629.225767
1441:                697906561 = 11.97.131.4993
1447:                 35571601 = 13.31.61.1447
1451:                153589801 = 151.701.1451
1453:                225745345 = 5.7.23.193.1453
1457:                237597361 = 31.47.313.521
1459:                129762001 = 19.31.151.1459
1463:               1419339691 = 7.11.19.103.9419
1465:              28021044745 = 5.109.293.379.463
1469:                 25603201 = 13.29.113.601
1471:                529782121 = 11.29.1129.1471
1473:               7397902401 = 3.491.1601.3137
1479:               2176838049 = 3.17.29.317.4643
1481:                271794601 = 13.19.743.1481
1483:              18929704561 = 17.31.53.457.1483
1487:              77111274241 = 37.79.113.157.1487
1489:               1309440001 = 41.89.241.1489
1493:             502565593321 = 11.1493.2857.10711
1495:                  1050985 = 5.13.19.23.37
1499:              66828386521 = 13.211.1499.16253
1501:                  8719309 = 19.37.79.157
1507:                 77826001 = 11.43.137.1201
1509:          881715504450705 = 3.5.17.47.89.113.503.14543
1511:               1521835381 = 11.19.61.79.1511
1513:                121247281 = 17.89.127.631
1517:                 48321001 = 37.41.53.601
1523:              13799091241 = 13.41.89.191.1523
1527:              53868563841 = 3.53.131.509.5081
1529:                  2704801 = 11.29.61.139
1531:                288120421 = 307.613.1531
1535:                602074585 = 5.7.137.307.409
1537:                 45890209 = 29.53.73.409
1541:                   340561 = 13.17.23.67
1543:             371345426881 = 11.13.853.1543.1973
1547:               2560104001 = 7.13.17.41.181.223
1549:                278152381 = 13.19.727.1549
1551:             126394016001 = 3.11.47.101.701.1151
1553:               1672719217 = 13.29.1553.2857
1559:                 26719701 = 3.29.197.1559
1561:               2199700321 = 7.13.61.223.1777
1563:                 11921001 = 3.29.263.521
1565:                  6054985 = 5.53.73.313
1567:               2201169601 = 31.113.401.1567
1571:            1301203515361 = 1571.25121.32971
1577:              18785465281 = 11.19.31.83.181.193
1579:              41812581601 = 7.37.1579.102241
1583:               2436691321 = 227.1583.6781
1585:               1776450565 = 5.317.523.2143
1589:              18382122451 = 7.11.19.227.55351
1591:                  8927101 = 31.37.43.181
1597:                 43331401 = 43.631.1597
1601:                 33302401 = 11.31.61.1601
1603:                  6840001 = 7.17.229.251
1605:          607368553651905 = 3.5.107.947.15137.26399
1607:                745864945 = 5.7.89.149.1607
1609:              11089049401 = 19.31.1609.11701
1613:              33300199505 = 5.17.89.1613.2729
1615:                   825265 = 5.7.17.19.73
1619:             666676060161 = 3.17.89.257.353.1619
1621:                 36765901 = 37.613.1621
1627:              60246018673 = 1627.3253.11383
1631:               2339165521 = 7.11.233.241.541
1633:                836515681 = 23.71.97.5281
1637:             153033820381 = 13.19.29.31.421.1637
1639:               9439491061 = 7.11.13.19.149.3331
1643:                 70561921 = 31.53.67.641
1645:               6295936465 = 5.7.13.37.47.73.109
1649:                 22665505 = 5.17.97.2749
1651:                426821473 = 13.127.419.617
1657:                227752993 = 13.97.109.1657
1661:                 40430401 = 11.101.151.241
1663:              13330320301 = 61.331.397.1663
1667:                569332177 = 239.1429.1667
1669:               8270944801 = 7.31.41.557.1669
1671:         3247889259130881 = 3.239.557.641.953.13313
1679:                934784929 = 13.23.73.113.379
1685:                 36121345 = 5.13.17.97.337
1687:                  9890881 = 7.11.13.41.241
1689:          158353658932305 = 3.5.17.89.149.563.83177
1691:                 84311569 = 19.73.89.683
1693:              10779325921 = 7.13.31.37.61.1693
1695:          294628486347105 = 3.5.53.113.11699.280337
1697:               3249390145 = 5.113.1697.3389
1699:              11542494601 = 11.43.53.271.1699
1707:            1334060626449 = 3.17.89.569.516539
1709:                 55462177 = 17.23.83.1709
1717:                151530401 = 11.17.71.101.113
1721:                153927961 = 11.47.173.1721
1723:               5165559169 = 43.113.617.1723
1727:                  6049681 = 11.31.113.157
1729:                     1729 = 7.13.19
1733:             155999871721 = 1733.5197.17321
1735:            1238761176445 = 5.13.19.347.523.5527
1739:                334783585 = 5.37.47.139.277
1741:                257495641 = 13.31.367.1741
1745:               1950276565 = 5.19.59.349.997
1747:               4212413569 = 7.13.1747.26497
1749:            2249558743641 = 3.11.53.59.4421.4931
1753:                393122521 = 11.19.29.37.1753
1757:                  6840001 = 7.17.229.251
1759:              97887454669 = 1759.3517.15823
1761:            4449488694321 = 3.11.587.5861.39191
1763:                 83966401 = 41.43.97.491
1765:                429553345 = 5.13.97.193.353
1769:                  2704801 = 11.29.61.139
1777:                  6313681 = 11.17.19.1777
1779:            6243651372801 = 3.59.593.641.92801
1781:                145124785 = 5.13.43.137.379
1783:                 15888313 = 7.19.67.1783
1787:            1527864562081 = 11.13.37.283.571.1787
1789:               3441837421 = 11.29.37.163.1789
1793:               2797002901 = 7.11.19.37.163.317
1795:                325546585 = 5.7.13.359.1993
1797:             718345813641 = 3.41.53.71.599.2591
1799:               1210178305 = 5.7.19.73.97.257
1801:                 48628801 = 13.31.67.1801
1807:                 41298985 = 5.7.13.139.653
1811:               1163659861 = 7.13.23.307.1811
1817:                106041937 = 17.23.79.3433
1819:                413631505 = 5.7.17.73.89.107
1823:            3695285036521 = 13.29.631.1823.8521
1829:                638959321 = 7.11.13.31.59.349
1831:                492559141 = 367.733.1831
1835:              99367251985 = 5.29.37.109.367.463
1837:             288572076001 = 11.73.151.167.14251
1841:              83056054081 = 7.11.13.31.263.10177
1843:                  2113921 = 19.31.37.97
1847:             660950414671 = 1847.12923.27691
1851:                662086041 = 3.89.617.4019
1853:                100427041 = 11.13.17.109.379
1855:                 13992265 = 5.7.19.53.397
1861:                775368901 = 373.1117.1861
1865:              41135881645 = 5.37.157.373.3797
1867:             663162938677 = 1867.11197.31723
1871:                139952671 = 131.571.1871
1873:               1027334881 = 53.79.131.1873
1877:              63734663077 = 269.1877.126229
1879:             835085057941 = 1879.16903.26293
1883:              12782849065 = 5.7.269.317.4283
1885:                440707345 = 5.13.29.113.2069
1889:                 99861985 = 5.97.109.1889
1891:                   172081 = 7.13.31.61
1895:                145124785 = 5.13.43.137.379
1897:                  4463641 = 7.13.181.271
1901:               2690867401 = 191.1901.7411
1903:                153927961 = 11.47.173.1721
1907:              97225715665 = 5.13.17.29.37.43.1907
1909:                 55462177 = 17.23.83.1709
1913:              83946864769 = 1913.5737.7649
1915:           55085381935585 = 5.23.383.8009.156157
1919:                 58489201 = 19.29.101.1051
1921:                   278545 = 5.17.29.113
1923:                174352641 = 3.71.641.1277
1927:               9216037441 = 13.37.41.47.61.163
1931:             238394136541 = 11.43.211.1237.1931
1933:                 11205601 = 11.17.31.1933
1937:                616463809 = 13.17.97.149.193
1939:                271481329 = 7.19.277.7369
1941:            7013994612801 = 3.11.281.491.647.2381
1943:                134857801 = 13.19.29.67.281
1945:              94706509885 = 5.13.197.389.19013
1947:            2249558743641 = 3.11.53.59.4421.4931
1949:             482368435201 = 19.101.1949.128971
1951:                 72286501 = 7.67.79.1951
1955:              23839510465 = 5.17.23.29.199.2113
1957:                 80927821 = 13.19.103.3181
1959:           39509680805445 = 3.5.653.27059.149069
1961:                  2433601 = 17.37.53.73
1963:                   838201 = 7.13.61.151
1969:               1362132541 = 7.11.37.179.2671
1973:              94572608065 = 5.13.349.1973.2113
1977:            1678722910593 = 3.29.53.113.659.4889
1979:               2117725921 = 17.19.1979.3313
1981:                182356993 = 7.13.73.97.283
1985:                 13992265 = 5.7.19.53.397
1987:              14983655041 = 17.31.41.349.1987
1991:                 67994641 = 11.13.37.71.181
1993:                325546585 = 5.7.13.359.1993
1997:             650186321401 = 41.73.181.601.1997
1999:              31956012001 = 67.397.601.1999
2001:            2273595031401 = 3.23.29.71.281.56951
2003:               1688214529 = 17.43.1153.2003
2011:               2607162961 = 13.31.2011.3217
2017:                  8134561 = 37.109.2017
2021:                301704985 = 5.43.47.73.409
2027:           19794508977127 = 2027.26339.370759
2029:               1773486001 = 7.23.61.89.2029
2031:          268563532783521 = 3.131.677.25541.39521
2033:               4340265931 = 19.43.107.131.379
2039:            3387719303201 = 2039.32609.50951
2045:                301704985 = 5.43.47.73.409
2047:                346808881 = 19.23.37.89.241
2049:            2710945737501 = 3.59.71.131.683.2411
2051:              19884155809 = 7.89.97.293.1123
2053:                 54767881 = 7.37.103.2053
2055:            4088711891265 = 3.5.137.233.239.35729
2059:                 64774081 = 29.71.163.193
2063:            5686932078001 = 17.31.37.109.1297.2063
2065:              15385904065 = 5.7.37.59.349.577
2069:                440707345 = 5.13.29.113.2069
2071:                   188461 = 7.13.19.109
2077:                 48628801 = 13.31.67.1801
2081:                 17316001 = 53.157.2081
2083:             469593692569 = 2083.8329.27067
2087:                552894301 = 43.61.101.2087
2089:                 43620409 = 7.19.157.2089
2091:               3022354401 = 3.11.17.41.101.1301
2093:                 27336673 = 7.13.23.37.353
2095:                590754385 = 5.13.109.199.419
2099:           17961771278977 = 29.43.1597.2099.4297
2101:                 72108421 = 7.11.191.4903
2103:             126394016001 = 3.11.47.101.701.1151
2111:             891024624721 = 7.11.61.73.1231.2111
2113:                 35703361 = 61.277.2113
2117:                    10585 = 5.29.73
2119:                  1082809 = 7.13.73.163
2123:                 37167361 = 7.11.41.61.193
2129:              27160421569 = 17.29.113.229.2129
2131:                776176261 = 7.61.853.2131
2137:                 13696033 = 13.17.29.2137
2141:              30189087001 = 73.233.829.2141
2143:                518706721 = 13.43.433.2143
2147:                  1569457 = 17.19.43.113
2149:                  1033669 = 7.13.37.307
2153:             353670332401 = 137.881.1361.2153
2157:           46748811068961 = 3.41.53.719.881.11321
2159:                 34196401 = 17.47.127.337
2161:                 88689601 = 7.11.13.41.2161
2165:                161242705 = 5.13.17.337.433
2167:                   656601 = 3.11.101.197
2171:              42646887361 = 13.17.19.61.167.997
2173:                 17812081 = 7.41.53.1171
2177:                181154701 = 7.13.37.173.311
2179:                593234929 = 7.19.23.89.2179
2183:                977737321 = 11.19.37.59.2143
2185:                  1050985 = 5.13.19.23.37
2191:                 44238481 = 7.61.313.331
2195:               4382684065 = 5.17.67.439.1753
2201:                382536001 = 31.71.151.1151
2203:            4259100803101 = 23.61.67.131.157.2203
2207:             225593397919 = 2207.6619.15443
2213:              20403012421 = 11.19.31.1423.2213
2215:                 60112885 = 5.7.443.3877
2219:               2797002901 = 7.11.19.37.163.317
2221:               1134044821 = 7.13.31.181.2221
2227:                931694401 = 11.17.73.131.521
2229:          227165699598321 = 3.11.29.71.743.1061.4241
2231:                  9582145 = 5.23.97.859
2235:          158353658932305 = 3.5.17.89.149.563.83177
2237:               4461725581 = 79.2237.25247
2239:            1223461962241 = 31.149.281.421.2239
2243:               5255104513 = 827.2243.2833
2245:                  5632705 = 5.13.193.449
2249:                181154701 = 7.13.37.173.311
2251:               1828377001 = 11.41.1801.2251
2257:                    29341 = 13.37.61
2261:                   825265 = 5.7.17.19.73
2263:                    15841 = 7.31.73
2267:               4351059901 = 31.101.613.2267
2269:                133800661 = 109.541.2269
2273:             152066684449 = 569.2273.117577
2279:               7687547869 = 43.53.149.22639
2281:                 93614521 = 7.11.13.41.2281
2283:             975648787041 = 3.107.137.761.29153
2285:               3575798785 = 5.13.17.73.97.457
2287:               5442435649 = 7.73.2287.4657
2291:                 18307381 = 29.61.79.131
2293:                 26280073 = 73.157.2293
2297:              15906120889 = 1723.2297.4019
2309:             636788093761 = 41.71.211.449.2309
2311:                122785741 = 13.61.67.2311
2315:               3263564305 = 5.53.67.397.463
2317:                 44238481 = 7.61.313.331
2319:          765157656692001 = 3.47.53.251.599.773.881
2321:                839275921 = 11.29.37.211.337
2323:                  9494101 = 23.61.67.101
2327:              56699735521 = 11.13.61.179.36313
2333:                168659569 = 13.67.83.2333
2335:            3408049527865 = 5.373.467.1399.2797
2339:           11104398708481 = 13.23.31.37.109.127.2339
2341:                115039081 = 157.313.2341
2343:             199438988001 = 3.11.41.71.431.4817
2345:                 40280065 = 5.7.67.89.193
2347:              27282539557 = 7.13.139.919.2347
2351:              51436355851 = 2351.4231.5171
2353:                  4463641 = 7.13.181.271
2357:                955134181 = 311.1303.2357
2363:              14527315201 = 7.17.31.41.139.691
2369:               6295079737 = 23.73.89.103.409
2371:              44431570261 = 13.397.2371.3631
2377:                146843929 = 163.379.2377
2381:                702683101 = 421.701.2381
2383:            2971847037601 = 13.19.31.271.601.2383
2387:                638959321 = 7.11.13.31.59.349
2389:                 62756641 = 109.241.2389
2391:       174470770903594881 = 3.23.41.53.797.12689.115061 [?]
2393:              30194397793 = 7.79.2393.22817
2395:            1348209080065 = 5.19.37.397.479.2017
2397:           97482954489537 = 3.17.47.55109.737969
2399:              12707942017 = 17.463.673.2399
2405:                  1050985 = 5.13.19.23.37
2407:              72042143041 = 11.19.29.71.83.2017
2411:              18500666251 = 1447.2411.5303
2413:                 12945745 = 5.19.29.37.127
2417:               7281824001 = 3.251.2417.4001
2419:              14483276281 = 19.41.59.181.1741
2423:              52364681461 = 61.347.1021.2423
2427:         1214896993439361 = 3.23.113.197.809.977681
2429:            7492890407905 = 5.7.37.97.347.397.433
2431:                    75361 = 11.13.17.31
2435:              33203881585 = 5.7.17.19.37.163.487
2437:               6512378041 = 13.19.31.349.2437
2441:                238244041 = 7.73.191.2441
2443:                638959321 = 7.11.13.31.59.349
2447:            5319173255761 = 113.2447.3271.5881
2449:                867800701 = 31.37.61.79.157
2453:               4077957961 = 7.11.31.47.163.223
2459:             534919693681 = 2459.9833.22123
2461:               4521794641 = 7.13.23.61.107.331
2463:           12996454877121 = 3.17.23.53.89.821.2861
2465:                     2465 = 5.17.29
2467:               8346731851 = 823.2467.4111
2471:                 27336673 = 7.13.23.37.353
2473:               9261585313 = 337.2473.11113
2477:            9035899110701 = 2477.17333.210461
2479:                403043257 = 19.37.43.67.199
2481:             330794193633 = 3.827.6569.20297
2483:               1825568641 = 13.31.37.191.641
2489:               4340265931 = 19.43.107.131.379
2491:               1070659201 = 17.47.53.131.193
2495:             534570793345 = 5.17.43.109.499.2689
2497:              18382122451 = 7.11.19.227.55351
2501:                   252601 = 41.61.101
2503:             235081952731 = 2503.7507.12511
2505:          222215555846145 = 3.5.29.167.449.653.10433
2507:               1162202581 = 23.43.109.10781
2509:                  3224065 = 5.13.193.257
2513:                325546585 = 5.7.13.359.1993
2515:                175997185 = 5.7.13.503.769
2517:        12832546007164521 = 3.11.29.71.281.839.801077
2519:                544101481 = 7.11.59.229.523
2521:                101649241 = 61.661.2521
2531:              15297796801 = 7.461.1873.2531
2533:                274569601 = 17.61.149.1777
2537:              17535604465 = 5.17.43.59.233.349
2539:              16851015469 = 19.163.2143.2539
2543:             550067193001 = 487.541.821.2543
2545:                 11119105 = 5.17.257.509
2549:              46652524465 = 5.17.197.1093.2549
2551:                683032801 = 11.101.241.2551
2555:                   825265 = 5.7.17.19.73
2557:               1954174465 = 5.353.433.2557
2561:                540066241 = 11.13.19.197.1009
2563:               2339165521 = 7.11.233.241.541
2567:                629692801 = 17.31.41.151.193
2569:                295643089 = 7.157.367.733
2571:       435262925087145321 = 3.23.857.2141.35597.96581 [?]
2573:              18785465281 = 11.19.31.83.181.193
2579:            1079942171239 = 2579.18047.23203
2581:               3576804001 = 29.89.101.13721
2587:                   670033 = 7.13.37.199
2589:    291226428348047343201 = 3.101.239.401.863.9011.1289621 [?]
2591:              34190968141 = 11.19.103.613.2591
2593:                120981601 = 13.37.97.2593
2595:       947087538769733505 = 3.5.17.23.173.929.2237.449153 [?]
2599:                934784929 = 13.23.73.113.379
2603:                130032865 = 5.19.97.103.137
2609:             111154590001 = 7.13.19.41.601.2609
2611:                 46483633 = 7.19.373.937
2615:               1776450565 = 5.317.523.2143
2617:             392807075761 = 19.37.89.2399.2617
2621:                542497201 = 263.787.2621
2623:                 10877581 = 11.13.29.43.61
2627:                 67994641 = 11.13.37.71.181
2629:                962500561 = 11.239.269.1361
2633:               5599487881 = 13.29.2633.5641
2641:                 81926461 = 19.67.139.463
2643:           46748811068961 = 3.41.53.719.881.11321
2647:               8355729313 = 17.19.29.337.2647
2651:                  9890881 = 7.11.13.41.241
2657:               3521441665 = 5.7.19.1993.2657
2659:             185602824001 = 7.31.67.2659.4801
2661:         8022231726890001 = 3.101.251.887.1091.109001
2663:             374811729601 = 727.2663.193601
2669:                977892241 = 17.31.53.157.223
2671:               1362132541 = 7.11.37.179.2671
2677:              12801448801 = 29.269.613.2677
2681:            1996385311921 = 7.11.13.17.31.41.241.383
2683:                957044881 = 13.23.1193.2683
2685: 114593508055911048606465 = 3.5.23.179.1409.8297.33287.4768493 [?]
2687:            1123391597833 = 307.953.1429.2687
2689:                238527745 = 5.113.157.2689
2693:                746706961 = 7.11.13.277.2693
2699:              28173681537 = 3.353.2699.9857
2701:                   294409 = 37.73.109
2703:           12996454877121 = 3.17.23.53.89.821.2861
2707:                710541481 = 13.61.331.2707
2711:                139592101 = 11.31.151.2711
2713:               3480174001 = 227.2713.5651
2717:                129255841 = 11.13.19.113.421
2719:              15157389061 = 19.181.1621.2719
2723:              82268656561 = 7.13.31.61.389.1229
2729:              33300199505 = 5.17.89.1613.2729
2731:                 14913991 = 43.127.2731
2733:              61811815521 = 3.71.113.911.2819
2735:               3637405045 = 5.43.157.197.547
2737:               1597009393 = 7.17.23.73.7993
2739:         3289207215669441 = 3.11.53.83.131.191.821.1103
2741:              12760070401 = 13.113.2741.3169
2743:                  3146221 = 13.31.37.211
2747:                975303121 = 13.31.41.67.881
2749:                 22665505 = 5.17.97.2749
2753:                 75765313 = 13.29.73.2753
2755:                   449065 = 5.19.29.163
2759:               3119101921 = 13.19.23.31.89.199
2761:                188689501 = 7.11.13.251.751
2765:               5368969165 = 5.7.53.79.36637
2767:               5487578041 = 11.29.2767.6217
2771:                545363281 = 17.23.43.163.199
2773:            7092343919761 = 47.59.3037.842161
2777:               4216799521 = 11.31.61.73.2777
2779:                 13992265 = 5.7.19.53.397
2785:           20910960976465 = 5.7.157.223.557.30637
2787:            3713121557601 = 3.17.131.281.929.2129
2789:              13654188181 = 37.307.431.2789
2791:                194675041 = 11.17.373.2791
2795:                115542505 = 5.13.43.67.617
2797:              49237316749 = 1399.2797.12583
2801:               1348964401 = 401.1201.2801
2803:             642716875801 = 7.11.13.37.41.151.2803
2807:                241242001 = 7.11.13.401.601
2813:                612347905 = 5.13.17.29.97.197
2815:            2652506486785 = 5.463.563.1009.2017
2819:              61811815521 = 3.71.113.911.2819
2821:                     2821 = 7.13.31
2823:           28148013211641 = 3.29.41.941.2423.3461
2827:               1031750401 = 11.31.61.193.257
2829:            1772996733201 = 3.23.41.89.101.113.617
2831:                 12261061 = 19.61.71.149
2833:                545570641 = 7.11.41.61.2833
2837:             479252075149 = 67.127.2837.19853
2839:              42646887361 = 13.17.19.61.167.997
2841:          607368553651905 = 3.5.107.947.15137.26399
2843:             261890754721 = 17.61.211.421.2843
2845:             251841872305 = 5.67.569.1033.1279
2849:                672389641 = 7.11.37.53.61.73
2851:               3030758401 = 11.241.401.2851
2857:               1672719217 = 13.29.1553.2857
2859:            7326285446481 = 3.23.53.281.953.7481
2861:               9139810681 = 859.2861.3719
2863:                602074585 = 5.7.137.307.409
2867:               4852062061 = 7.11.31.47.61.709
2869:                 78120001 = 19.73.151.373
2879:               8956911601 = 11.17.127.131.2879
2881:                115542505 = 5.13.43.67.617
2885:                 84417985 = 5.29.577.1009
2887:               9739972945 = 5.17.19.2089.2887
2893:              29483017201 = 11.31.263.547.601
2897:             128295478801 = 7.37.163.1049.2897
2899:               2199700321 = 7.13.61.223.1777
2903:             733547013841 = 2903.8707.29021
2905:              18390744505 = 5.7.83.1453.4357
2909:              41983866145 = 5.13.17.37.353.2909
2911:                548871961 = 11.41.61.71.281
2913:            5587772812161 = 3.23.29.353.971.8147
2917:              12299638429 = 13.19.43.397.2917
2921:               2342644921 = 23.31.41.127.631
2923:                  8719309 = 19.37.79.157
2927:              20871450601 = 463.2927.15401
2929:                 58489201 = 19.29.101.1051
2931:         1299934624255521 = 3.59.881.977.2411.3539
2933:               1615335085 = 5.7.13.37.229.419
2935:             510675333805 = 5.7.13.587.1087.1759
2939:            2583708107761 = 11.31.41.227.277.2939
2941:               4752717761 = 11.17.107.173.1373
2949:     13053581557039793157 = 3.173.983.9203.27179.102293 [?]
2951:              27360228961 = 13.17.31.73.227.241
2953:                897880321 = 13.19.1231.2953
2955:              77403893505 = 3.5.197.227.257.449
2957:               2159003281 = 17.29.1481.2957
2959:                962500561 = 11.239.269.1361
2963:              33604861537 = 13.17.19.37.73.2963
2965:                 28787185 = 5.7.19.73.593
2969:                484662529 = 13.29.433.2969
2971:                 26474581 = 7.19.67.2971
2977:                 18900973 = 7.13.229.907
2981:                   658801 = 11.13.17.271
2983:                  8719309 = 19.37.79.157
2987:              17163788881 = 29.103.113.211.241
2993:                   410041 = 41.73.137
2995:                 15403285 = 5.37.139.599
2999:           63237358424809 = 2999.137909.152899```

This list has been extended (in December 2007) to all divisors below 10000.
We also have (since 2003) a complete list of the  least  Carmichael multiples of all odd primes below 10000.

I put online the first version of the above table in 2003  (Gérard P. Michon,  2003-12-01).  At first, it was strictly a compilation of the smallest Carmichael multiples (with 16 digits or less) of all divisors up to 2999.

An integer can have a Carmichael multiple only if it's an odd number coprime to its Euler totient (i.e., a  cyclic number  other than 2).  Many years ago, I formulated the conjecture that this necessary condition was also sufficient  (i.e., all odd cyclic numbers have Carmichael multiples )  and the table was meant to provide computational support for that conjecture.  Among all such numbers below 3000, the original table featured only  8  gaps  (885, 2391, 2517, 2571, 2589, 2595, 2685 and 2949).  This is how it remained for over 4 years...

On  2007-08-04,  Max Alekseyev  ("Maxal")  kindly credited me with that conjecture in the Open Problem Garden and challenged people to plug those gaps.  As chronicled below, that challenge was met in December 2007  by  Joe K. Crump  (starting with the divisor 2517).  Joe used tools which need not produce the smallest Carmichael multiple of a given divisor.

In the above table, a question mark [?] is used to indicate that the Carmichael number listed need not be the smallest Carmichael multiple of the relevant divisor.  No such mark is needed for the Carmichael multiple of 2517 first discovered by Joe Crump, though...  Once Joe had paved the way, it took us only a few hours (on 2007-12-22) to establish that it's indeed the smallest one there is  (it happens to be only 28% above the arbitrary cutoff limit we used in 2003).

DivisorCarmichael Multiple(s) AuthorDate

885:24354644805191195265  Joe Crump2007-12-21
2391:174470770903594881582506871340419201 Joe Crump2007-12-21
2517:12832546007164521  Joe Crump2007-12-20
2571:4352629250871453211340771505059480001 Joe Crump2007-12-21
2589: 291226428348047343201    401998541941991167041    Joe Crump    2007-12-21
2595:947087538769733505  Joe Crump2007-12-21
2685: 114593508055911048606465  Joe Crump2007-12-24
2949:13053581557039793157  Joe Crump2007-12-21