Carmichael numbers 的分解

蔡家雄 · 发表于 2026-7-10 22:21

本帖最后由蔡家雄于 2026-7-31 07:52 编辑

设 m=6k，

若 m^2+1,  2m^2+1,  3m^2+1 都是质数，

则 (m^2+1)(2m^2+1)(3m^2+1) 必是卡迈克尔数。

设 m=84k+6 或 m=84k+78，

若 m^2+1,  3m^2+1,  56m^2+1 都是质数，

则 (m^2+1)(3m^2+1)(56m^2+1) 必是卡迈克尔数。

设 m=42k+6 或 m=42k+36，

若 m^2+1,  2m^2+1,  12m^2+1,  21m^2+1 都是质数，

则 (m^2+1)(2m^2+1)(12m^2+1)(21m^2+1) 必是卡迈克尔数。

设 m=70k+6 或 m=70k+64，

若 m^2+1,  2m^2+1,  5m^2+1,  70m^2+1 都是质数，

则 (m^2+1)(2m^2+1)(5m^2+1)(70m^2+1) 必是卡迈克尔数。

设 m=90k+6 或 m=90k+84，

若 m^2+1,  2m^2+1,  45m^2+1,  60m^2+1 都是质数，

则 (m^2+1)(2m^2+1)(45m^2+1)(60m^2+1) 必是卡迈克尔数。

设 m=510k+6 或 m=510k+504，

若 2m^2+1,  3m^2+1,  5m^2+1,  15m^2+1,  17m^2+1 都是质数，

则 (2m^2+1)(3m^2+1)(5m^2+1)(15m^2+1)(17m^2+1) 必是卡迈克尔数。

设 (m+1, 2m+1, 3m+1) 与 (6m+1, 12m+1, 18m+1) 都是质数，

且 m=36k+6，

则 (m+1)(2m+1)(3m+1) * (6m+1)(12m+1)(18m+1) 必是卡迈克尔数。

如 509033161=(7*13*19) * (37*73*109) = 两个卡迈克尔数的乘积。

设 (2m+1, 10m+1, 66m+1) 与 (5m+1, 30m+1, 55m+1) 都是质数，

且 m=330k+6，

则 (2m+1)(10m+1)(66m+1) * (5m+1)(30m+1)(55m+1) 必是卡迈克尔数。

如 584698468861=(13*61*397) * (31*181*331) = 两个卡迈克尔数的乘积。

是否存在 7个素因子的卡迈克尔数 = 两个卡迈克尔数的乘积？并且有两种不同的分拆方式？？

设 (m+1, 2m+1, 5m+1, 10m+1) 与 (6m+1, 12m+1, 30m+1) 都是质数，

且 m=60k+6，

则 (m+1)(2m+1)(5m+1)(10m+1) * (6m+1)(12m+1)(30m+1) 必是卡迈克尔数，

则 (m+1)(5m+1)(12m+1) * (2m+1)(6m+1)(10m+1)(30m+1) 必是卡迈克尔数。

如 84127131361=(7*13*31*61) * (37*73*181) = 两个卡迈克尔数的乘积，

且 84127131361=(7*31*73) * (13*37*61*181) = 两个卡迈克尔数的乘积。

如 167322186003243570600968222134860395423562961=(359407*718813*1797031*3594061) * (2156437*4312873*10782181)

且 167322186003243570600968222134860395423562961=(359407*1797031*4312873) * (718813*2156437*3594061*10782181)

是否存在 8个素因子的卡迈克尔数 = 两个卡迈克尔数的乘积？并且有两种不同的分拆方式？？

例1（最小的双分拆 8素因子卡迈克尔数）
C = 39218375198807825413908500199133921
  = 163*379*2377*16633*216217*277993*432433*617761

分拆一（4+4）
C = (163*379*432433*617761) * (2377*16633*216217*277993)
  = 16503122761725601 * 2376421466715616321

分拆二（3+5）
C = (216217*277993*617761) * (163*379*2377*16633*432433)
  = 37131644585075041 * 1056198173742391681

例2
C = 38610448457205183805452289211975246401
  = 73*1171*5347*66529*99793*151201*432433*194594401

分拆一（3+5）
C = (66529*99793*432433) * (73*1171*5347*151201*194594401)
  = 2870978253343201 * 13448533931681311663201

分拆二（4+4）
C = (73*1171*5347*151201) * (66529*99793*432433*194594401)
  = 69110590348801 * 558676293493346446017601

例3
C = 8819897625708057066460592134761234830532001
  = 163*379*118801*432433*617761*3088801*7484401*194594401

分拆一（3+5）
C = (118801*3088801*7484401) * (163*379*432433*617761*194594401)
  = 2746420762657572001 * 3211415288447459052960001

分拆二（4+4）
C = (163*379*432433*617761) * (118801*3088801*7484401*194594401)
  = 16503122761725601 * 534438103203313391648966401

是否存在 9个素因子的卡迈克尔数 = 两个卡迈克尔数的乘积？并且有两种不同的分拆方式？？

例1（4+5 与 3+6 双分拆）
C = 2789987203657877406282581090230702081
  = 199*421*1093*23167*23761*66529*72073*96097*120121

分拆一（4+5）
C = (421*1093*66529*72073) * (199*23167*23761*96097*120121)
  = 2206408150346401 * 1264492792604965603681

分拆二（3+6）
C = (72073*96097*120121) * (199*421*1093*23167*23761*66529)
  = 831957935608801 * 3353519552182949429281

例2（4+5 与 3+6 双分拆）
C = 140246659764577195950187264754865147841
  = 199*4621*9241*23167*23761*36037*72073*96097*120121

分拆一（4+5）
C = (4621*9241*36037*72073) * (199*23167*23761*96097*120121)
  = 110911395133899361 * 1264492792604965603681

分拆二（3+6）
C = (72073*96097*120121) * (199*4621*9241*23167*23761*36037)
  = 831957935608801 * 168574219635213939587041

例3（两种不同的 4+5 分拆）
C = 160388716420554107462919949518832321
  = 163*379*1093*2377*8737*16633*25741*432433*617761

分拆一（4+5）
C = (163*379*432433*617761) * (1093*2377*8737*16633*25741)
  = 16503122761725601 * 9718688925500274721

分拆二（4+5）
C = (1093*8737*25741*617761) * (163*379*2377*16633*432433)
  = 151854756434821441 * 1056198173742391681

是否存在 10个素因子的卡迈克尔数 = 两个卡迈克尔数的乘积？并且有两种不同的分拆方式？？？？

类型一：4 种分拆方式（两种3+7，两种4+6）

C = 2014399835982717990242168544555837782792946991468321
  = 2269*7561*8317*66529*99793*432433*540541*1297297*1621621*4324321

分拆1（3+7）: (66529*99793*432433) * (2269*7561*8317*540541*1297297*1621621*4324321)
  = 2870978253343201 * 701642317783837857979218071025741121

分拆2（3+7）: (540541*1621621*4324321) * (2269*7561*8317*66529*99793*432433*1297297)
  = 3790494975615828481 * 531434508933874917972801012452641

分拆3（4+6）: (2269*7561*8317*1297297) * (66529*99793*432433*540541*1621621*4324321)
  = 185105724264901441 * 10882428644399710517655351643507681

分拆4（4+6）: (432433*540541*1297297*1621621) * (2269*7561*8317*66529*99793*4324321)
  = 491740799472344388526561 * 4096466752696220568878372161

类型二：两种不同的 5+5 分拆

C = 13356580255947768358117079760227126886393285601
  = 5281*7393*8317*21061*23167*45361*51481*72073*270271*1853281

分拆1（5+5）: (5281*7393*8317*21061*45361) * (23167*51481*72073*270271*1853281)
  = 310216707031800048481 * 43055644500083603735867521

分拆2（5+5）: (5281*7393*23167*270271*1853281) * (8317*21061*45361*51481*72073)
  = 453051313870384009740961 * 29481385103694958674241

类型三：4+6 与 5+5 双分拆

C = 824906498112295473518874025533340783820641
  = 313*5281*7393*8317*21061*21841*26209*45361*120121*123553

分拆1（4+6）: (8317*21061*45361*123553) * (313*5281*7393*21841*26209*120121)
  = 981706360459144321 * 840278245448553973981921

分拆2（5+5）: (313*21841*26209*120121*123553) * (5281*7393*8317*21061*45361)
  = 2659129825743830799361 * 310216707031800048481

类型四：3+7 与 5+5 双分拆

C = 913167546501014199003549106284032498522178241
  = 157*313*3169*6553*21061*28513*393121*540541*1621621*4324321

分拆1（3+7）: (540541*1621621*4324321) * (157*313*3169*6553*21061*28513*393121)
  = 3790494975615828481 * 240909842217283260430368961

分拆2（5+5）: (157*313*393121*540541*4324321) * (3169*6553*21061*28513*1621621)
  = 45156138800535398956321 * 20222445292204370735521

cz1 · 发表于 2026-8-11 18:21

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蔡家雄 · 发表于 2026-7-19 10:09

求 10 个素因子的卡迈克尔数，且每个素因子均为 36k+1 的形式。

设 S = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 68344819201 是前 8个素因子的乘积，

如下是 39 个例子的前 34 个例子，

C1 = S * 205034457601 * 5809241287180801.

C2 = S * 11345239987201 * 181523839795201.
C3 = S * 11345239987201 * 49216286397912883201.
C4 = S * 11345239987201 * 27249002007424394803201.
C5 = S * 11345239987201 * 2975075296467435876556801.
C6 = S * 11345239987201 * 5950150592934871753113601.
C7 = S * 11345239987201 * 6279030803985991084440323481601.
C8 = S * 11345239987201 * 12558061607971982168880646963201.
C9 = S * 11345239987201 * 5301476058244096965499019509937155799222476801.
C10 = S * 11345239987201 * 359345312864408661027575227799999036527372825267201.
C11 = S * 11345239987201 * 795817959318121983677432065723061364566112453910348801.
C12 = S * 11345239987201 * 3452302873327734980023786237302320690924211527360512073932801.

C13 = S * 36947619328435201 * 2525548586368162051846195201.
C14 = S * 36947619328435201 * 17810155541038401357488179201.
C15 = S * 36947619328435201 * 480230510944954759394744908801.
C16 = S * 36947619328435201 * 718047558010384441527573218995201.
C17 = S * 36947619328435201 * 829044930279796544789717253580801.
C18 = S * 36947619328435201 * 1092288138988387159881422453024870401.
C19 = S * 36947619328435201 * 3544866596315143670612033350015113864038401.
C20 = S * 36947619328435201 * 28334616543107429035525369902228653758310401.
C21 = S * 36947619328435201 * 692252379258740168432562869724143277003878401.
C22 = S * 36947619328435201 * 4958976501742598197648639622460618573633992585395201.

C23 = S * 1262827317735244801 * 5051309270940979201.
C24 = S * 1262827317735244801 * 19999613437271722359705601.
C25 = S * 1262827317735244801 * 568013821273948063300070401.
C26 = S * 1262827317735244801 * 1704041463821844189900211201.
C27 = S * 1262827317735244801 * 7384179676561324822900915201.
C28 = S * 1262827317735244801 * 3972555779637591207696775527854882976558505284084715066598401.

C29 = S * 114802483430476801 * 77376873832141363201.
C30 = S * 114802483430476801 * 12783489888302845909608499201.
C31 = S * 114802483430476801 * 280262174751081153623244709986328655613270813423363058022401.
C32 = S * 114802483430476801 * 531001182725713105603684710166975805961642179141891135155201.

C33 = S * 1888247272648665601 * 251136887262272524801.
C34 = S * 1888247272648665601 * 102440051774961184467350899201.

蔡家雄 · 发表于 2026-7-19 09:21

求 9个素因子的卡迈克尔数，且每个素因子均为 36k+1 的形式。

主族 10 个例子，

设 S = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 68344819201 是前 8个素因子的乘积，

C1 = S * 205034457601.
C2 = S * 11345239987201.
C3 = S * 36947619328435201.
C4 = S * 114802483430476801.
C5 = S * 1262827317735244801.
C6 = S * 1888247272648665601.
C7 = S * 1723969759928231692801.
C8 = S * 23892258015652650921302121514981339081682918401.
C9 = S * 330509569216528337744679347623908523963280371201.
C10 = S * 1114808776967350083212803439535443451328144692057601.

蔡家雄 · 发表于 2026-7-19 09:08

求 8个素因子的卡迈克尔数，且每个素因子均为 36k+1 的形式。

8 个例子（仅第 8 个素因子不同）

C1 = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 68344819201.
C2 = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 700534396801.
C3 = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 2451870388801.
C4 = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 4903740777601.
C5 = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 19614963110401.
C6 = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 4520446056527873018299201.
C7 = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 508642968793126133600323201.
C8 = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401 * 20854361720518171477613251201.

蔡家雄 · 发表于 2026-7-19 08:53

求 7个素因子的卡迈克尔数，且每个素因子均为 36k+1 的形式。

例 1（43 位）
C = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 8543102401.

例 2（43 位）
C = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 25629307201.

例 3（43 位）
C = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241 * 64073268001.

这三个例子：前六个素因子竟然是：完全相同。

蔡家雄 · 发表于 2026-7-19 08:38

求 6个素因子的卡迈克尔数，且每个素因子均为 36k+1 的形式。

例 1（33 位）

C = 1297 * 2593 * 3889 * 567649 * 19867681 * 854310241.

例 2（33 位）

C = 1297 * 2593 * 3889 * 567649 * 60170689 * 361024129.

蔡家雄 · 发表于 2026-7-18 18:19

是否存在 10个素因子的卡迈克尔数 = 两个卡迈克尔数的乘积？并且有两种不同的分拆方式？？？？

类型一：4 种分拆方式（两种3+7，两种4+6）

N = 2014399835982717990242168544555837782792946991468321
  = 2269*7561*8317*66529*99793*432433*540541*1297297*1621621*4324321

分拆1（3+7）: (66529*99793*432433) * (2269*7561*8317*540541*1297297*1621621*4324321)
  = 2870978253343201 * 701642317783837857979218071025741121

分拆2（3+7）: (540541*1621621*4324321) * (2269*7561*8317*66529*99793*432433*1297297)
  = 3790494975615828481 * 531434508933874917972801012452641

分拆3（4+6）: (2269*7561*8317*1297297) * (66529*99793*432433*540541*1621621*4324321)
  = 185105724264901441 * 10882428644399710517655351643507681

分拆4（4+6）: (432433*540541*1297297*1621621) * (2269*7561*8317*66529*99793*4324321)
  = 491740799472344388526561 * 4096466752696220568878372161

类型二：两种不同的 5+5 分拆

N = 13356580255947768358117079760227126886393285601
  = 5281*7393*8317*21061*23167*45361*51481*72073*270271*1853281

分拆1（5+5）: (5281*7393*8317*21061*45361) * (23167*51481*72073*270271*1853281)
  = 310216707031800048481 * 43055644500083603735867521

分拆2（5+5）: (5281*7393*23167*270271*1853281) * (8317*21061*45361*51481*72073)
  = 453051313870384009740961 * 29481385103694958674241

类型三：4+6 与 5+5 双分拆

N = 824906498112295473518874025533340783820641
  = 313*5281*7393*8317*21061*21841*26209*45361*120121*123553

分拆1（4+6）: (8317*21061*45361*123553) * (313*5281*7393*21841*26209*120121)
  = 981706360459144321 * 840278245448553973981921

分拆2（5+5）: (313*21841*26209*120121*123553) * (5281*7393*8317*21061*45361)
  = 2659129825743830799361 * 310216707031800048481

类型四：3+7 与 5+5 双分拆

N = 913167546501014199003549106284032498522178241
  = 157*313*3169*6553*21061*28513*393121*540541*1621621*4324321

分拆1（3+7）: (540541*1621621*4324321) * (157*313*3169*6553*21061*28513*393121)
  = 3790494975615828481 * 240909842217283260430368961

分拆2（5+5）: (157*313*393121*540541*4324321) * (3169*6553*21061*28513*1621621)
  = 45156138800535398956321 * 20222445292204370735521

蔡家雄 · 发表于 2026-7-18 18:18

10个素因子的卡迈克尔数 = 3个素因子的卡迈克尔数 * 3个素因子的卡迈克尔数 * 4个素因子的卡迈克尔数，

例1
N = 3925412143946591773794095422858607946270721
  = (66529*99793*432433) * (72073*96097*120121) * (43*547*7561*9241)
C3a = 2870978253343201 = 66529*99793*432433
C3b = 831957935608801 = 72073*96097*120121
C4  = 1643440518721 = 43*547*7561*9241

例2
N = 6024922928628578439411173683193240291268481
  = (66529*99793*432433) * (72073*96097*120121) * (79*1249*3121*8191)
C3a = 2870978253343201 = 66529*99793*432433
C3b = 831957935608801 = 72073*96097*120121
C4  = 2522436396481 = 79*1249*3121*8191

例3
N = 178848020168077207290378838822281478967150401
  = (66529*99793*432433) * (108109*540541*648649) * (43*547*7561*9241)
C3a = 2870978253343201 = 66529*99793*432433
C3b = 37905326674094881 = 108109*540541*648649
C4  = 1643440518721 = 43*547*7561*9241

例4
N = 12069973453748547706639927719378691864200013542241
  = (66529*99793*432433) * (108109*540541*648649) * (4621*9241*36037*72073)
C3a = 2870978253343201 = 66529*99793*432433
C3b = 37905326674094881 = 108109*540541*648649
C4  = 110911395133899361 = 4621*9241*36037*72073

10个素因子的卡迈克尔数 = 5个素因子的卡迈克尔数 * 5个素因子的卡迈克尔数，

例1
N = 806554041147262860120789121
  = (19*37*811*1621*2377) * (31*61*2161*2971*30241)
C5a = 2196789154561 = 19*37*811*1621*2377
C5b = 367151321496961 = 31*61*2161*2971*30241

例2
N = 153523043513129795284952172001
  = (19*43*2017*5281*48049) * (31*61*2161*2971*30241)
C5a = 418146509420641 = 19*43*2017*5281*48049
C5b = 367151321496961 = 31*61*2161*2971*30241

例3
N = 68563976841990527861918391877441
  = (19*109*10531*25741*332641) * (31*61*2161*2971*30241)
C5a = 186745826114527681 = 19*109*10531*25741*332641
C5b = 367151321496961 = 31*61*2161*2971*30241

例4
N = 269902391078637526403113921
  = (19*127*241*547*2311) * (31*61*2161*2971*30241)
C5a = 735125751361 = 19*127*241*547*2311
C5b = 367151321496961 = 31*61*2161*2971*30241

10个素因子的卡迈克尔数 = 4个素因子的卡迈克尔数 * 6个素因子的卡迈克尔数，

例1
N = 891735484108862543505395041
  = (43*547*7561*9241) * (19*31*181*211*859*28081)
C4 = 1643440518721 = 43*547*7561*9241
C6 = 542602834693921 = 19*31*181*211*859*28081

例2
N = 18005865586532801171982627841
  = (43*547*7561*9241) * (19*31*79*397*1783*332641)
C4 = 1643440518721 = 43*547*7561*9241
C6 = 10956201567030721 = 19*31*79*397*1783*332641

例3
N = 146359577790385302582439201
  = (43*547*7561*9241) * (19*79*157*181*1171*1783)
C4 = 1643440518721 = 43*547*7561*9241
C6 = 89056814726881 = 19*79*157*181*1171*1783

例4
N = 481968437161231950359189761
  = (43*547*7561*9241) * (19*67*157*271*631*8581)
C4 = 1643440518721 = 43*547*7561*9241
C6 = 293267953218241 = 19*67*157*271*631*8581

10个素因子的卡迈克尔数 = 3个素因子的卡迈克尔数 * 7个素因子的卡迈克尔数，

例1
N = 3925412143946591773794095422858607946270721
  = (66529*99793*432433) * (43*547*7561*9241*72073*96097*120121)
C3 = 2870978253343201 = 66529*99793*432433
C7 = 1367273381250980232372863521 = 43*547*7561*9241*72073*96097*120121

例2
N = 178848020168077207290378838822281478967150401
  = (66529*99793*432433) * (43*547*7561*9241*108109*540541*648649)
C3 = 2870978253343201 = 66529*99793*432433
C7 = 62295149731563448943810767201 = 43*547*7561*9241*108109*540541*648649

例3
N = 17884624176296529104797750533707923134587796001
  = (66529*99793*432433) * (43*547*7561*9241*540541*1621621*4324321)
C3 = 2870978253343201 = 66529*99793*432433
C7 = 6229453028935421405232805492801 = 43*547*7561*9241*540541*1621621*4324321

例4
N = 6024922928628578439411173683193240291268481
  = (72073*96097*120121) * (79*1249*3121*8191*66529*99793*432433)
C3 = 831957935608801 = 72073*96097*120121
C7 = 7241860039738339421401675681 = 79*1249*3121*8191*66529*99793*432433

有意思的是：这里的 C7 = 两个卡迈克尔数的乘积，

所以这些 N 同时兼具：10 = 3 * 7 和 10 = 3 * (3 * 4) 两种不同的分拆方式。

蔡家雄 · 发表于 2026-7-18 18:16

是否存在 9个素因子的卡迈克尔数 = 两个卡迈克尔数的乘积？并且有两种不同的分拆方式？？

例1（4+5 与 3+6 双分拆）
N = 2789987203657877406282581090230702081
  = 199*421*1093*23167*23761*66529*72073*96097*120121

分拆一（4+5）
N = (421*1093*66529*72073) * (199*23167*23761*96097*120121)
  = 2206408150346401 * 1264492792604965603681

分拆二（3+6）
N = (72073*96097*120121) * (199*421*1093*23167*23761*66529)
  = 831957935608801 * 3353519552182949429281

例2（4+5 与 3+6 双分拆）
N = 140246659764577195950187264754865147841
  = 199*4621*9241*23167*23761*36037*72073*96097*120121

分拆一（4+5）
N = (4621*9241*36037*72073) * (199*23167*23761*96097*120121)
  = 110911395133899361 * 1264492792604965603681

分拆二（3+6）
N = (72073*96097*120121) * (199*4621*9241*23167*23761*36037)
  = 831957935608801 * 168574219635213939587041

例3（两种不同的 4+5 分拆）
N = 160388716420554107462919949518832321
  = 163*379*1093*2377*8737*16633*25741*432433*617761

分拆一（4+5）
N = (163*379*432433*617761) * (1093*2377*8737*16633*25741)
  = 16503122761725601 * 9718688925500274721

分拆二（4+5）
N = (1093*8737*25741*617761) * (163*379*2377*16633*432433)
  = 151854756434821441 * 1056198173742391681

蔡家雄 · 发表于 2026-7-18 15:54

9个素因子的卡迈克尔数 = 3个素因子的卡迈克尔数 * 3个素因子的卡迈克尔数 * 3个素因子的卡迈克尔数，

例1
N = 90538128975031592128008078029861032320349766881
  = (66529*99793*432433) * (72073*96097*120121) * (108109*540541*648649)
C3a = 2870978253343201 = 66529*99793*432433
C3b = 831957935608801 = 72073*96097*120121
C3c = 37905326674094881 = 108109*540541*648649

例2
N = 9053722869404865918005515557890602177317854700481
  = (66529*99793*432433) * (72073*96097*120121) * (540541*1621621*4324321)
C3a = 2870978253343201 = 66529*99793*432433
C3b = 831957935608801 = 72073*96097*120121
C3c = 3790494975615828481 = 540541*1621621*4324321

例3
N = 141374605565107635677482717829544357717593012814448321
  = (96097*432433*4084081) * (123553*216217*2625481) * (656371*1969111*9189181)
C3a = 169716085176718081 = 96097*432433*4084081
C3b = 70137779436204481 = 123553*216217*2625481
C3c = 11876716472538677761 = 656371*1969111*9189181

例4
N = 1751508671143825689759237284786702259289453884433426081
  = (96097*432433*4084081) * (123553*216217*2625481) * (816817*1633633*110270161)
C3a = 169716085176718081 = 96097*432433*4084081
C3b = 70137779436204481 = 123553*216217*2625481
C3c = 147142209898425661921 = 816817*1633633*110270161

9个素因子的卡迈克尔数 = 4个素因子的卡迈克尔数 * 5个素因子的卡迈克尔数，

例1
N = 3610292307692396883036481
  = (43*547*7561*9241) * (19*37*811*1621*2377)
C4 = 1643440518721 = 43*547*7561*9241
C5 = 2196789154561 = 19*37*811*1621*2377

例2
N = 1054747974424110203081164321
  = (79*1249*3121*8191) * (19*43*2017*5281*48049)
C4 = 2522436396481 = 79*1249*3121*8191
C5 = 418146509420641 = 19*43*2017*5281*48049

例3
N = 3081889293607912923250174640861281
  = (163*379*432433*617761) * (19*109*10531*25741*332641)
C4 = 16503122761725601 = 163*379*432433*617761
C5 = 186745826114527681 = 19*109*10531*25741*332641

例4
N = 181122459218423982014383948321
  = (271*2593*270271*1297297) * (19*127*241*547*2311)
C4 = 246382960851387361 = 271*2593*270271*1297297
C5 = 735125751361 = 19*127*241*547*2311

9个素因子的卡迈克尔数 = 3个素因子的卡迈克尔数 * 6个素因子的卡迈克尔数，

例1
N = 31455016438189901107916923477921
  = (66529*99793*432433) * (19*31*79*397*1783*332641)
C3 = 2870978253343201 = 66529*99793*432433
C6 = 10956201567030721 = 19*31*79*397*1783*332641

例2
N = 43326653797049296866999504071774401
  = (72073*96097*120121) * (19*31*127*21841*24571*1297297)
C3 = 831957935608801 = 72073*96097*120121
C6 = 52077938009382885601 = 19*31*127*21841*24571*1297297

例3
N = 20567537703362979006507347918401
  = (108109*540541*648649) * (19*31*181*211*859*28081)
C3 = 37905326674094881 = 108109*540541*648649
C6 = 542602834693921 = 19*31*181*211*859*28081

例4
N = 18430727670359758177838222317629121
  = (540541*1621621*4324321) * (19*31*199*331*541*231661)
C3 = 3790494975615828481 = 540541*1621621*4324321
C6 = 4862353805749441 = 19*31*199*331*541*231661

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