问题及解答

关于 $10^n+1$ 的因子分解

11
101
1001 = 7 * 11 * 13
10001 = 73 * 137
100001 = 11 * 9091
1000001 = 101 * 9901
10000001 = 11 * 909091
100000001 = 17 * 5882353
1000000001 = 7 * 11 * 13 * 19 * 52579
10000000001 = 101 * 3541 * 27961
100000000001 = 11 * 11 * 23 * 4093 * 8779
1000000000001 = 73 * 137 * 99990001
10000000000001 = 11 * 859 * 1058313049
100000000000001 = 29 * 101 * 281 * 121499449
1000000000000001 = 7 * 11 * 13 * 211 * 241 * 2161 * 9091
10000000000000001 = 353 * 449 * 641 * 1409 * 69857
100000000000000001 = 11 * 103 * 4013 * 21993833369
1000000000000000001 = 101 * 9901 * 999999000001
10000000000000000001 = 11 * 909090909090909091
100000000000000000001 = 73 * 137 * 1676321 * 5964848081
1000000000000000000001 = 7 * 7 * 11 * 13 * 127 * 2689 * 909091 * 459691
10000000000000000000001 = 89 * 101 * 1056689261 * 1052788969
100000000000000000000001 = 11 * 47 * 139 * 2531 * 549797184491917
1000000000000000000000001 = 17 * 5882353 * 9999999900000001
10000000000000000000000001 = 11 * 251 * 5051 * 9091 * 78875943472201
100000000000000000000000001 = 101 * 521 * 1900381976777332243781
1000000000000000000000000001 = 7 * 11 * 13 * 19 * 52579 * 70541929 * 14175966169
10000000000000000000000000001 = 73 * 137 * 7841 * 127522001020150503761
100000000000000000000000000001 = 11 * 59 * 154083204930662557781201849
1000000000000000000000000000001 = 61 * 101 * 3541 * 9901 * 27961 * 4188901 * 39526741
10000000000000000000000000000001 = 11 * 909090909090909090909090909091
100000000000000000000000000000001 = 976193 * 19841 * 6187457 * 834427406578561
1000000000000000000000000000000001 = 7 * 11 * 11 * 13 * 23 * 4093 * 8779 * 599144041 * 183411838171
10000000000000000000000000000000001 = 101 * 28559389 * 1491383821 * 2324557465671829
100000000000000000000000000000000001 = 11 * 9091 * 4147571 * 909091 * 265212793249617641
1000000000000000000000000000000000001 = 73 * 137 * 3169 * 98641 * 99990001 * 3199044596370769
10000000000000000000000000000000000001 = 11 * 7253 * 422650073734453 * 296557347313446299
100000000000000000000000000000000000001 = 101 * 722817036322379041 * 1369778187490592461
1000000000000000000000000000000000000001 = 7 * 11 * 13 * 13 * 157 * 859 * 6397 * 216451 * 1058313049 * 388847808493
10000000000000000000000000000000000000001 = 17 * 5882353 * 5070721 * 19721061166646717498359681
100000000000000000000000000000000000000001 = 11 * 2670502781396266997 * 3404193829806058997303
1000000000000000000000000000000000000000001 = 29 * 101 * 281 * 9901 * 226549 * 121499449 * 4458192223320340849
10000000000000000000000000000000000000000001 = 11 * 57009401 * 2182600451 * 7306116556571817748755241
100000000000000000000000000000000000000000001 = 73 * 137 * 617 * 16205834846012967584927082656402106953
1000000000000000000000000000000000000000000001 = 7 * 11 * 13 * 19 * 211 * 241 * 2161 * 9091 * 29611 * 52579 * 3762091 * 8985695684401
10000000000000000000000000000000000000000000001 = 101 * 1289 * 18371524594609 * 4181003300071669867932658901
100000000000000000000000000000000000000000000001 = 11 * 6299 * 297262705009139006771611927 * 4855067598095567
1000000000000000000000000000000000000000000000001 = 97 * 353 * 449 * 641 * 1409 * 69857 * 206209 * 66554101249 * 75118313082913
10000000000000000000000000000000000000000000000001 = 11 * 197 * 909091 * 5076141624365532994918781726395939035533
100000000000000000000000000000000000000000000000001 = 101 * 3541 * 27961 * 60101 * 7019801 * 14103673319201 * 1680588011350901
1000000000000000000000000000000000000000000000000001 = 7 * 11 * 13 * 103 * 4013 * 21993833369 * 291078844423 * 377526955309799110357
10000000000000000000000000000000000000000000000000001 = 73 * 137 * 1580801 * 632527440202150745090622412245443923049201
100000000000000000000000000000000000000000000000000001 = 11 * 9090909090909090909090909090909090909090909090909091
1000000000000000000000000000000000000000000000000000001 = 101 * 109 * 9901 * 153469 * 999999000001 * 59779577156334533866654838281
10000000000000000000000000000000000000000000000000000001 = 11 * 11 * 23 * 331 * 4093 * 5171 * 8779 * 9091 * 20163494891 * 318727841165674579776721
100000000000000000000000000000000000000000000000000000001 = 17 * 113 * 5882353 * 73765755896403138401 * 119968369144846370226083377
1000000000000000000000000000000000000000000000000000000001 = 7 * 11 * 13 * 1458973 * 909090909090909091 * 753201806271328462547977919407
10000000000000000000000000000000000000000000000000000000001 = 101 * 349 * 38861 * 618049 * 11811806375201836408679635736258669583187541
100000000000000000000000000000000000000000000000000000000001 = 11 * 1889 * 1090805842068098677837 * 4411922770996074109644535362851087
1000000000000000000000000000000000000000000000000000000000001 = 73 * 137 * 1676321 * 100009999999899989999000000010001 * 5964848081 * 99990001
10000000000000000000000000000000000000000000000000000000000001 = 11 * 81131 * 11205222530116836855321528257890437575145023592596037161
100000000000000000000000000000000000000000000000000000000000001 = 101 * 2049349 * 483128549554512237305554588359039822397307149685578249
1000000000000000000000000000000000000000000000000000000000000001 = 7 * 7 * 11 * 13 * 19 * 127 * 2689 * 52579 * 5274739 * 909091 * 459691 * 189772422673235585874485732659
10000000000000000000000000000000000000000000000000000000000000001 = 1265011073 * 15343168188889137818369 * 515217525265213267447869906815873
100000000000000000000000000000000000000000000000000000000000000001 = 11 * 131 * 859 * 9091 * 1058313049 * 8396862596258693901610602298557167100076327481
1000000000000000000000000000000000000000000000000000000000000000001 = 89 * 101 * 9901 * 789390798020221 * 2361000305507449 * 5419170769 * 1052788969 * 1056689261
10000000000000000000000000000000000000000000000000000000000000000001 = 11 * 909090909090909090909090909090909090909090909090909090909090909091
100000000000000000000000000000000000000000000000000000000000000000001 = 73 * 137 * 152533657 * 65552746171882583264230070868884366877803237222654400793
1000000000000000000000000000000000000000000000000000000000000000000001 = 7 * 11 * 13 * 47 * 139 * 2531 * 31051 * 24649445347649059192745899 * 549797184491917 * 143574021480139
10000000000000000000000000000000000000000000000000000000000000000000001 = 29 * 101 * 281 * 421 * 3541 * 27961 * 3471301 * 121499449 * 13489841 * 60368344121 * 848654483879497562821
100000000000000000000000000000000000000000000000000000000000000000000001 = 11 * 290249 * 31321069464181068355415209323405389541706979493156189716729115659
1000000000000000000000000000000000000000000000000000000000000000000000001 = 17 * 8929 * 5882353 * 9999999900000001 * 111994624258035614290513943330720125433979169