yangchuanju：网友帮个忙，提供数据(70-140数据值)

太阳 · 发表于 2021-3-8 07:34

太阳发表于 2021-3-8 07:05
看一下，原帖(大素数试除法)。查看一下，有没有m取最小值条件

查看了一下，(f取值...)原帖，有m取最小值，条件，我写失误了

太阳 · 发表于 2021-3-8 07:43

yangchuanju 发表于 2021-3-7 21:30
再分析一下
m/(m-k)=y
m=10000000001/11=9090909091

查到错的原因，10000000001/11=9090909091，不对

太阳 · 发表于 2021-3-8 07:48

本帖最后由太阳于 2021-3-8 07:54 编辑

yangchuanju 发表于 2021-3-7 21:30
再分析一下
m/(m-k)=y
m=10000000001/11=9090909091

终于找到错误原因是，没有保证k取最小值，1到m之间数，m-k最大值，y最小值，导致错误原因

太阳 · 发表于 2021-3-8 07:53

再分析一下
m/(m-k)=y
m=10000000001/11=9090909091
4093*8779=35932447
假定我们误认为35932447是素数，
并令y=11*23=253
得m-k=m/y=9090909091/253=35932477
k=9090909091-35932447=9054976644
k更小些，y是整数，符合条件，能断定m-k必定是素数吗
终于找到错误原因是，没有保证k取最小值，1到m之间数，m-k最大值，y最小值，导致错误原因

yangchuanju · 发表于 2021-3-8 08:00

太阳发表于 2021-3-8 07:53
再分析一下
m/(m-k)=y
m=10000000001/11=9090909091

白天我有事，要出门了！晚上再交流！

太阳 · 发表于 2021-3-8 08:01

yangchuanju 发表于 2021-3-7 21:29
“ 给出例子：m-k必定是合数，100000000001/11=m=11*23*4093*8779
m/(m-k)=y，y取正整数，k取最小值，验 ...

这里没有保证k取最小值，导致错误存在

太阳 · 发表于 2021-3-8 09:16

100000000001=11^2×23×4093×8779
m/(m-k)=y
m=10000000001/11=9090909091
y=11*23*4093=1035529
m-k=8779
k=9090909092-8779=9090900312
1035529>8779
8779是一个素数，怎么说m-k必定是合数？
k没有取最小值，导致错误存在
重新检验，k取最小值，1到m之间数，(k取最小值，必定有y最小值)，有等式关系，m/(m-k)=11
100000000001/(100000000001-k)=11，求出k=90909090910
m-k=100000000001-90909090910=9090909091必定是合数
验证9090909091=11*23*4093*8799，是合数

yangchuanju · 发表于 2021-3-9 06:01

太阳发表于 2021-3-8 09:16
100000000001=11^2×23×4093×8779
m/(m-k)=y
m=10000000001/11=9090909091

帮忙帮到底
既然太阳老师请我帮个忙，那我就帮到底。
太阳老师在《f取值7,13,17,19,23，有可能都是正确的》一文中说：
“已知：整数a>0,f>0,k>0.m>0, (9*10^a+1)/f=m, f取值7,13,17,19,23, m/(m-k)=y, m取最小值，小到大顺序排列。求证：m-k必定是素数。”
太阳老师已认识到“m取最小值”是错误的，并把代数式中的条件作了改正，条件变为k取最小值，求证：m-k必定是素数。
单独改一个条件是无用的！或者再加上一个“y也取最小值”还是无用的！

假定m是一个双因子合数，令m=p1*p2，p1<p2，则当代数式m/(m-k)=y中的m-k=p2,，y=p1时符合条件，k取最小值，m-k是最大素数p2，此时y=p1最小。
假定m是一个三因子合数，令m=p1*p2*p3，p1≤p2≤p3，则当代数式m/(m-k)=y中的m-k=p3，y=p1*p2时， m-k是素数且最大；
但当m-k=p3*p2，y=p1时k的值为最小，y的值也为最小，然而m-k不是素数，所以说“先生的说法无道理”。

只有当令m-k=p1为最小，y=p2*p3最大，m-k=m/y，k=m-m/y=p1*p2*p3-p1最大时代数式才成立。
老师最近的一系列帖子均要求k取最小值，意图求大素数，是求不出的；
若将这些帖子改为求最小素数未尝不可，代数式中的m-k取最小值，k自然是最大值，y也相应的是最大值了，这时才会有“m-k必定是素数”。

实际上分解任一个合数，总是先求小素数，分解完后剩余一个大素数，没有先找大素数的。
再者，老师的判断m-k的两个条件也不对，请老师好好想一想。

yangchuanju · 发表于 2021-3-9 06:51

本帖最后由 yangchuanju 于 2021-3-9 07:01 编辑

帮忙帮到底2
各段（行）开头的101,1001……为10^1,10^2……，请自行添加上乘方符合“^”!
101+1 = 11 = 11(100.00%)
102+1 = 101 = 101(100.00%)
103+1 = 1001 = 7 × 11 × 13(100.00%)
104+1 = 10001 = 73 × 137(100.00%)
105+1 = 100001 = 11 × 9091(100.00%)
106+1 = 1000001 = 101 × 9901(100.00%)
107+1 = 10000001 = 11 × 909091(100.00%)
108+1 = 100000001 = 17 × 5882353(100.00%)
109+1 = 1000000001<10> = 7 × 11 × 13 × 19 × 52579(100.00%)
1010+1 = 10000000001<11> = 101 × 3541 × 27961(100.00%)
1011+1 = 100000000001<12> = 112 × 23 × 4093 × 8779(100.00%)
1012+1 = 1000000000001<13> = 73 × 137 × 99990001(100.00%)
1013+1 = 10000000000001<14> = 11 × 859 × 1058313049<10>(100.00%)
1014+1 = 100000000000001<15> = 29 × 101 × 281 × 121499449(100.00%)
1015+1 = 1000000000000001<16> = 7 × 11 × 13 × 211 × 241 × 2161 × 9091(100.00%)
1016+1 = 10000000000000001<17> = 353 × 449 × 641 × 1409 × 69857(100.00%)
1017+1 = 100000000000000001<18> = 11 × 103 × 4013 × 21993833369<11>(100.00%)
1018+1 = 1000000000000000001<19> = 101 × 9901 × 999999000001<12>(100.00%)
1019+1 = 10000000000000000001<20> = 11 × 909090909090909091<18>(100.00%)
1020+1 = 100000000000000000001<21> = 73 × 137 × 1676321 × 5964848081<10>(100.00%)
1021+1 = 1000000000000000000001<22> = 72 × 11 × 13 × 127 × 2689 × 459691 × 909091(100.00%)
1022+1 = 10000000000000000000001<23> = 89 × 101 × 1052788969<10> × 1056689261<10>(100.00%)
1023+1 = 100000000000000000000001<24> = 11 × 47 × 139 × 2531 × 549797184491917<15>(100.00%)
1024+1 = 1000000000000000000000001<25> = 17 × 5882353 × 9999999900000001<16>(100.00%)
1025+1 = 10000000000000000000000001<26> = 11 × 251 × 5051 × 9091 × 78875943472201<14>(100.00%)
1026+1 = 100000000000000000000000001<27> = 101 × 521 × 1900381976777332243781<22>(100.00%)
1027+1 = 1000000000000000000000000001<28> = 7 × 11 × 13 × 19 × 52579 × 70541929 × 14175966169<11>(100.00%)
1028+1 = 10000000000000000000000000001<29> = 73 × 137 × 7841 × 127522001020150503761<21>(100.00%)
1029+1 = 100000000000000000000000000001<30> = 11 × 59 × 154083204930662557781201849<27>(100.00%)
1030+1 = 1000000000000000000000000000001<31> = 61 × 101 × 3541 × 9901 × 27961 × 4188901 × 39526741(100.00%)
1031+1 = 10000000000000000000000000000001<32> = 11 × 909090909090909090909090909091<30>(100.00%)
1032+1 = 100000000000000000000000000000001<33> = 19841 × 976193 × 6187457 × 834427406578561<15>(100.00%)
1033+1 = 1000000000000000000000000000000001<34> = 7 × 112 × 13 × 23 × 4093 × 8779 × 599144041 × 183411838171<12>(100.00%)
1034+1 = 10000000000000000000000000000000001<35> = 101 × 28559389 × 1491383821<10> × 2324557465671829<16>(100.00%)
1035+1 = 100000000000000000000000000000000001<36> = 11 × 9091 × 909091 × 4147571 × 265212793249617641<18>(100.00%)
1036+1 = 1000000000000000000000000000000000001<37> = 73 × 137 × 3169 × 98641 × 99990001 × 3199044596370769<16>(100.00%)
1037+1 = 10000000000000000000000000000000000001<38> = 11 × 7253 × 422650073734453<15> × 296557347313446299<18>(100.00%)
1038+1 = 100000000000000000000000000000000000001<39> = 101 × 722817036322379041<18> × 1369778187490592461<19>(100.00%)
1039+1 = 1000000000000000000000000000000000000001<40> = 7 × 11 × 132 × 157 × 859 × 6397 × 216451 × 1058313049<10> × 388847808493<12>(100.00%)
1040+1 = 10000000000000000000000000000000000000001<41> = 17 × 5070721 × 5882353 × 19721061166646717498359681<26>(100.00%)
1041+1 = 100000000000000000000000000000000000000001<42> = 11 × 2670502781396266997<19> × 3404193829806058997303<22>(100.00%)
1042+1 = 1000000000000000000000000000000000000000001<43> = 29 × 101 × 281 × 9901 × 226549 × 121499449 × 4458192223320340849<19>(100.00%)
1043+1 = 10000000000000000000000000000000000000000001<44> = 11 × 57009401 × 2182600451<10> × 7306116556571817748755241<25>(100.00%)
1044+1 = 100000000000000000000000000000000000000000001<45> = 73 × 137 × 617 × 16205834846012967584927082656402106953<38>(100.00%)
1045+1 = 1000000000000000000000000000000000000000000001<46> = 7 × 11 × 13 × 19 × 211 × 241 × 2161 × 9091 × 29611 × 52579 × 3762091 × 8985695684401<13>(100.00%)
1046+1 = 10000000000000000000000000000000000000000000001<47> = 101 × 1289 × 18371524594609<14> × 4181003300071669867932658901<28>(100.00%)
1047+1 = 100000000000000000000000000000000000000000000001<48> = 11 × 6299 × 4855067598095567<16> × 297262705009139006771611927<27>(100.00%)
1048+1 = 1000000000000000000000000000000000000000000000001<49> = 97 × 353 × 449 × 641 × 1409 × 69857 × 206209 × 66554101249<11> × 75118313082913<14>(100.00%)
1049+1 = 10000000000000000000000000000000000000000000000001<50> = 11 × 197 × 909091 × 5076141624365532994918781726395939035533<40>(100.00%)
1050+1 = 100000000000000000000000000000000000000000000000001<51> = 101 × 3541 × 27961 × 60101 × 7019801 × 14103673319201<14> × 1680588011350901<16>(100.00%)
1051+1 = 1000000000000000000000000000000000000000000000000001<52> = 7 × 11 × 13 × 103 × 4013 × 21993833369<11> × 291078844423<12> × 377526955309799110357<21>(100.00%)
1052+1 = 10000000000000000000000000000000000000000000000000001<53> = 73 × 137 × 1580801 × 632527440202150745090622412245443923049201<42>(100.00%)
1053+1 = 100000000000000000000000000000000000000000000000000001<54> = 11 × 9090909090909090909090909090909090909090909090909091<52>(100.00%)
1054+1 = 1000000000000000000000000000000000000000000000000000001<55> = 101 × 109 × 9901 × 153469 × 999999000001<12> × 59779577156334533866654838281<29>(100.00%)
1055+1 = 10000000000000000000000000000000000000000000000000000001<56> = 112 × 23 × 331 × 4093 × 5171 × 8779 × 9091 × 20163494891<11> × 318727841165674579776721<24>(100.00%)
1056+1 = 100000000000000000000000000000000000000000000000000000001<57> = 17 × 113 × 5882353 × 73765755896403138401<20> × 119968369144846370226083377<27>(100.00%)
1057+1 = 1000000000000000000000000000000000000000000000000000000001<58> = 7 × 11 × 13 × 1458973 × 909090909090909091<18> × 753201806271328462547977919407<30>(100.00%)
1058+1 = 10000000000000000000000000000000000000000000000000000000001<59> = 101 × 349 × 38861 × 618049 × 11811806375201836408679635736258669583187541<44>(100.00%)
1059+1 = 100000000000000000000000000000000000000000000000000000000001<60> = 11 × 1889 × 1090805842068098677837<22> × 4411922770996074109644535362851087<34>(100.00%)
1060+1 = 1000000000000000000000000000000000000000000000000000000000001<61> = 73 × 137 × 1676321 × 99990001 × 5964848081<10> × 100009999999899989999000000010001<33>(100.00%)
1061+1 = 10000000000000000000000000000000000000000000000000000000000001<62> = 11 × 81131 × 11205222530116836855321528257890437575145023592596037161<56>(100.00%)
1062+1 = 100000000000000000000000000000000000000000000000000000000000001<63> = 101 × 2049349 × 483128549554512237305554588359039822397307149685578249<54>(100.00%)
1063+1 = 1000000000000000000000000000000000000000000000000000000000000001<64> = 72 × 11 × 13 × 19 × 127 × 2689 × 52579 × 459691 × 909091 × 5274739 × 189772422673235585874485732659<30>(100.00%)
1064+1 = 10000000000000000000000000000000000000000000000000000000000000001<65> = 1265011073<10> × 15343168188889137818369<23> × 515217525265213267447869906815873<33>(100.00%)
1065+1 = 100000000000000000000000000000000000000000000000000000000000000001<66> = 11 × 131 × 859 × 9091 × 1058313049<10> × 8396862596258693901610602298557167100076327481<46>(100.00%)
1066+1 = 1000000000000000000000000000000000000000000000000000000000000000001<67> = 89 × 101 × 9901 × 1052788969<10> × 1056689261<10> × 5419170769<10> × 789390798020221<15> × 2361000305507449<16>(100.00%)
1067+1 = 10000000000000000000000000000000000000000000000000000000000000000001<68> = 11 × 909090909090909090909090909090909090909090909090909090909090909091<66>(100.00%)
1068+1 = 100000000000000000000000000000000000000000000000000000000000000000001<69> = 73 × 137 × 152533657 × 65552746171882583264230070868884366877803237222654400793<56>(100.00%)
1069+1 = 1000000000000000000000000000000000000000000000000000000000000000000001<70> = 7 × 11 × 13 × 47 × 139 × 2531 × 31051 × 143574021480139<15> × 549797184491917<15> × 24649445347649059192745899<26>(100.00%)
1070+1 = 10000000000000000000000000000000000000000000000000000000000000000000001<71> = 29 × 101 × 281 × 421 × 3541 × 27961 × 3471301 × 13489841 × 121499449 × 60368344121<11> × 848654483879497562821<21>(100.00%)
1071+1 = 100000000000000000000000000000000000000000000000000000000000000000000001<72> = 11 × 290249 × 31321069464181068355415209323405389541706979493156189716729115659<65>(100.00%)
1072+1 = 1000000000000000000000000000000000000000000000000000000000000000000000001<73> = 17 × 8929 × 5882353 × 9999999900000001<16> × 111994624258035614290513943330720125433979169<45>(100.00%)
1073+1 = 10000000000000000000000000000000000000000000000000000000000000000000000001<74> = 11 × 293 × 10826684964539959837294043117<29> × 286578888976194997999922592330908602103011<42>(100.00%)
1074+1 = 100000000000000000000000000000000000000000000000000000000000000000000000001<75> = 101 × 149 × 3109 × 111149 × 708840373781<12> × 669031686661427842829<21> × 40548140514062774758071840361<29>(100.00%)
1075+1 = 1000000000000000000000000000000000000000000000000000000000000000000000000001<76> = 7 × 11 × 13 × 211 × 241 × 251 × 2161 × 5051 × 9091 × 78875943472201<14> × 10000099999999989999899999000000000100001<41>(100.00%)
1076+1 = 10000000000000000000000000000000000000000000000000000000000000000000000000001<77> = 73 × 137 × 457 × 1403417 × 5240808656722481737<19> × 297478330786365628414805305290302483555043017<45>(100.00%)
1077+1 = 100000000000000000000000000000000000000000000000000000000000000000000000000001<78> = 112 × 23 × 463 × 4093 × 8779 × 24179 × 590437 × 909091 × 7444361 × 4539402627853030477<19> × 4924630160315726207887<22>(100.00%)
1078+1 = 1000000000000000000000000000000000000000000000000000000000000000000000000000001<79> = 101 × 521 × 3121 × 9901 × 53397071018461<14> × 1900381976777332243781<22> × 6060517860310398033985611921721<31>(100.00%)
1079+1 = 10000000000000000000000000000000000000000000000000000000000000000000000000000001<80> = 11 × 1423 × 9615060929<10> × 66443174541490579097997510158021076958392938976011506949065646573<65>(100.00%)
1080+1 = 100000000000000000000000000000000000000000000000000000000000000000000000000000001<81> = 353 × 449 × 641 × 1409 × 69857 × 1634881 × 18453761 × 947147262401<12> × 349954396040122577928041596214187605761<39>(100.00%)
1081+1 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000001<82> = 7 × 11 × 13 × 19 × 1459 × 52579 × 70541929 × 2458921051<10> × 14175966169<11> × 456502382570032651<18> × 610600386089858349939139<24>(100.00%)
1082+1 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000001<83> = 101 × 68389 × 1447745997018511893740076606031686237538345362413531560645573104006506749609<76>(100.00%)
1083+1 = 100000000000000000000000000000000000000000000000000000000000000000000000000000000001<84> = 11 × 167 × 997 × 3565183 × 2097307081<10> × 7742098247001476863<19> × 943176903141330068482602900960294299878841<42>(100.00%)
1084+1 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000001<85> = 73 × 137 × 7841 × 99990001 × 11189053009<11> × 603812429055411913<18> × 127522001020150503761<21> × 148029423400750506553<21>(100.00%)
1085+1 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000001<86> = 11 × 103 × 4013 × 9091 × 87211 × 787223761 × 21993833369<11> × 160220794821014452066741918303580917664386555934641<51>(100.00%)
1086+1 = 100000000000000000000000000000000000000000000000000000000000000000000000000000000000001<87> = 101 × 338669 × 2923500556298303355222653948542706598448925085853709961673200056984872843366529<79>(100.00%)
1087+1 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<88> = 7 × 11 × 13 × 59 × 638453709757<12> × 135080726389891<15> × 154083204930662557781201849<27> × 1274194732898148471766404179653<31>(100.00%)
1088+1 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<89> = 17 × 5882353 × 10100113 × 9900879227786858424257223656804730798555422102713108259184822982673560177<73>(100.00%)
1089+1 = 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<90> = 11 × 179 × 12147237304901893<17> × 4180967272673252032291190917188955510245874180001164839931077197586653<70>(100.00%)
1090+1 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<91> = 61 × 101 × 181 × 3541 × 9901 × 27961 × 4188901 × 39526741 × 999999000001<12> × 4999437541453012143121<22> × 1105097795002994798105101<25>(100.00%)
1091+1 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<92> = 11 × 859 × 909091 × 21705503 × 1058313049<10> × 50678387411703889101759125785290439894389920385627096501794498837<65>(100.00%)
1092+1 = 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<93> = 73 × 137 × 2393 × 4178437150016715837818641871709193476807772628503969494400330129962348520684914375257<85>(100.00%)
1093+1 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<94> = 7 × 11 × 13 × 373 × 44641 × 3590254957<10> × 909090909090909090909090909091<30> × 18381907262281244633158190677786966663091011<44>(100.00%)
1094+1 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<95> = 101 × 45121 × 2144906157509411684424913774078958939881<40> × 1023037643093214557651333120422980213172396059301<49>(100.00%)
1095+1 = 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<96> = 11 × 9091 × 1812604116731<13> × 121450506296081<15> × 909090909090909091<18> × 4996731930447843676185843959746621491531100801<46>(100.00%)
1096+1 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<97> = 193 × 769 × 19841 × 976193 × 6187457 × 834427406578561<15> × 1253224535459902849<19> × 53763491189967221358575546107279034709697<41>(100.00%)
1097+1 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<98> = 11 × 102527361354613106010527<24> × 323338434891034089173475790125293<33> × 27422699366054621683295623079471066588881<41>(100.00%)
1098+1 = 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<99> = 29 × 101 × 281 × 121499449 × 999999999999990000000000000099999999999999000000000000009999999999999900000000000001<84>(100.00%)
1099+1 = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<100> = 7 × 112 × 13 × 19 × 23 × 4093 × 8779 × 52579 × 599144041 × 7093127053<10> × 183411838171<12> × 141122524877886182282233539317796144938305111168717<51>(100.00%)
10100+1 = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<101> = 73 × 137 × 401 × 1201 × 1601 × 1676321 × 5964848081<10> × 129694419029057750551385771184564274499075700947656757821537291527196801<72>(100.00%)

yangchuanju · 发表于 2021-3-9 07:03

本帖最后由 yangchuanju 于 2021-3-9 07:34 编辑

帮忙帮到底3
各段（行）第一个等号后的101,1001……为10^1,10^2……，请自行添加上乘方符合“^”!
101-19,102-19……为(10^1-1)/9,(10^2-1)/9……，请自行改过了！
R1 = 101-19 = 1
R2 = 102-19 = 11 = 11(100.00%)
R3 = 103-19 = 111 = 3 × 37(100.00%)
R4 = 104-19 = 1111 = 11 × 101(100.00%)
R5 = 105-19 = 11111 = 41 × 271(100.00%)
R6 = 106-19 = 111111 = 3 × 7 × 11 × 13 × 37(100.00%)
R7 = 107-19 = 1111111 = 239 × 4649(100.00%)
R8 = 108-19 = 11111111 = 11 × 73 × 101 × 137(100.00%)
R9 = 109-19 = 111111111 = 32 × 37 × 333667(100.00%)
R10 = 1010-19 = 1111111111<10> = 11 × 41 × 271 × 9091(100.00%)
R11 = 1011-19 = 11111111111<11> = 21649 × 513239(100.00%)
R12 = 1012-19 = 111111111111<12> = 3 × 7 × 11 × 13 × 37 × 101 × 9901(100.00%)
R13 = 1013-19 = 1111111111111<13> = 53 × 79 × 265371653(100.00%)
R14 = 1014-19 = 11111111111111<14> = 11 × 239 × 4649 × 909091(100.00%)
R15 = 1015-19 = 111111111111111<15> = 3 × 31 × 37 × 41 × 271 × 2906161(100.00%)
R16 = 1016-19 = 1111111111111111<16> = 11 × 17 × 73 × 101 × 137 × 5882353(100.00%)
R17 = 1017-19 = 11111111111111111<17> = 2071723 × 5363222357<10>(100.00%)
R18 = 1018-19 = 111111111111111111<18> = 32 × 7 × 11 × 13 × 19 × 37 × 52579 × 333667(100.00%)
R19 = 1019-19 = 1111111111111111111<19> = 1111111111111111111<19>(100.00%)
R20 = 1020-19 = 11111111111111111111<20> = 11 × 41 × 101 × 271 × 3541 × 9091 × 27961(100.00%)
R21 = 1021-19 = 111111111111111111111<21> = 3 × 37 × 43 × 239 × 1933 × 4649 × 10838689(100.00%)
R22 = 1022-19 = 1111111111111111111111<22> = 112 × 23 × 4093 × 8779 × 21649 × 513239(100.00%)
R23 = 1023-19 = 11111111111111111111111<23> = 11111111111111111111111<23>(100.00%)
R24 = 1024-19 = 111111111111111111111111<24> = 3 × 7 × 11 × 13 × 37 × 73 × 101 × 137 × 9901 × 99990001(100.00%)
R25 = 1025-19 = 1111111111111111111111111<25> = 41 × 271 × 21401 × 25601 × 182521213001<12>(100.00%)
R26 = 1026-19 = 11111111111111111111111111<26> = 11 × 53 × 79 × 859 × 265371653 × 1058313049<10>(100.00%)
R27 = 1027-19 = 111111111111111111111111111<27> = 33 × 37 × 757 × 333667 × 440334654777631<15>(100.00%)
R28 = 1028-19 = 1111111111111111111111111111<28> = 11 × 29 × 101 × 239 × 281 × 4649 × 909091 × 121499449(100.00%)
R29 = 1029-19 = 11111111111111111111111111111<29> = 3191 × 16763 × 43037 × 62003 × 77843839397<11>(100.00%)
R30 = 1030-19 = 111111111111111111111111111111<30> = 3 × 7 × 11 × 13 × 31 × 37 × 41 × 211 × 241 × 271 × 2161 × 9091 × 2906161(100.00%)
R31 = 1031-19 = 1111111111111111111111111111111<31> = 2791 × 6943319 × 57336415063790604359<20>(100.00%)
R32 = 1032-19 = 11111111111111111111111111111111<32> = 11 × 17 × 73 × 101 × 137 × 353 × 449 × 641 × 1409 × 69857 × 5882353(100.00%)
R33 = 1033-19 = 111111111111111111111111111111111<33> = 3 × 37 × 67 × 21649 × 513239 × 1344628210313298373<19>(100.00%)
R34 = 1034-19 = 1111111111111111111111111111111111<34> = 11 × 103 × 4013 × 2071723 × 5363222357<10> × 21993833369<11>(100.00%)
R35 = 1035-19 = 11111111111111111111111111111111111<35> = 41 × 71 × 239 × 271 × 4649 × 123551 × 102598800232111471<18>(100.00%)
R36 = 1036-19 = 111111111111111111111111111111111111<36> = 32 × 7 × 11 × 13 × 19 × 37 × 101 × 9901 × 52579 × 333667 × 999999000001<12>(100.00%)
R37 = 1037-19 = 1111111111111111111111111111111111111<37> = 2028119 × 247629013 × 2212394296770203368013<22>(100.00%)
R38 = 1038-19 = 11111111111111111111111111111111111111<38> = 11 × 909090909090909091<18> × 1111111111111111111<19>(100.00%)
R39 = 1039-19 = 111111111111111111111111111111111111111<39> = 3 × 37 × 53 × 79 × 265371653 × 900900900900990990990991<24>(100.00%)
R40 = 1040-19 = 1111111111111111111111111111111111111111<40> = 11 × 41 × 73 × 101 × 137 × 271 × 3541 × 9091 × 27961 × 1676321 × 5964848081<10>(100.00%)
R41 = 1041-19 = 11111111111111111111111111111111111111111<41> = 83 × 1231 × 538987 × 201763709900322803748657942361<30>(100.00%)
R42 = 1042-19 = 111111111111111111111111111111111111111111<42> = 3 × 72 × 11 × 13 × 37 × 43 × 127 × 239 × 1933 × 2689 × 4649 × 459691 × 909091 × 10838689(100.00%)
R43 = 1043-19 = 1111111111111111111111111111111111111111111<43> = 173 × 1527791 × 1963506722254397<16> × 2140992015395526641<19>(100.00%)
R44 = 1044-19 = 11111111111111111111111111111111111111111111<44> = 112 × 23 × 89 × 101 × 4093 × 8779 × 21649 × 513239 × 1052788969<10> × 1056689261<10>(100.00%)
R45 = 1045-19 = 111111111111111111111111111111111111111111111<45> = 32 × 31 × 37 × 41 × 271 × 238681 × 333667 × 2906161 × 4185502830133110721<19>(100.00%)
R46 = 1046-19 = 1111111111111111111111111111111111111111111111<46> = 11 × 47 × 139 × 2531 × 549797184491917<15> × 11111111111111111111111<23>(100.00%)
R47 = 1047-19 = 11111111111111111111111111111111111111111111111<47> = 35121409 × 316362908763458525001406154038726382279<39>(100.00%)
R48 = 1048-19 = 111111111111111111111111111111111111111111111111<48> = 3 × 7 × 11 × 13 × 17 × 37 × 73 × 101 × 137 × 9901 × 5882353 × 99990001 × 9999999900000001<16>(100.00%)
R49 = 1049-19 = 1111111111111111111111111111111111111111111111111<49> = 239 × 4649 × 505885997 × 1976730144598190963568023014679333<34>(100.00%)
R50 = 1050-19 = 11111111111111111111111111111111111111111111111111<50> = 11 × 41 × 251 × 271 × 5051 × 9091 × 21401 × 25601 × 182521213001<12> × 78875943472201<14>(100.00%)
R51 = 1051-19 = 111111111111111111111111111111111111111111111111111<51> = 3 × 37 × 613 × 210631 × 2071723 × 52986961 × 5363222357<10> × 13168164561429877<17>(100.00%)
R52 = 1052-19 = 1111111111111111111111111111111111111111111111111111<52> = 11 × 53 × 79 × 101 × 521 × 859 × 265371653 × 1058313049<10> × 1900381976777332243781<22>(100.00%)
R53 = 1053-19 = 11111111111111111111111111111111111111111111111111111<53> = 107 × 1659431 × 1325815267337711173<19> × 47198858799491425660200071<26>(100.00%)
R54 = 1054-19 = 111111111111111111111111111111111111111111111111111111<54> = 33 × 7 × 11 × 13 × 19 × 37 × 757 × 52579 × 333667 × 70541929 × 14175966169<11> × 440334654777631<15>(100.00%)
R55 = 1055-19 = 1111111111111111111111111111111111111111111111111111111<55> = 41 × 271 × 1321 × 21649 × 62921 × 513239 × 83251631 × 1300635692678058358830121<25>(100.00%)
R56 = 1056-19 = 11111111111111111111111111111111111111111111111111111111<56> = 11 × 29 × 73 × 101 × 137 × 239 × 281 × 4649 × 7841 × 909091 × 121499449 × 127522001020150503761<21>(100.00%)
R57 = 1057-19 = 111111111111111111111111111111111111111111111111111111111<57> = 3 × 37 × 21319 × 10749631 × 1111111111111111111<19> × 3931123022305129377976519<25>(100.00%)
R58 = 1058-19 = 1111111111111111111111111111111111111111111111111111111111<58> = 11 × 59 × 3191 × 16763 × 43037 × 62003 × 77843839397<11> × 154083204930662557781201849<27>(100.00%)
R59 = 1059-19 = 11111111111111111111111111111111111111111111111111111111111<59> = 2559647034361<13> × 4340876285657460212144534289928559826755746751<46>(100.00%)
R60 = 1060-19 = 111111111111111111111111111111111111111111111111111111111111<60> = 3 × 7 × 11 × 13 × 31 × 37 × 41 × 61 × 101 × 211 × 241 × 271 × 2161 × 3541 × 9091 × 9901 × 27961 × 2906161 × 4188901 × 39526741(100.00%)
R61 = 1061-19 = 1111111111111111111111111111111111111111111111111111111111111<61> = 733 × 4637 × 329401 × 974293 × 1360682471<10> × 106007173861643<15> × 7061709990156159479<19>(100.00%)
R62 = 1062-19 = 11111111111111111111111111111111111111111111111111111111111111<62> = 11 × 2791 × 6943319 × 57336415063790604359<20> × 909090909090909090909090909091<30>(100.00%)
R63 = 1063-19 = 111111111111111111111111111111111111111111111111111111111111111<63> = 32 × 37 × 43 × 239 × 1933 × 4649 × 10837 × 23311 × 45613 × 333667 × 10838689 × 45121231 × 1921436048294281<16>(100.00%)
R64 = 1064-19 = 1111111111111111111111111111111111111111111111111111111111111111<64> = 11 × 17 × 73 × 101 × 137 × 353 × 449 × 641 × 1409 × 19841 × 69857 × 976193 × 5882353 × 6187457 × 834427406578561<15>(100.00%)
R65 = 1065-19 = 11111111111111111111111111111111111111111111111111111111111111111<65> = 41 × 53 × 79 × 271 × 265371653 × 162503518711<12> × 5538396997364024056286510640780600481<37>(100.00%)
R66 = 1066-19 = 111111111111111111111111111111111111111111111111111111111111111111<66> = 3 × 7 × 112 × 13 × 23 × 37 × 67 × 4093 × 8779 × 21649 × 513239 × 599144041 × 183411838171<12> × 1344628210313298373<19>(100.00%)
R67 = 1067-19 = 1111111111111111111111111111111111111111111111111111111111111111111<67> = 493121 × 79863595778924342083<20> × 28213380943176667001263153660999177245677<41>(100.00%)
R68 = 1068-19 = 11111111111111111111111111111111111111111111111111111111111111111111<68> = 11 × 101 × 103 × 4013 × 2071723 × 28559389 × 1491383821<10> × 5363222357<10> × 21993833369<11> × 2324557465671829<16>(100.00%)
R69 = 1069-19 = 111111111111111111111111111111111111111111111111111111111111111111111<69> = 3 × 37 × 277 × 203864078068831<15> × 11111111111111111111111<23> × 1595352086329224644348978893<28>(100.00%)
R70 = 1070-19 = 1111111111111111111111111111111111111111111111111111111111111111111111<70> = 11 × 41 × 71 × 239 × 271 × 4649 × 9091 × 123551 × 909091 × 4147571 × 102598800232111471<18> × 265212793249617641<18>(100.00%)
R71 = 1071-19 = 11111111111111111111111111111111111111111111111111111111111111111111111<71> = 241573142393627673576957439049<30> × 45994811347886846310221728895223034301839<41>(100.00%)
R72 = 1072-19 = 111111111111111111111111111111111111111111111111111111111111111111111111<72> = 32 × 7 × 11 × 13 × 19 × 37 × 73 × 101 × 137 × 3169 × 9901 × 52579 × 98641 × 333667 × 99990001 × 999999000001<12> × 3199044596370769<16>(100.00%)
R73 = 1073-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111<73> = 12171337159<11> × 1855193842151350117<19> × 49207341634646326934001739482502131487446637<44>(100.00%)
R74 = 1074-19 = 11111111111111111111111111111111111111111111111111111111111111111111111111<74> = 11 × 7253 × 2028119 × 247629013 × 422650073734453<15> × 296557347313446299<18> × 2212394296770203368013<22>(100.00%)
R75 = 1075-19 = 111111111111111111111111111111111111111111111111111111111111111111111111111<75> = 3 × 31 × 37 × 41 × 151 × 271 × 4201 × 21401 × 25601 × 2906161 × 182521213001<12> × 15763985553739191709164170940063151<35>(100.00%)
R76 = 1076-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111111<76> = 11 × 101 × 722817036322379041<18> × 909090909090909091<18> × 1111111111111111111<19> × 1369778187490592461<19>(100.00%)
R77 = 1077-19 = 11111111111111111111111111111111111111111111111111111111111111111111111111111<77> = 239 × 4649 × 5237 × 21649 × 42043 × 513239 × 29920507 × 136614668576002329371496447555915740910181043<45>(100.00%)
R78 = 1078-19 = 111111111111111111111111111111111111111111111111111111111111111111111111111111<78> = 3 × 7 × 11 × 132 × 37 × 53 × 79 × 157 × 859 × 6397 × 216451 × 265371653 × 1058313049<10> × 388847808493<12> × 900900900900990990990991<24>(100.00%)
R79 = 1079-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111111111<79> = 317 × 6163 × 10271 × 307627 × 49172195536083790769<20> × 3660574762725521461527140564875080461079917<43>(100.00%)
R80 = 1080-19 = 11111111111111111111111111111111111111111111111111111111111111111111111111111111<80> = 11 × 17 × 41 × 73 × 101 × 137 × 271 × 3541 × 9091 × 27961 × 1676321 × 5070721 × 5882353 × 5964848081<10> × 19721061166646717498359681<26>(100.00%)
R81 = 1081-19 = 111111111111111111111111111111111111111111111111111111111111111111111111111111111<81> = 34 × 37 × 163 × 757 × 9397 × 333667 × 2462401 × 440334654777631<15> × 676421558270641<15> × 130654897808007778425046117<27>(100.00%)
R82 = 1082-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111111111111<82> = 11 × 83 × 1231 × 538987 × 2670502781396266997<19> × 3404193829806058997303<22> × 201763709900322803748657942361<30>(100.00%)
R83 = 1083-19 = 11111111111111111111111111111111111111111111111111111111111111111111111111111111111<83> = 3367147378267<13> × 9512538508624154373682136329<28> × 346895716385857804544741137394505425384477<42>(100.00%)
R84 = 1084-19 = 111111111111111111111111111111111111111111111111111111111111111111111111111111111111<84> = 3 × 72 × 11 × 13 × 29 × 37 × 43 × 101 × 127 × 239 × 281 × 1933 × 2689 × 4649 × 9901 × 226549 × 459691 × 909091 × 10838689 × 121499449 × 4458192223320340849<19>(100.00%)
R85 = 1085-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111<85> = 41 × 271 × 2071723 × 262533041 × 5363222357<10> × 8119594779271<13> × 4222100119405530170179331190291488789678081<43>(100.00%)
R86 = 1086-19 = 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111<86> = 11 × 173 × 1527791 × 57009401 × 2182600451<10> × 1963506722254397<16> × 2140992015395526641<19> × 7306116556571817748755241<25>(100.00%)
R87 = 1087-19 = 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<87> = 3 × 37 × 3191 × 4003 × 16763 × 43037 × 62003 × 72559 × 77843839397<11> × 310170251658029759045157793237339498342763245483<48>(100.00%)
R88 = 1088-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<88> = 112 × 23 × 73 × 89 × 101 × 137 × 617 × 4093 × 8779 × 21649 × 513239 × 1052788969<10> × 1056689261<10> × 16205834846012967584927082656402106953<38>(100.00%)
R89 = 1089-19 = 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<89> = 497867 × 103733951 × 104984505733<12> × 5078554966026315671444089<25> × 403513310222809053284932818475878953159<39>(100.00%)
R90 = 1090-19 = 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<90> = 32 × 7 × 11 × 13 × 19 × 31 × 37 × 41 × 211 × 241 × 271 × 2161 × 9091 × 29611 × 52579 × 238681 × 333667 × 2906161 × 3762091 × 8985695684401<13> × 4185502830133110721<19>(100.00%)
R91 = 1091-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<91> = 53 × 79 × 239 × 547 × 4649 × 14197 × 17837 × 4262077 × 265371653 × 43442141653<11> × 316877365766624209<18> × 110742186470530054291318013<27>(100.00%)
R92 = 1092-19 = 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<92> = 11 × 47 × 101 × 139 × 1289 × 2531 × 18371524594609<14> × 549797184491917<15> × 11111111111111111111111<23> × 4181003300071669867932658901<28>(100.00%)
R93 = 1093-19 = 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<93> = 3 × 37 × 2791 × 6943319 × 57336415063790604359<20> × 900900900900900900900900900900990990990990990990990990990991<60>(100.00%)
R94 = 1094-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<94> = 11 × 6299 × 35121409 × 4855067598095567<16> × 297262705009139006771611927<27> × 316362908763458525001406154038726382279<39>(100.00%)
R95 = 1095-19 = 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<95> = 41 × 191 × 271 × 59281 × 63841 × 1111111111111111111<19> × 1289981231950849543985493631<28> × 965194617121640791456070347951751<33>(100.00%)
R96 = 1096-19 = 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<96> = 3 × 7 × 11 × 13 × 17 × 37 × 73 × 97 × 101 × 137 × 353 × 449 × 641 × 1409 × 9901 × 69857 × 206209 × 5882353 × 99990001 × 66554101249<11> × 75118313082913<14> × 9999999900000001<16>(100.00%)
R97 = 1097-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<97> = 12004721 × 846035731396919233767211537899097169<36> × 109399846855370537540339266842070119107662296580348039<54>(100.00%)
R98 = 1098-19 = 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<98> = 11 × 197 × 239 × 4649 × 909091 × 505885997 × 1976730144598190963568023014679333<34> × 5076141624365532994918781726395939035533<40>(100.00%)
R99 = 1099-19 = 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<99> = 32 × 37 × 67 × 199 × 397 × 21649 × 34849 × 333667 × 513239 × 1344628210313298373<19> × 362853724342990469324766235474268869786311886053883<51>(100.00%)
R100 = 10100-19 = 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111<100> = 11 × 41 × 101 × 251 × 271 × 3541 × 5051 × 9091 × 21401 × 25601 × 27961 × 60101 × 7019801 × 182521213001<12> × 14103673319201<14> × 78875943472201<14> × 1680588011350901<16>(100.00%)

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