101桁までの素因数分解結果は以下のとおり。 121 (3) = 11^2 12321 (5) = (3 * 37)^2 1234321 (7) = (11 * 101)^2 123454321 (9) = (41 * 271)^2 12345654321 (11) = (3 * 7 * 11 * 13 * 37)^2 1234567654321 (13) = (239 * 4649)^2 123456787654321 (15) = (11 * 73 * 101 * 137)^2 12345678987654321 (17) = (3^2 * 37 * 333667)^2 ここまでは、11...11 の２乗。 これ以下、未知の世界に入る。 1234567890987654321 (19) = 3^2 * 7 * 19 * 928163 * 1111211111 123456789010987654321 (21) = 11 * 19 * 157 * 257 * 3324301 * 4403881 12345678901210987654321 (23) = 11195538763 * 1102732004467 1234567890123210987654321 (25) = 3^2 * 11 * 7309 * 1706168111713953031 123456789012343210987654321 (27) = prime 12345678901234543210987654321 (29) = 7 * 11 * 17 * 7532639 * 8983031 * 139381546141 1234567890123456543210987654321 (31) = 3^2 * 7 * 31 * 179 * 5069639 * 19552681 * 35626762037 123456789012345676543210987654321 (33) = 11 * 227 * 4319141 * 9697807373 * 1180389939601 12345678901234567876543210987654321 (35) = 17 * 47 * 1087 * 5909237 * 10410656689 * 231062315069 1234567890123456789876543210987654321 (37) = 3^2 * 11 * 12517 * 22147 * 40486211 * 1111111111111111111 123456789012345678909876543210987654321 (39) = 3^2 * 13^2 * 101 * 2633 * 3541 * 27961 * 90971 * 145783411 * 232446937 12345678901234567890109876543210987654321 (41) = 754382617 * 16365274892375426898403567725913 1234567890123456789012109876543210987654321 (43) = 2697973 * 457590898842744826954202238696684877 123456789012345678901232109876543210987654321 (45) = 3^3 * 1429 * 26981 * 1624849 * 257814857164651 * 283100081192273 12345678901234567890123432109876543210987654321 (47) = 29 * 47 * 101 * 139 * 293 * 2693 * 24171053 * 116472957001 * 290441252876449 1234567890123456789012345432109876543210987654321 (49) = 7 * 989095062551024749 * 178311315184742237670292673347 123456789012345678901234565432109876543210987654321 (51) = 3^3 * 13 * 351728743624916464106081382997464035735643839471 12345678901234567890123456765432109876543210987654321 (53) = 257 * 518153 * 92709414196768000057037798643027413094609001 1234567890123456789012345678765432109876543210987654321 (55) = 101 * 503 * 3121 * 2472929 * 21747522864335857 * 144780611313897950987339 123456789012345678901234567898765432109876543210987654321 (57) = 3^2 * 2087 * 3191 * 16763 * 43037 * 62003 * 11622001 * 77843839397 * 50899277731560617 12345678901234567890123456789098765432109876543210987654321 (59) = 3^3 * 7 * 13 * 31 * 37^2 * 79 * 211 * 241 * 2161 * 2906161 * 167833717 * 27961755855588755458483759 1234567890123456789012345678901098765432109876543210987654321 (61) = 64171927 * 19238441914381919511507667190687584704010990297100023 123456789012345678901234567890121098765432109876543210987654321 (63) = 5711 * 1640804591 * 37892841367103 * 347687264218149421448968617367193807 12345678901234567890123456789012321098765432109876543210987654321 (65) = 3^2 * 37^2 * 178973 * 402797980807189080979668443 * 13899341226223424136966323359 1234567890123456789012345678901234321098765432109876543210987654321 (67) = 11923 * 103545071720494572591826359045645753677662117932556952378678827 123456789012345678901234567890123454321098765432109876543210987654321 (69) = 47 * 70619 * 600257071 * 3828475817 * 16185732662535344329537105457940660675044171 12345678901234567890123456789012345654321098765432109876543210987654321 (71) = 3^2 * 7 * 13 * 37^2 * 11011021922933834835836837837848848837837925926014024012022011011 1234567890123456789012345678901234567654321098765432109876543210987654321 (73) = 509 * 2111 * 2330123 * 36150023409978389533 * 13640224930645368092678207617173126202181 123456789012345678901234567890123456787654321098765432109876543210987654321 (75) = 43 * 793511 * 116681552066449 * 31009257881910261316773667074236420540923939064047973 12345678901234567890123456789012345678987654321098765432109876543210987654321 (77) = 3^3 * 37^2 * 53 * 79 * 39359 * 71887 * 858127 * 265371653 * 137425482585508591037 * 900900900900990990990991 1234567890123456789012345678901234567890987654321098765432109876543210987654321 (79) = 3^2 * 7 * 73 * 101 * 137 * 733 * 3541 * 27961 * 663979 * 1676321 * 2131859 * 5964848081 * 18886767401751871209053141830859 123456789012345678901234567890123456789010987654321098765432109876543210987654321 (81) = 47 * 743 * 2797 * 1263967301897695483818638190311755587505930441416290582577559580920600333 12345678901234567890123456789012345678901210987654321098765432109876543210987654321 (83) = 239 * 4649 * 3876143 * 12895689623 * 222286540771976216063014187484239874426613120480496565036799 1234567890123456789012345678901234567890123210987654321098765432109876543210987654321 (85) = 3^2 * 1871 * 73315986111019466061663143826903887872802613634280795836971639177497270812458439 123456789012345678901234567890123456789012343210987654321098765432109876543210987654321 (87) = 41 * 101 * 177337 * 478531 * 351317927541588208916308217982663026223388555903223807173846940779850623 12345678901234567890123456789012345678901234543210987654321098765432109876543210987654321 (89) = 7 * 59 * 19081 * 109533511 * 213379321 * 67029264870507497762665159895914227093453821730540394862944748147 1234567890123456789012345678901234567890123456543210987654321098765432109876543210987654321 (91) = 3^2 * 7 * 31 * 214651 * 91604750235377 * 14417553889396033 * 84532641918911973121 * 26378238901642713765948189231187 123456789012345678901234567890123456789012345676543210987654321098765432109876543210987654321 (93) = 103 * 977 * 1823 * 8951 * 940351 * 2963869 * 26975901546561168867373495776776242982739591259907220564590514025493 12345678901234567890123456789012345678901234567876543210987654321098765432109876543210987654321 (95) = 73 * 101 * 103 * 137 * 1291 * 5850391259392829503 * 15710926526485838214102181799889507003783142523065678939078230559 1234567890123456789012345678901234567890123456789876543210987654321098765432109876543210987654321 (97) = 3^2 * 41 * 239 * 379 * 4649 * 23269 * 505885997 * 51551814703 * 6623236046311999035689159423 * 1976730144598190963568023014679333 123456789012345678901234567890123456789012345678909876543210987654321098765432109876543210987654321 (99) = 3^2 * 13 * 251 * 5051 * 10259 * 21401 * 25601 * 182521213001 * 5885829414749 * 78875943472201 * 1747496902201617503155408881090698956843 12345678901234567890123456789012345678901234567890109876543210987654321098765432109876543210987654321 (101) = 66263354027131 * 3939930092843683 * 47288228674717904126615070147425240066917213450061137254574399064225377 場合によっては素数になることもあり、例えば、 123456789012343210987654321 (27桁) は素数となる。1001桁以下で素数となるのはこれだけ。 ちなみに、 1234567890987654321 ではなく、 12345678900987654321 と、２つずつ入れていったときの素因数分解結果は以下のとおり。 12345678900987654321 = 3^2 * 11 * 2153 * 57920960187043 1234567890110987654321 = 11 * 101 * 547 * 2031484868962013 123456789012210987654321 = 3 * 7 * 11 * 13 * 23 * 37 * 2251 * 21461229061907 12345678901233210987654321 = 3 * 11 * 59 * 6340872573822912679843 1234567890123443210987654321 11 * 23 * 41 * 271 * 19697 * 21683 * 94331 * 10901027 123456789012345543210987654321 = 3 * 11 * 37 * 101 * 149 * 17033183 * 394453540654603 12345678901234566543210987654321 = 3 * 11 * 6211601182253 * 60227865711091829 1234567890123456776543210987654321 = 11 * 29 * 479 * 30406419829 * 265719540721079149 123456789012345678876543210987654321 = 3^4 * 7 * 11^2 * 13 * 19 * 37 * 12517 * 22147 * 52579 * 333667 * 40486211 12345678901234567899876543210987654321 3^2 * 11^2 * 41 * 101 * 271 * 3541 * 9091 * 12517 * 22147 * 27961 * 40486211 1234567890123456789009876543210987654321 = 3^2 * 11 * 37 * 71 * 101 * 647 * 3541 * 27961 * 236909051 * 3096947021341 123456789012345678901109876543210987654321 = 11 * 239 * 4649 * 14009 * 721037263202377907924919773789 12345678901234567890122109876543210987654321 = 3 * 11 * 5388007 * 69434112066965200002029816020200391 1234567890123456789012332109876543210987654321 = 3 * 7 * 11 * 13^2 * 37 * 101 * 1283 * 1321 * 12696611 * 22246051 * 17677586805042589 123456789012345678901234432109876543210987654321 = 11 * 41 * 59 * 101 * 271 * 196878749 * 5961344400491 * 144428434944686621 12345678901234567890123455432109876543210987654321 = 3 * 11 * 47 * 663301 * 899464250117207 * 13341621655860372536394053 1234567890123456789012345665432109876543210987654321 = 3 * 11^2 * 19 * 37 * 1051 * 102121 * 12609029 * 273565030747709 * 13067515593775919 123456789012345678901234567765432109876543210987654321 = 11 * 31 * 101 * 58129 * 86969272325821 * 709055999909704915865900034509 12345678901234567890123456788765432109876543210987654321 = 3^2 * 11 * 29 * 101 * 239 * 281 * 2087 * 4649 * 909091 * 11622001 * 121499449 * 50899277731560617 1234567890123456789012345678998765432109876543210987654321 = 3^3 * 7 * 11 * 13 * 31 * 37 * 41 * 211 * 241 * 271 * 2087 * 2161 * 9091 * 2906161 * 11622001 * 50899277731560617 123456789012345678901234567890098765432109876543210987654321 = 3^3 * 7 * 11 * 13 * 31 * 37 * 211 * 241 * 2161 * 2906161 * 12470382727272727272727272727282703579 12345678901234567890123456789011098765432109876543210987654321 = 11 * 19 * 43 * 73 * 101 * 137 * 1359989121447028436148510935549979476538827677124983 1234567890123456789012345678901221098765432109876543210987654321 = 3 * 11 * 23 * 29 * 37 * 307 * 1032067 * 16350683 * 21300898963693 * 13737046898073357472194175073 123456789012345678901234567890123321098765432109876543210987654321 = 3 * 11 * 37 * 47 * 12401 * 2105669 * 82386232739968607099021366900549123963176158655207 12345678901234567890123456789012344321098765432109876543210987654321 = 11 * 41 * 271 * 56031401 * 1802758960321413738011161514704251877111088516635898701 1234567890123456789012345678901234554321098765432109876543210987654321 3 * 7 * 11 * 13 * 37 * 101 * 181 * 3144179 * 39960722102064876110671 * 4837459946274405944243807940059 123456789012345678901234567890123456654321098765432109876543210987654321 = 3 * 7^2 * 11^2 * 13 * 37 * 443 * 26317 * 1237733339089370628375588074867730236170365869279018666653 12345678901234567890123456789012345677654321098765432109876543210987654321 = 11 * 1297 * 8239669 * 381572674607 * 275229691907079144000796054804801421173712365145561 1234567890123456789012345678901234567887654321098765432109876543210987654321 3^2 * 11 * 37 * 39359 * 71887 * 858127 * 909090909090909091 * 1111111111111111111 * 137425482585508591037 123456789012345678901234567890123456789987654321098765432109876543210987654321 = 3^2 * 11 * 37 * 41 * 73 * 101 * 137 * 271 * 3541 * 9091 * 27961 * 39359 * 71887 * 858127 * 1676321 * 5964848081 * 137425482585508591037 12345678901234567890123456789012345678900987654321098765432109876543210987654321 = 3^2 * 11^2 * 73 * 101 * 137 * 3541 * 27961 * 168559 * 456559 * 1676321 * 5964848081 * 23779840069 * 6194828868817936425433501 1234567890123456789012345678901234567890110987654321098765432109876543210987654321 11 * 17 * 229 * 22560763 * 415535012863625645831 * 3075222063145892980805711417199095141125173030259 123456789012345678901234567890123456789012210987654321098765432109876543210987654321 = 3 * 7 * 11 * 13 * 37 * 31746607473677 * 673886468172011 * 6568290032211769 * 7907178476452060041460203817763377 12345678901234567890123456789012345678901233210987654321098765432109876543210987654321 = 3 * 11 * 41 * 101 * 6724007044319 * 13435927356149996091251815927629713730022128688912483128349203260203 1234567890123456789012345678901234567890123443210987654321098765432109876543210987654321 11 * 29 * 41 * 101 * 271 * 1217261 * 3148351 * 6065602327 * 13460018279 * 2447332929630504506467 * 4503708603243233968703789 123456789012345678901234567890123456789012345543210987654321098765432109876543210987654321 3 * 11 * 37 * 43458637 * 3293321819719 * 135617106492395050602517951556623 * 5209242393733277484698768036933129 12345678901234567890123456789012345678901234566543210987654321098765432109876543210987654321 = 3 * 11 * 53 * 18798691 * 365536775053 * 74271944125657819 * 13830621314838195781578087623893944405215771109079217 1234567890123456789012345678901234567890123456776543210987654321098765432109876543210987654321 = 11 * 67 * 73 * 101 * 137 * 10936691 * 151634054062743998152686005593525944687538032278950156388927718048387150807263 123456789012345678901234567890123456789012345678876543210987654321098765432109876543210987654321 = 3^3 * 7 * 11 * 13 * 17 * 37 * 41 * 73 * 101 * 137 * 379 * 9901 * 23269 * 5882353 * 99990001 * 51551814703 * 9999999900000001 * 6623236046311999035689159423 12345678901234567890123456789012345678901234567899876543210987654321098765432109876543210987654321 = 3^2 * 11 * 41^2 * 251 * 271 * 379 * 5051 * 9091 * 21401 * 23269 * 25601 * 51551814703 * 182521213001 * 78875943472201 * 6623236046311999035689159423 1234567890123456789012345678901234567890123456789009876543210987654321098765432109876543210987654321 = 3^2 * 11 * 37 * 251 * 2749 * 5051 * 21401 * 25601 * 8519447483 * 182521213001 * 78875943472201 * 1439103033201033699180846772543955595478801 123456789012345678901234567890123456789012345678901109876543210987654321098765432109876543210987654321 = 11 * 101 * 1245658612333593629442233 * 89207605706004910191508269034469607961626409373787132246203032042117075567