Search a number
Carmichael numbers
A composite n such that an-1 - 1 is divisible by n for each a coprime to n. more

The first 600 Carmichael numbers :
561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 410041, 449065, 488881, 512461, 530881, 552721, 656601, 658801, 670033, 748657, 825265, 838201, 852841, 997633, 1024651, 1033669, 1050985, 1082809, 1152271, 1193221, 1461241, 1569457, 1615681, 1773289, 1857241, 1909001, 2100901, 2113921, 2433601, 2455921, 2508013, 2531845, 2628073, 2704801, 3057601, 3146221, 3224065, 3581761, 3664585, 3828001, 4335241, 4463641, 4767841, 4903921, 4909177, 5031181, 5049001, 5148001, 5310721, 5444489, 5481451, 5632705, 5968873, 6049681, 6054985, 6189121, 6313681, 6733693, 6840001, 6868261, 7207201, 7519441, 7995169, 8134561, 8341201, 8355841, 8719309, 8719921, 8830801, 8927101, 9439201, 9494101, 9582145, 9585541, 9613297, 9890881, 10024561, 10267951, 10402561, 10606681, 10837321, 10877581, 11119105, 11205601, 11921001, 11972017, 12261061, 12262321, 12490201, 12945745, 13187665, 13696033, 13992265, 14469841, 14676481, 14913991, 15247621, 15403285, 15829633, 15888313, 16046641, 16778881, 17098369, 17236801, 17316001, 17586361, 17812081, 18162001, 18307381, 18900973, 19384289, 19683001, 20964961, 21584305, 22665505, 23382529, 25603201, 26280073, 26474581, 26719701, 26921089, 26932081, 27062101, 27336673, 27402481, 28787185, 29020321, 29111881, 31146661, 31405501, 31692805, 32914441, 33302401, 33596641, 34196401, 34657141, 34901461, 35571601, 35703361, 36121345, 36765901, 37167361, 37280881, 37354465, 37964809, 38151361, 38624041, 38637361, 39353665, 40160737, 40280065, 40430401, 40622401, 40917241, 41298985, 41341321, 41471521, 42490801, 43286881, 43331401, 43584481, 43620409, 44238481, 45318561, 45877861, 45890209, 46483633, 47006785, 48321001, 48628801, 49333201, 50201089, 53245921, 53711113, 54767881, 55462177, 56052361, 58489201, 60112885, 60957361, 62756641, 64377991, 64774081, 65037817, 65241793, 67371265, 67653433, 67902031, 67994641, 68154001, 69331969, 70561921, 72108421, 72286501, 74165065, 75151441, 75681541, 75765313, 76595761, 77826001, 78091201, 78120001, 79411201, 79624621, 80282161, 80927821, 81638401, 81926461, 82929001, 83099521, 83966401, 84311569, 84350561, 84417985, 87318001, 88689601, 90698401, 92625121, 93030145, 93614521, 93869665, 94536001, 96895441, 99036001, 99830641, 99861985, 100427041, 101649241, 101957401, 102090781, 104404861, 104569501, 104852881, 105117481, 105309289, 105869401, 106041937, 107714881, 109393201, 109577161, 111291181, 114910489, 115039081, 115542505, 116682721, 118901521, 119327041, 120981601, 121247281, 122785741, 124630273, 127664461, 128697361, 129255841, 129762001, 130032865, 130497361, 132511681, 133205761, 133344793, 133800661, 134809921, 134857801, 135556345, 136625941, 139592101, 139952671, 140241361, 144218341, 145124785, 146843929, 150846961, 151530401, 151813201, 153589801, 153927961, 157731841, 158404141, 158864833, 159492061, 161035057, 161242705, 161913961, 163954561, 167979421, 168659569, 169057801, 169570801, 170947105, 171454321, 171679561, 172290241, 172430401, 172947529, 173085121, 174352641, 175997185, 176659201, 178451857, 178482151, 178837201, 180115489, 181154701, 182356993, 184353001, 186393481, 186782401, 187188001, 188516329, 188689501, 189941761, 193708801, 193910977, 194120389, 194675041, 196358977, 200753281, 206955841, 208969201, 212027401, 213835861, 214850881, 214852609, 216821881, 221884001, 225745345, 226509361, 227752993, 228842209, 230630401, 230996949, 231194965, 237597361, 238244041, 238527745, 241242001, 242641153, 246446929, 247095361, 250200721, 252141121, 255160621, 256828321, 257495641, 258634741, 266003101, 270857521, 271481329, 271794601, 273769921, 274569601, 275283401, 277241401, 278152381, 279377281, 280067761, 280761481, 288120421, 289766701, 289860481, 291848401, 292244833, 292776121, 295643089, 295826581, 296559361, 299736181, 300614161, 301704985, 302751505, 306871201, 311388337, 318266641, 321197185, 321602401, 325546585, 328573477, 329769721, 333065305, 333229141, 334783585, 338740417, 346808881, 348612265, 354938221, 357277921, 357380101, 358940737, 360067201, 362569201, 364590721, 366532321, 366652201, 367804801, 367939585, 368113411, 382304161, 382536001, 390489121, 392099401, 393122521, 393513121, 393716701, 395044651, 395136505, 396262945, 399906001, 403043257, 403317421, 405739681, 413058601, 413138881, 413631505, 416964241, 417241045, 419520241, 426821473, 429553345, 434330401, 434932961, 438359041, 440306461, 440707345, 455106601, 458368201, 461502097, 461854261, 462199681, 471441001, 471905281, 473847121, 477726145, 481239361, 483006889, 484662529, 490099681, 490503601, 492559141, 496050841, 499310197, 503758801, 507726901, 509033161, 510825601, 511338241, 516684961, 517937581, 518117041, 518706721, 527761081, 529782121, 530443201, 532758241, 533860309, 540066241, 542497201, 544101481, 545363281, 545570641, 547652161, 548871961, 549117205, 549333121, 549538081, 551672221, 552894301, 555465601, 556199281, 556450777, 557160241, 557795161, 558570961, 558977761, 561481921, 561777121, 564651361, 568227241, 569332177, 573896881, 577240273, 579606301, 580565233, 590754385, 593234929, 595405201, 597717121, 600892993, 602074585, 602426161, 602593441, 606057985, 609865201, 611397865, 612347905, 612816751, 616463809, 618068881, 620169409, 621101185, 625060801, 625482001, 629692801, 631071001, 633639097, 638959321, 642708001, 652969351, 656187001, 662086041, 672389641, 683032801, 683379841, 684106401, 686059921, 689880801, 697906561, 698548201, 702683101, 703995733, 704934361, 705101761, 707926801, 710382401, 710541481, 711374401, 713588401, 717164449, 721244161, 722923201, 727083001, 739444021, 743404663, 744866305, 745864945, 746706961, 752102401, 759472561, 765245881, 771043201, 775368901, 775866001, 776176261, 781347841, 784966297, 790020001, 790623289, 794937601, 798770161, 804978721, 809702401, 809883361, 814056001, 822531841, 824389441, 824405041, 829678141, 832060801, 833608321, 834244501, 834720601, 836515681, 839275921, 841340521, 842202361, 843704401, 847491361, 849064321, 851703301, 851934601, 852729121, 854197345.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 8241 values, from 561 to 999629786233).

n\r 0  1 
208241 2 
361811664 3 
4080930148 4 
56276575327344368 5 
608116061064 6 
713344613432496450454462 7 
8070990730994075 8 
9063992528884223383317 9 
10065750344062703270368 10 
1113242770473457442466440458475465471

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.