Last update [ May 26, 2023 ] ---------------------------------------------------------------------- Appending 1's to number k until prime WONPLATE_197 ---------------------------------------------------------------------- Still searching for [603][1^^n] n > 300000 603*10^n+R(n) [1244][1^^n] n > 200000 1244*10^n+R(n) [1861][1^^n] n > 200000 1861*10^n+R(n) [2277][1^^n] n > 43000 2277*10^n+R(n) [2294][1^^n] n > 38000 2294*10^n+R(n) [2587][1^^n] n > 30000 2587*10^n+R(n) [2702][1^^n] n > 34000 2702*10^n+R(n) [3092][1^^n] n > 32000 3092*10^n+R(n) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- [1][1^^1] = prime! = 11 first delayed prime record nr 1 [2][1^^2] = prime! = 211 a new delayed prime record nr 2 [3][1^^1] = prime! = 31 [4][1^^1] = prime! = 41 [5][1^^5] = prime! = 511111 a new delayed prime record nr 3 [6][1^^1] = prime! = 61 [7][1^^1] = prime! = 71 [8][1^^2] = prime! = 811 [9][1^^2] = prime! = 911 [10][1^^1] = prime! = 1011 [11][1^^17] = prime! = [1][1^^18] = 1111111111111111111 The famous Repunits ! a new delayed prime record nr 4 ____________________________________________________________________________________________________________________________________________________________________________________ [12][1^^n] --------- rule 1 : when m is multiple of 3 then [12][1^^m] is divisible by 3 rule 2 : [12][1^^m] ; m=2+6k, k=0,1,2,... divisible by 7 rule 3 : when m is odd in [12][1^^m] then all is divisible by 11 after rule 3 2 4 (6) 8 10 (12) 14 16 (18) 20 22 (24) 26 28 (30) 32 34 (36) 38 40 (42) 44 46 (48) 50 52 (54) 56 58 (60) 62 64 (66) 68 70 (72) 74 76 (78) 80 82 (84) 86 88 (90) 92 94 (96) 98 100 after rule 1 (2) 4 (8) 10 (14) 16 (20) 22 (26) 28 (32) 34 (38) 40 (44) 46 (50) 52 (56) 58 (62) 64 (68) 70 (74) 76 (80) 82 (86) 88 (92) 94 (98) 100 after rule 2 4 10 16 22 28 34 40 46 52 58 64 70 76 82 88 94 100 (+6) [12][1^^1] = 11^2 [12][1^^2] = 7 x 173 [12][1^^3] = 3 x 11 x 367 [12][1^^4] = 281 x 431 [12][1^^5] = 11 x 23 x 4787 [12][1^^6] = 3^2 x 31 x 83 x 523 [12][1^^7] = 11 x 17 x 19 x 89 x 383 [12][1^^8] = 7 x 6329 x 27337 [12][1^^9] = 3 x 11 x 367003367 [12][1^^10] = 61 x 1985428051 [12][1^^11] = 11 x 43 x 47 x 54478481 [12][1^^12] = 3 x 6089 x 13759 x 48187 [12][1^^13] = 11 x 11010101010101 [12][1^^14] = 7 x 131 x 1320731855083 [12][1^^15] = 3^4 x 11 x 13592717296421 [12][1^^16] = 683 x 177322271026517 [12][1^^22] = 29 x 71 x 58820355080675624629 [12][1^^28] = 857 x 1163 x 11321 x 63803 x 168227721121567 [12][1^^34] = 10149217781 x 102964488541 x 115894799982791 [12][1^^40] = 2543 x 10035853 x 11989979 x 28875871 x 13706602606732201 [12][1^^46] = 659 x 101869 x 14008987 x 128780408603998284751736229136643 [12][1^^52] = 53189 x 2276995452276055408281996486324448873096149788699 [12][1^^58] = 55070759743427 x 2199190853283377710977425780027771103398181293 [12][1^^64] = 113 x 727 x 69390227 x 81700584262805637977 x 260044494523518665693132852211059 [12][1^^70] = 61 x 394996378522919344363663663 x 5026446213067289278810565027627976912002077 [12][1^^76] = 7957837 x 191188890341 x 79602424711757074199833325474324096006321504506550380156583 [12][1^^82] = 275677 x 217369494376596052979 x 2021086305258534929370038807688442789993542202111661007617 [12][1^^88] = 83 x 173 x 281 x 7517 x 7862766797 x 2023268012128158269 x 251003693656776258082162819725543681209217166336789 [12][1^^94] = 11798849 x 6414552501403703691611 x 1600213689189496550862051077391575365484324222775694235608027454149 [12][1^^100] = 43487 x 24519903637423 x 13802420025544751 x 77808763291935474486367962787 x 105760142911172063761372095743947822003 [12][1^^106] = 29 x 51844008518139780937 x 205684852153212157356661 x 391638256441175787893920508317342061606067691105114297349415887 [12][1^^112] = 1669 x 3631 x 16021277011 x 1247395788356056811432307881747805673997713101257428563788376960635139258954458827611174590119159 [12][1^^118] = 509 x 44687 x 1064059 x 5004022996553145854266660456319462993942832189317003676762752789387649346082308156707362271278612607236263 [12][1^^124] = 48806874723807083108356867 x 1058854399362990511245392179859 x 2343509638161628145225929956310157547974760516143237740348954466076287 [12][1^^130] = 61 x 36369136999488198605614748630621486653942384326441069497849 x 54591013557175174392624128776602653952926159478844296854111853300509099 [12][1^^136] = prime! ____________________________________________________________________________________________________________________________________________________________________________________ [12][1^^136] = prime! a new delayed prime record nr 5 [13][1^^1] = prime! [14][1^^9] = prime! [15][1^^1] = prime! [16][1^^3] = prime! [17][1^^8] = prime! [18][1^^1] = prime! [19][1^^1] = prime! [20][1^^2] = prime! [21][1^^1] = prime! = [2][1^^2] [22][1^^3] = prime! [23][1^^2] = prime! [24][1^^1] = prime! [25][1^^1] = prime! [26][1^^3] = prime! [27][1^^1] = prime! [28][1^^1] = prime! [29][1^^6] = prime! [30][1^^2] = prime! [31][1^^1] = prime! = [3][1^^2] [32][1^^35] = prime! [33][1^^1] = prime! [34][1^^6] = prime! [35][1^^2] = prime! [36][1^^4] = prime! ____________________________________________________________________________________________________________________________________________________________________________________ [37][1^^n] --------- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 after divisible by 3 : {2 +3} 1 (2) 3 4 (5) 6 7 (8) 9 10 (11) 12 13 (14) 15 16 (17) 18 19 (20) 21 22 (23) 24 25 (26) 27 28 (29) 30 31 (32) 33 34 (35) 36 37 (38) 39 40 (41) 42 43 (44) 45 46 (47) 48 49 (50) 51 52 (53) 54 55 (56) 57 58 (59) 60 61 (62) 63 64 (65) 66 67 (68) 69 70 (71) 72 73 (74) 75 76 (77) 78 79 (80) 81 82 (83) 84 85 (86) 87 88 (89) 90 91 (92) 93 94 (95) 96 97 (98) 99 100 after divisible by 7 : {1 +6} (1) (2) 3 4 (5) 6 (7) (8) 9 10 (11) 12 (13) (14) 15 16 (17) 18 (19) (20) 21 22 (23) 24 (25) (26) 27 28 (29) 30 (31) (32) 33 34 (35) 36 (37) (38) 39 40 (41) 42 (43) (44) 45 46 (47) 48 (49) (50) 51 52 (53) 54 (55) (56) 57 58 (59) 60 (61) (62) 63 64 (65) 66 (67) (68) 69 70 (71) 72 (73) (74) 75 76 (77) 78 (79) (80) 81 82 (83) 84 (85) (86) 87 88 (89) 90 (91) (92) 93 94 (95) 96 (97) (98) 99 100 after divisible by 37 : {3 +3} (1) (2) (3) 4 (5) (6) (7) (8) (9) 10 (11) (12) (13) (14) (15) 16 (17) (18) (19) (20) (21) 22 (23) (24) (25) (26) (27) 28 (29) (30) (31) (32) (33) 34 (35) (36) (37) (38) (39) 40 (41) (42) (43) (44) (45) 46 (47) (48) (49) (50) (51) 52 (53) (54) (55) (56) (57) 58 (59) (60) (61) (62) (63) 64 (65) (66) (67) (68) (69) 70 (71) (72) (73) (74) (75) 76 (77) (78) (79) (80) (81) 82 (83) (84) (85) (86) (87) 88 (89) (90) (91) (92) (93) 94 (95) (96) (97) (98) (99) 100 after divisible by 13 : {4 +6} (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48) (49) (50) (51) (52) (53) (54) (55) (56) (57) (58) (59) (60) (61) (62) (63) (64) (65) (66) (67) (68) (69) (70) (71) (72) (73) (74) (75) (76) (77) (78) (79) (80) (81) (82) (83) (84) (85) (86) (87) (88) (89) (90) (91) (92) (93) (94) (95) (96) (97) (98) (99) (100) so all the range is eliminated after deleting with these four rules ! [37][1^^1] = 7 x 53 set of six divisors (7, 3, 37, 13, 3, 37) that appear periodically [37][1^^2] = 3 x 1237 [37][1^^3] = 17 x 37 x 59 [37][1^^4] = 13 x 28547 [37][1^^5] = 3 x 1237037 [37][1^^6] = 37 x 1003003 [37][1^^7] = 7 x 79 x 671087 [37][1^^8] = 3^2 x 23 x 17928073 [37][1^^9] = 37 x 1003003003 [37][1^^10] = 13 x 28547008547 [37][1^^11] = 3 x 29 x 1279 x 33351407 [37][1^^12] = 19 x 37 x 112501 x 469237 [37][1^^13] = 7 x 742009 x 71449097 [37][1^^14] = 3 x 53 x 23340321453529 [37][1^^15] = 37 x 467 x 871463 x 2464543 [37][1^^16] = 13 x 3613 x 7901192512319 [37][1^^17] = 3^3 x 91951 x 1494802228043 [37][1^^18] = 37 x 252383 x 3974130599141 [37][1^^19] = 7 x 17 x 131 x 10391 x 2291017230589 [37][1^^20] = 3 x 79 x 109 x 487 x 2371 x 183383 x 678437 [37][1^^21] = 37 x 281 x 636300337 x 5609624099 [37][1^^22] = 13 x 6761 x 7243 x 12451 x 46819519339 [37][1^^23] = 3 x 127 x 1153 x 436974611 x 19332742657 [37][1^^76] = 371111111111111111111111111111111111111111111111111111111111111111111111111111 = 13 x 23963557135906000356801831334617467 x 191267572886117692078844800545652749797241 ____________________________________________________________________________________________________________________________________________________________________________________ [38][1^^n] --------- With k = 38 only every third (starting with 3 1's) is candidate for primeness [38][1^^1] = 3 x 127 [38][1^^2] = 37 x 103 [38][1^^3] = 23 x 1657 [38][1^^4] = 3 x 127037 [38][1^^5] = 17 x 37 x 73 x 83 [38][1^^6] = 233 x 163567 [38][1^^7] = 3^2 x 42345679 [38][1^^8] = 37 x 113 x 613 x 1487 [38][1^^9] = 31 x 2333 x 526957 [38][1^^10] = 3 x 2399 x 52954163 [38][1^^11] = 37 x 103003003003 [38][1^^12] = 23333 x 1633356667 [38][1^^13] = 3 x 73 x 1740233384069 [38][1^^14] = 37 x 2287 x 45038479669 [38][1^^15] = 353 x 661 x 163333566667 [38][1^^16] = 3^2 x 131 x 323249458109509 [38][1^^17] = 37 x 114346289 x 900798827 [38][1^^18] = 19 x 227 x 541 x 2857 x 5716953331 [38][1^^19] = 3 x 879449 x 1140233 x 126685261 [38][1^^20] = 37 x 393380951 x 261840342653 [38][1^^21] = 17 x 73 x 1372549 x 22374429543379 Here is a nice infinite semiprime pattern [38][1^^3] = 38111 = 23 x 1657 [38][1^^6] = 38111111 = 233 x 163567 [38][1^^9] = 38111111111 = 2333 x (16335667 = 31 x 526957) [38][1^^12] = 38111111111111 = 23333 x 1633356667 [38][1^^15] = 38111111111111111 = (233333 = 353 x 661) x 163333566667 [38][1^^18] = 38111111111111111111 = (2333333 = 19 x 227 x 541) x (16333335666667 = 2857 x 5716953331) [38][1^^21] = 38111111111111111111111 = (23333333 = 17 x 1372549) x (1633333356666667 = 73 x 22374429543379) [38][1^^24] = 38111111111111111111111111 = 29 x 31 x 47 x 193 x 887 x 2254501 x 2337021457 [38][1^^27] = 38111111111111111111111111111 = 10163 x 71671 x 229591 x 5274397 x 43207441 [38][1^^30] = 38111111111111111111111111111111 = 139 x 52181443 x 23333333333 x 225187324171 [38][1^^33] = 38111111111111111111111111111111111 = 97 x 569 x 77863831 x 410076157 x 21625558049581 [38][1^^36] = 38111111111111111111111111111111111111 = 19 x 103 x 283 x 1091 x 1734907 x 2138710663 x 16998921361351 [38][1^^39] = 38111111111111111111111111111111111111111 = 31 x 2617 x 752688172043 x 624124315373846643739651 [38][1^^42] = 38111111111111111111111111111111111111111111 = 59 x 1890877 x 104708784487 x 824951521633 x 3954802259887 [38][1^^45] = 38111111111111111111111111111111111111111111111 = 73 x 311 x 1861 x 749803 x 10006201 x 120227991530060695506662839 [38][1^^48] = 38111111111111111111111111111111111111111111111111 = 223 x 8353 x 1425757 x 23333333333333333 x 615009703935993642649 [38][1^^51] = 38111111111111111111111111111111111111111111111111111 = 61 x 199 x 58119797 x 91670701 x 4014696289 x 146778133769777095367653 [38][1^^54] = 38111111111111111111111111111111111111111111111111111111 = 19 x 31 x 337 x 1453 x 10531 x 47292001 x 4765201503353 x 55680384760401664885213 [38][1^^57] = 38111111111111111111111111111111111111111111111111111111111 = 444007 x 11661407 x 2000902063819 x 5279715166766653 x 696746049022087777 [38][1^^60] = 38111111111111111111111111111111111111111111111111111111111111 = 109 x 457 x 23909 x 2567991577 x 2078874843217 x 89534183063893 x 66947858033184859 [38][1^^63] = 38111111111111111111111111111111111111111111111111111111111111111 = 1583 x 1030069 x 361713277 x 408413539 x 3609073609 x 30879705642673 x 1419616067167483 [38][1^^66] = 38111111111111111111111111111111111111111111111111111111111111111111 = 23333333333333333333333 x 1633333333333333333333356666666666666666666667 ____________________________________________________________________________________________________________________________________________________________________________________ [39][1^^2] = prime! [40][1^^1] = prime! [41][1^^2] = prime! = [4][1^^3] [42][1^^1] = prime! [43][1^^1] = prime! [44][1^^3] = prime! [45][1^^772] = prime! a new delayed prime record nr 6 [46][1^^1] = prime! [47][1^^3] = prime! [48][1^^5] = prime! [49][1^^1] = prime! [50][1^^2] = prime! [51][1^^4] = prime! = [5][1^^5] [52][1^^1] = prime! [53][1^^9] = prime! [54][1^^1] = prime! [55][1^^31] = prime! ____________________________________________________________________________________________________________________________________________________________________________________ [56][1^^n] --------- series 1 4 7 10 13 or {1 +3} are divisible by 3 series {6 +6} are divisible by 7 only {2 +6} are eligible for primeness! all odd are divisible by 11 [56][1^^1] = 561 = 3 x 11 x 17 [56][1^^2] = 5611 = 31 x 181 [56][1^^3] = 56111 = 11 x 5101 [56][1^^4] = 561111 = 3 x 53 x 3529 [56][1^^5] = 5611111 = 11 x 510101 [56][1^^6] = 56111111 = 7 x 757 x 10589 [56][1^^7] = 561111111 = 3^3 x 11 x 29 x 65147 [56][1^^8] = 5611111111 = 22073 x 254207 [56][1^^9] = 56111111111 = 11^2 x 97 x 4780703 [56][1^^10] = 561111111111 = 3 x 1031 x 181413227 [56][1^^11] = 5611111111111 = 11 x 23 x 61 x 877 x 414571 [56][1^^12] = 56111111111111 = 7 x 19^2 x 397 x 797 x 70177 [56][1^^13] = 561111111111111 = 3 x 11 x 60887 x 279261041 [56][1^^14] = 5611111111111111 = 2861 x 167879 x 11682469 [56][1^^15] = 56111111111111111 = 11 x 43936957 x 116098393 [56][1^^16] = 561111111111111111 = 3^2 x 103 x 605297854488793 [56][1^^17] = 5611111111111111111 = 11 x 17 x 31 x 53 x 18262898217071 [56][1^^18] = 56111111111111111111 = 7 x 71 x 112899619941873463 [56][1^^19] = 561111111111111111111 = 3 x 11 x 93329 x 198733 x 916744531 [56][1^^20] = 5611111111111111111111 = 131 x 163 x 84697 x 87049 x 35641679 [56][1^^18470] = prime! a new delayed prime record nr 7 ____________________________________________________________________________________________________________________________________________________________________________________ [57][1^^1] = prime! [58][1^^3] = prime! [59][1^^18] = prime! [60][1^^1] = prime! [61][1^^4] = prime! = [6][1^^5] [62][1^^2] = prime! [63][1^^1] = prime! [64][1^^1] = prime! [65][1^^3] = prime! [66][1^^1] = prime! [67][1^^210] = prime! [68][1^^3] = prime! [69][1^^1] = prime! [70][1^^1] = prime! [71][1^^6] = prime! = [7][1^^7] [72][1^^2] = prime! [73][1^^7] = prime! [74][1^^2] = prime! [75][1^^1] = prime! [76][1^^1] = prime! [77][1^^9] = prime! [78][1^^4] = prime! [79][1^^3] = prime! [80][1^^2] = prime! [81][1^^1] = prime! = [8][1^^2] [82][1^^1] = prime! [83][1^^2] = prime! [84][1^^5] = prime! [85][1^^6] = prime! [86][1^^3] = prime! [87][1^^149] = prime! [88][1^^1] = prime! [89][1^^6] = prime! [90][1^^2] = prime! [91][1^^1] = prime! = [9][1^^2] [92][1^^3] = prime! [93][1^^2] = prime! [94][1^^1] = prime! [95][1^^2] = prime! [96][1^^7] = prime! [97][1^^1] = prime! [98][1^^2] = prime! [99][1^^1] = prime! [100][1^^10] = prime! [101][1^^2] = prime! = [10][1^^3] [102][1^^1] = prime! [103][1^^3] = prime! [104][1^^44] = prime! [105][1^^1] = prime! [106][1^^1] = prime! [107][1^^2] = prime! [108][1^^5] = prime! [109][1^^1] = prime! [110][1^^17] = prime! [111][1^^16] = prime! = [11][1^^17] = [1][1^^18] [112][1^^3] = prime! [113][1^^2] = prime! [114][1^^2] = prime! [115][1^^1] = prime! [116][1^^9] = prime! [117][1^^1] = prime! [118][1^^1] = prime! [119][1^^5] = prime! [120][1^^1] = prime! [121][1^^135] = prime! = [12][1^^136] [122][1^^2] = prime! [123][1^^1] = prime! [124][1^^6] = prime! [125][1^^2] = prime! [126][1^^2] = prime! [127][1^^4] = prime! [128][1^^3] = prime! [129][1^^1] = prime! [130][1^^1] = prime! [131][1^^3] = prime! = [13][1^^4] [132][1^^1] = prime! [133][1^^2890] = prime! [134][1^^2] = prime! [135][1^^4] = prime! [136][1^^1] = prime! [137][1^^2] = prime! [138][1^^1] = prime! [139][1^^24] = prime! [140][1^^2] = prime! [141][1^^8] = prime! = [14][1^^9] [142][1^^3] = prime! [143][1^^3] = prime! [144][1^^2] = prime! [145][1^^1] = prime! [146][1^^5] = prime! [147][1^^1] = prime! [148][1^^1] = prime! [149][1^^3] = prime! [150][1^^7] = prime! [151][1^^1] = prime! = [15][1^^2] [152][1^^3] = prime! [153][1^^1] = prime! [154][1^^3] = prime! [155][1^^2] = prime! [156][1^^4] = prime! [157][1^^1] = prime! [158][1^^6] = prime! [159][1^^119] = prime! [160][1^^1] = prime! [161][1^^2] = prime! = [16][1^^3] [162][1^^1] = prime! [163][1^^6] = prime! [164][1^^2] = prime! [165][1^^11] = prime! [166][1^^4] = prime! [167][1^^5] = prime! [168][1^^2] = prime! [169][1^^3] = prime! [170][1^^2] = prime! [171][1^^7] = prime! = [17][1^^8] [172][1^^1] = prime! [173][1^^11] = prime! [174][1^^1] = prime! [175][1^^16] = prime! 1751111111111111111 is prime ____________________________________________________________________________________________________________________________________________________________________________________ [176][1^^n] ---------- [176][1^^n] is always composite! set of six divisors (3, 11, 13, 3, 7, 11) that appear periodically [176][1^^1] = 3 x 587 [176][1^^2] = 11 x 1601 [176][1^^3] = 13 x 19 x 23 x 31 [176][1^^4] = 3^2 x 11 x 17789 [176][1^^5] = 7 x 2515873 [176][1^^6] = 11 x 16010101 [176][1^^7] = 3 x 673 x 872269 [176][1^^8] = 11 x 1601010101 [176][1^^9] = 13 x 13547008547 [176][1^^10] = 3 x 11 x 115057 x 463831 [176][1^^11] = 7^2 x 359410430839 [176][1^^12] = 11^3 x 17 x 59 x 97 x 1359991 all {1 +3} divisible by 3 all {2 +4} divisible by 11 all {3 +6} divisible by 13 all {5 +6} divisible by 7 ____________________________________________________________________________________________________________________________________________________________________________________ [177][1^^22] = prime! 1771111111111111111111111 is prime [178][1^^10] = prime! [179][1^^2] = prime! [180][1^^1] = prime! [181][1^^1] = prime! = [18][1^^2] [182][1^^2] = prime! [183][1^^1] = prime! [184][1^^3] = prime! [185][1^^14] = prime! [186][1^^1] = prime! [187][1^^1] = prime! [188][1^^186] = prime! [189][1^^2] = prime! [190][1^^1] = prime! [191][1^^11] = prime! = [19][1^^12] [192][1^^2] = prime! [193][1^^1] = prime! [194][1^^6] = prime! [195][1^^1] = prime! [196][1^^3] = prime! [197][1^^12] = prime! [198][1^^101] = prime! [199][1^^6] = prime! [200][1^^2] = prime! [201][1^^1] = prime! [202][1^^31] = prime! 2021111111111111111111111111111111 is prime [203][1^^5] = prime! [204][1^^2] = prime! [205][1^^3] = prime! [206][1^^2] = prime! [207][1^^14] = prime! [208][1^^1] = prime! [209][1^^n] = always composite! set of six divisors (3, 11, 7, 3, 13, 11) that appear periodically [210][1^^2] = prime! [211][1^^1] = prime! = [21][1^^2] = [2][1^^3] [212][1^^2] = prime! [213][1^^1] = prime! [214][1^^1] = prime! [215][1^^653] = prime! [216][1^^1] = prime! [217][1^^3] = prime! [218][1^^3] = prime! [219][1^^2] = prime! [220][1^^67] = prime! [221][1^^2] = prime! = [22][1^^3] [222][1^^1] = prime! [223][1^^7] = prime! [224][1^^5] = prime! [225][1^^1] = prime! [226][1^^4] = prime! [227][1^^3] = prime! [228][1^^1] = prime! [229][1^^39] = prime! 229111111111111111111111111111111111111111 is prime [230][1^^2] = prime! [231][1^^1] = prime! = [23][1^^2] [232][1^^684] = prime! [233][1^^2] = prime! [234][1^^1] = prime! [235][1^^1] = prime! [236][1^^3] = prime! [237][1^^1] = prime! [238][1^^1] = prime! [239][1^^2] = prime! [240][1^^4] = prime! [241][1^^1] = prime! = [24][1^^2] [242][1^^33] = prime! 242111111111111111111111111111111111 is prime [243][1^^478] = prime! [244][1^^1] = prime! [245][1^^32] = prime! 24511111111111111111111111111111111 is prime [246][1^^2] = prime! [247][1^^28] = prime! 2471111111111111111111111111111 is prime [248][1^^6] = prime! [249][1^^5] = prime! [250][1^^217] = prime! [251][1^^2] = prime! = [25][1^^3] [252][1^^1] = prime! [253][1^^1] = prime! [254][1^^2] = prime! [255][1^^1] = prime! [256][1^^6] = prime! [257][1^^9] = prime! [258][1^^5] = prime! [259][1^^1] = prime! [260][1^^3] = prime! [261][1^^2] = prime = [26][1^^3] [262][1^^1] = prime! [263][1^^3] = prime! [264][1^^7] = prime! [265][1^^4] = prime! [266][1^^3] = prime! [267][1^^1] = prime! [268][1^^6] = prime! [269][1^^5] = prime! [270][1^^2] = prime! [271][1^^1] = prime! = [27][1^^2] [272][1^^2] = prime! [273][1^^1] = prime! [274][1^^1] = prime! [275][1^^21] = prime! 275111111111111111111111 is prime [276][1^^2] = prime! [277][1^^6] = prime! [278][1^^3] = prime! [279][1^^1] = prime! [280][1^^1] = prime! [281][1^^2] = prime! = [28][1^^3] [282][1^^2] = prime! [283][1^^3] = prime! [284][1^^2] = prime! [285][1^^1] = prime! [286][1^^1] = prime! [287][1^^2] = prime! [288][1^^50] = prime! 28811111111111111111111111111111111111111111111111111 is prime [289][1^^3] = prime! [290][1^^6] = prime! [291][1^^5] = prime! = [29][1^^6] [292][1^^4] = prime! [293][1^^2] = prime! [294][1^^2] = prime! [295][1^^3] = prime! [296][1^^2] = prime! [297][1^^1] = prime! [298][1^^24] = prime! 298111111111111111111111111 is prime [299][1^^15] = prime! [300][1^^1] = prime! [301][1^^1] = prime! = [30][1^^2] [302][1^^2] = prime! [303][1^^11] = prime! [304][1^^1] = prime! [305][1^^3] = prime! [306][1^^1] = prime! [307][1^^180] = prime [308][1^^23] = prime! 30811111111111111111111111 is prime [309][1^^2] = prime! [310][1^^3] = prime! [311][1^^3] = prime! = [31][1^^4] = [3][1^^5] [312][1^^1] = prime! [313][1^^15] = prime! [314][1^^20] = prime! 31411111111111111111111 is prime [315][1^^2] = prime! [316][1^^6] = prime! [317][1^^17] = prime! 31711111111111111111 is prime [318][1^^1] = prime! [319][1^^1] = prime! [320][1^^864] = prime! [321][1^^34] = prime! = [32][1^^35] 3211111111111111111111111111111111111 is prime [322][1^^1] = prime! [323][1^^6] = prime! [324][1^^2] = prime! [325][1^^1] = prime! [326][1^^2] = prime! [327][1^^1] = prime! [328][1^^6] = prime! [329][1^^2] = prime! [330][1^^1] = prime! [331][1^^24] = prime! = [33][1^^25] 331111111111111111111111111 is prime [332][1^^2] = prime! [333][1^^1] = prime! [334][1^^12] = prime! [335][1^^44] = prime! 33511111111111111111111111111111111111111111111 is prime [336][1^^1] = prime! [337][1^^1] = prime! [338][1^^2] = prime! [339][1^^1] = prime! [340][1^^3] = prime! [341][1^^5] = prime! = [34][1^^6] [342][1^^2] = prime! [343][1^^10] = prime! [344][1^^3] = prime! [345][1^^2] = prime! [346][1^^1] = prime! [347][1^^5] = prime! [348][1^^4] = prime! [349][1^^1] = prime! [350][1^^3] = prime! [351][1^^1] = prime! = [35][1^^2] [352][1^^3] = prime! [353][1^^2] = prime! [354][1^^1] = prime! [355][1^^3] = prime! [356][1^^6] = prime! [357][1^^1] = prime! [358][1^^1] = prime! [359][1^^2] = prime! [360][1^^2] = prime! [361][1^^3] = prime! = [36][1^^4] [362][1^^66] = prime! 362111111111111111111111111111111111111111111111111111111111111111111 is prime [363][1^^1] = prime! [364][1^^22] = prime! [365][1^^6] = prime! [366][1^^4] = prime! [367][1^^1] = prime! [368][1^^3] = prime! [369][1^^1] = prime! [370][1^^1] = prime! [371][1^^n] = always composite! see case [37][1^^n] set of six divisors (3, 37, 13, 3, 37, 7) that appear periodically [372][1^^7] = prime! [373][1^^64] = prime! [374][1^^3] = prime! [375][1^^2] = prime! [376][1^^1] = prime! [377][1^^5] = prime! [378][1^^2] = prime! [379][1^^7] = prime! [380][1^^2] = prime! [381][1^^n] = always composite! see case [38][1^^n] [382][1^^1] = prime! [383][1^^6] = prime! [384][1^^4] = prime! [385][1^^1] = prime! [386][1^^2] = prime! [387][1^^2] = prime! [388][1^^1] = prime! [389][1^^3] = prime! [390][1^^4] = prime! [391][1^^1] = prime! = [39][1^^2] [392][1^^3] = prime! [393][1^^1] = prime! [394][1^^4] = prime! [395][1^^2] = prime! [396][1^^13] = prime! [397][1^^24] = prime! [398][1^^6] = prime! [399][1^^4] = prime! [400][1^^1] = prime! [401][1^^2] = prime! = [40][1^^3] [402][1^^1] = prime! [403][1^^91] = prime! [404][1^^6] = prime! [405][1^^1] = prime! [406][1^^57] = prime! 406111111111111111111111111111111111111111111111111111111111 is prime [407][1^^n] = always composite! set of six divisors (3, 11, 37, 3, 7, 11) that appear periodically [408][1^^4] = prime! [409][1^^1] = prime! [410][1^^2] = prime! [411][1^^1] = prime! = [41][1^^2] = [4][1^^3] [412][1^^4] = prime! [413][1^^3] = prime! [414][1^^2] = prime! [415][1^^3] = prime! [416][1^^2] = prime! [417][1^^8] = prime! [418][1^^9] = prime! [419][1^^2] = prime! [420][1^^1] = prime! [421][1^^1] = prime! = [42][1^^2] [422][1^^3] = prime! [423][1^^1] = prime! [424][1^^1] = prime! [425][1^^15] = prime! [426][1^^1] = prime! [427][1^^1] = prime! [428][1^^9] = prime! [429][1^^137] = prime! [430][1^^6] = prime! [431][1^^6] = prime! = [43][1^^7] [432][1^^11] = prime! [433][1^^16] = prime! [434][1^^2] = prime! [435][1^^7] = prime! [436][1^^6] = prime! [437][1^^2] = prime! [438][1^^5] = prime! [439][1^^1] = prime! [440][1^^5] = prime! [441][1^^2] = prime! = [44][1^^3] [442][1^^1] = prime! [443][1^^9] = prime! [444][1^^1] = prime! [445][1^^1] = prime! [446][1^^3] = prime! [447][1^^2] = prime! [448][1^^1] = prime! [449][1^^8] = prime! [450][1^^5] = prime! [451][1^^771] = prime! [452][1^^6] = prime! [453][1^^1943] = prime! [454][1^^6] = prime! [455][1^^5] = prime! [456][1^^1] = prime! [457][1^^6] = prime! [458][1^^5] = prime! [459][1^^1] = prime! [460][1^^3] = prime! [461][1^^17] = prime! = [46][1^^18] [462][1^^1] = prime! [463][1^^4] = prime! [464][1^^2] = prime! [465][1^^1] = prime! [466][1^^7] = prime! [467][1^^6] = prime! [468][1^^2] = prime! [469][1^^1] = prime! [470][1^^12] = prime! [471][1^^2] = prime! = [47][1^^3] [472][1^^1] = prime! [473][1^^5] = prime! [474][1^^4] = prime! [475][1^^1] = prime! [476][1^^3] = prime! [477][1^^2] = prime! [478][1^^3] = prime! [479][1^^2] = prime! [480][1^^1] = prime! [481][1^^4] = prime! = [48][1^^5] [482][1^^1704] = prime! [483][1^^1] = prime! [484][1^^3] = prime! [485][1^^14] = prime! [486][1^^1] = prime! [487][1^^1] = prime! [488][1^^101] = prime! [489][1^^10] = prime! [490][1^^3] = prime! [491][1^^9] = prime! = [49][1^^10] [492][1^^2] = prime! [493][1^^1] = prime! [494][1^^2] = prime! [495][1^^1] = prime! [496][1^^108] = prime! [497][1^^2] = prime! [498][1^^2] = prime! [499][1^^30] = prime! 499111111111111111111111111111111 is prime [500][1^^3] = prime! [501][1^^1] = prime! = [50][1^^2] [502][1^^1] = prime! [503][1^^2] = prime! [504][1^^2] = prime! [505][1^^1] = prime! [506][1^^5] = prime! [507][1^^4] = prime! [508][1^^1] = prime! [509][1^^6] = prime! [510][1^^1] = prime! [511][1^^3] = prime! = [51][1^^4] = [5][1^^5] [512][1^^8] = prime! [513][1^^4] = prime! [514][1^^10] = prime! [515][1^^2] = prime! [516][1^^4] = prime! [517][1^^1] = prime! [518][1^^14] = prime! [519][1^^145] = prime! [520][1^^3] = prime! [521][1^^44] = prime! 52111111111111111111111111111111111111111111111 is prime = [52][1^^45] [522][1^^19] = prime! [523][1^^1] = prime! [524][1^^8] = prime! [525][1^^2] = prime! [526][1^^1] = prime! [527][1^^2] = prime! [528][1^^1] = prime! [529][1^^2778] = prime! note : next 3-PRP! is 529*10^9378+R(9378) [530][1^^24] = prime! 530111111111111111111111111 is prime [531][1^^8] = prime! = [53][1^^9] [532][1^^4] = prime! [533][1^^3] = prime! [534][1^^2] = prime! [535][1^^1] = prime! [536][1^^2] = prime! [537][1^^10] = prime! [538][1^^1] = prime! [539][1^^3] = prime! [540][1^^2] = prime! [541][1^^6] = prime! = [54][1^^7] [542][1^^3] = prime! [543][1^^1] = prime! [544][1^^1] = prime! [545][1^^6] = prime! [546][1^^49] = prime! 5461111111111111111111111111111111111111111111111111 is prime [547][1^^1] = prime! [548][1^^12] = prime! [549][1^^22] = prime! 5491111111111111111111111 is prime [550][1^^1] = prime! [551][1^^30] = prime! 551111111111111111111111111111111 is prime = [55][1^^31] [552][1^^1] = prime! [553][1^^1] = prime! [554][1^^2] = prime! [555][1^^2] = prime! [556][1^^10] = prime! [557][1^^2] = prime! [558][1^^1] = prime! [559][1^^1] = prime! [560][1^^51] = prime! 560111111111111111111111111111111111111111111111111111 is prime [561][1^^18469] = prime! see record delayed prime [56][1^^18470] [562][1^^6] = prime! [563][1^^2] = prime! [564][1^^1] = prime! [565][1^^1] = prime! [566][1^^2] = prime! [567][1^^2] = prime! [568][1^^6] = prime! [569][1^^2] = prime! [570][1^^1] = prime! [571][1^^1] = prime! = [57][1^^2] [572][1^^11] = prime! [573][1^^14] = prime! [574][1^^1] = prime! [575][1^^8] = prime! [576][1^^5] = prime! [577][1^^3] = prime! [578][1^^17] = prime! [579][1^^1] = prime! [580][1^^1] = prime! [581][1^^2] = prime! = [58][1^^3] [582][1^^1] = prime! [583][1^^9] = prime! [584][1^^2] = prime! [585][1^^1] = prime! [586][1^^1] = prime! [587][1^^2] = prime! [588][1^^1] = prime! [589][1^^3] = prime! [590][1^^2] = prime! [591][1^^17] = prime! = [59][1^^18] [592][1^^67] = prime! [593][1^^3] = prime! [594][1^^35] = prime! 59411111111111111111111111111111111111 is prime [595][1^^88] = prime! [596][1^^2] = prime! [597][1^^17] = prime! [598][1^^1] = prime! [599][1^^6] = prime! [600][1^^67] = prime! 6001111111111111111111111111111111111111111111111111111111111111111111 is prime [601][1^^1] = prime! = [60][1^^2] [602][1^^3] = prime! ************************************************************************************************************************************************************************************ [603][1^^?] n >= 300000 a new delayed prime record nr 8 all {3 +3} divisible by 3 all {5 +6} (always odd) divisible by 7 all {1 +3} divisible by 37 all {2 +5} divisible by 41 ONLY {8 +6} gives possible candidates for prime numbers ! [603][1^^8] = 113 x 227 x 1926811 [603][1^^14] = 23934637 x 2519825603 (semiprime!) [603][1^^20] = 43 x 83 x 3573413 x 4728980993963 [603][1^^26] = 1193 x 24197 x 1159381 x 1802059733297111 etc. ************************************************************************************************************************************************************************************ [604][1^^9] = prime! [605][1^^23] = prime! [606][1^^2] = prime! [607][1^^64] = prime! 6071111111111111111111111111111111111111111111111111111111111111111 is prime [608][1^^2] = prime! [609][1^^1] = prime! [610][1^^1] = prime! [611][1^^3] = prime! = [61][1^^4] = [6][1^^5] [612][1^^1] = prime! [613][1^^1] = prime! [614][1^^9] = prime! [615][1^^1] = prime! [616][1^^3] = prime! [617][1^^5760] = prime! [618][1^^5] = prime! [619][1^^3] = prime! [620][1^^2] = prime! [621][1^^1] = prime! = [62][1^^2] [622][1^^1] = prime! [623][1^^2] = prime! [624][1^^4] = prime! [625][1^^3] = prime! [626][1^^29] = prime! 62611111111111111111111111111111 is prime [627][1^^1] = prime! [628][1^^82] = prime! 6281111111111111111111111111111111111111111111111111111111111111111111111111111111111 is prime [629][1^^5] = prime! [630][1^^1] = prime! [631][1^^1] = prime! = [63][1^^2] [632][1^^2] = prime! [633][1^^2] = prime! [634][1^^7] = prime! [635][1^^5] = prime! [636][1^^1] = prime! [637][1^^4] = prime! [638][1^^753] = prime! [639][1^^8] = prime! [640][1^^15] = prime! [641][1^^11] = prime! =[64][1^^12] [642][1^^1] = prime! [643][1^^390] = prime! [644][1^^11] = prime! [645][1^^1] = prime! [646][1^^6] = prime! [647][1^^3] = prime! [648][1^^1] = prime! [649][1^^1] = prime! [650][1^^2] = prime! [651][1^^2] = prime! = [65][1^^3] [652][1^^1] = prime! [653][1^^3] = prime! [654][1^^7] = prime! [655][1^^1] = prime! [656][1^^6] = prime! [657][1^^1] = prime! [658][1^^1] = prime! [659][1^^15] = prime! [660][1^^29] = prime! 66011111111111111111111111111111 is prime [661][1^^192] = prime! = [66][1^^193] [662][1^^3] = prime! [663][1^^5] = prime! [664][1^^594] = prime! [665][1^^3] = prime! [666][1^^1] = prime! followed by [666][1^^79], [1^^86], [1^^100], [1^^148], [1^^182], [1^^232], [1^^368], [1^^482], [1^^1237], [1^^4118], [1^^8509] [667][1^^4] = prime! [668][1^^3] = prime! [669][1^^1] = prime! [670][1^^1] = prime! [671][1^^209] = prime! = [67][1^^210] [672][1^^2] = prime! [673][1^^3] = prime! [674][1^^2] = prime! [675][1^^2] = prime! [676][1^^1] = prime! [677][1^^3] = prime! [678][1^^1] = prime! [679][1^^1] = prime! [680][1^^6] = prime! [681][1^^2] = prime! = [68][1^^3] [682][1^^133] = prime! [683][1^^2] = prime! [684][1^^1] = prime! [685][1^^4] = prime! [686][1^^2] = prime! [687][1^^1] = prime! [688][1^^3] = prime! [689][1^^5] = prime! [690][1^^2] = prime! [691][1^^1] = prime! = [69][1^^2] [692][1^^6] = prime! [693][1^^5] = prime! [694][1^^4] = prime! [695][1^^3] = prime! [696][1^^1] = prime! [697][1^^1] = prime! [698][1^^3] = prime! [699][1^^1] = prime! [700][1^^1] = prime! [701][1^^2] = prime! = [70][1^^3] [702][1^^4] = prime! [703][1^^4] = prime! [704][1^^3] = prime! [705][1^^4] = prime! [706][1^^4] = prime! [707][1^^3] = prime! [708][1^^37156] = PRP! [709][1^^6] = prime! [710][1^^2] = prime! [711][1^^5] = prime! = [71][1^^6] [712][1^^1] = prime! [713][1^^5] = prime! [714][1^^2] = prime! [715][1^^1] = prime! [716][1^^12] = prime! [717][1^^2] = prime! [718][1^^19] = prime! [719][1^^5] = prime! [720][1^^8] = prime! [721][1^^1] = prime! = [72][1^^2] [722][1^^2] = prime! [723][1^^14] = prime! [724][1^^3] = prime! [725][1^^3] = prime! [726][1^^11] = prime! [727][1^^4] = prime! [728][1^^23] = prime! [729][1^^2] = prime! [730][1^^3] = prime! [731][1^^6] = prime! = [73][1^^7] [732][1^^1] = prime! [733][1^^1] = prime! [734][1^^5] = prime! [735][1^^1] = prime! [736][1^^3] = prime! [737][1^^3] = prime! [738][1^^118] = prime! [739][1^^3] = prime! [740][1^^1955] = prime! [741][1^^1] = prime! = [74][1^^2] [742][1^^3] = prime! [743][1^^2] = prime! [744][1^^2] = prime! [745][1^^1] = prime! [746][1^^2] = prime! [747][1^^13] = prime! [748][1^^1] = prime! [749][1^^22850] = PRP! [750][1^^2] = prime! [751][1^^6] = prime! = [75][1^^7] [752][1^^2] = prime! [753][1^^47] = prime! 75311111111111111111111111111111111111111111111111 is prime [754][1^^1] = prime! [755][1^^2] = prime! [756][1^^1] = prime! [757][1^^3] = prime! [758][1^^3] = prime! [759][1^^1] = prime! [760][1^^12] = prime! [761][1^^11] = prime! = [76][1^^12] [762][1^^1] = prime! [763][1^^3] = prime! [764][1^^3] = prime! [765][1^^2] = prime! [766][1^^3] = prime! [767][1^^3] = prime! [768][1^^1] = prime! [769][1^^1] = prime! [770][1^^3] = prime! [771][1^^8] = prime! = [77][1^^9] [772][1^^12] = prime! [773][1^^54] = prime! 773111111111111111111111111111111111111111111111111111111 is prime [774][1^^1] = prime! [775][1^^4] = prime! [776][1^^2] = prime! [777][1^^2] = prime! [778][1^^3] = prime! [779][1^^3] = prime! [780][1^^13] = prime! [781][1^^3] = prime! = [78][1^^4] [782][1^^6] = prime! [783][1^^2] = prime! [784][1^^1] = prime! [785][1^^2] = prime! [786][1^^4] = prime! [787][1^^12] = prime! [788][1^^8] = prime! [789][1^^23] = prime! [790][1^^1] = prime! [791][1^^2] = prime! = [79][1^^3] [792][1^^7] = prime! [793][1^^124] = prime! [794][1^^2] = prime! [795][1^^1] = prime! [796][1^^7] = prime! [797][1^^8] = prime! [798][1^^2] = prime! [799][1^^9] = prime! [800][1^^11] = prime! [801][1^^1] = prime! = [80][1^^2] [802][1^^18] = prime! [803][1^^11] = prime! [804][1^^20] = prime! [805][1^^3] = prime! [806][1^^2] = prime! [807][1^^4] = prime! [808][1^^1] = prime! [809][1^^2] = prime! [810][1^^1] = prime! [811][1^^1] = prime! = [81][1^^2] = [8][1^^3] [812][1^^11] = prime! [813][1^^4] = prime! [814][1^^n] = always composite! set of six divisors (7, 3, 37, 11, 3, 11) that appear periodically [815][1^^18] = prime! [816][1^^1] = prime! [817][1^^1] = prime! [818][1^^74] = prime! [819][1^^1] = prime! [820][1^^4] = prime! [821][1^^11] = prime! = [82][1^^12] [822][1^^1] = prime! [823][1^^1] = prime! [824][1^^5] = prime! [825][1^^161] = prime! [826][1^^4] = prime! [827][1^^54] = prime! 827111111111111111111111111111111111111111111111111111111 is prime [828][1^^2] = prime! [829][1^^1] = prime! [830][1^^3] = prime! [831][1^^1] = prime! = [83][1^^2] [832][1^^4] = prime! [833][1^^2] = prime! [834][1^^22] = prime! [835][1^^4] = prime! [836][1^^17] = prime! [837][1^^38] = prime! 83711111111111111111111111111111111111111 is prime [838][1^^6] = prime! [839][1^^2] = prime! [840][1^^2] = prime! [841][1^^4] = prime! = [84][1^^5] [842][1^^2] = prime! [843][1^^1] = prime! [844][1^^3] = prime! [845][1^^3] = prime! [846][1^^1] = prime! [847][1^^249] = prime! [848][1^^2] = prime! [849][1^^35] = prime! 84911111111111111111111111111111111111 is prime [850][1^^1] = prime! [851][1^^5] = prime! = [85][1^^6] [852][1^^1] = prime! [853][1^^6] = prime! [854][1^^2] = prime! [855][1^^14] = prime! [856][1^^3] = prime! [857][1^^2] = prime! [858][1^^1] = prime! [859][1^^48] = prime! 859111111111111111111111111111111111111111111111111 is prime [860][1^^2] = prime! [861][1^^2] = prime! = [86][1^^3] [862][1^^1221] = prime! [863][1^^2] = prime! [864][1^^1] = prime! [865][1^^13] = prime! [866][1^^5] = prime! [867][1^^2] = prime! [868][1^^1] = prime! [869][1^^1569] = prime! [870][1^^2] = prime! [871][1^^148] = prime! = [87][1^^149] [872][1^^2] = prime! [873][1^^1] = prime! [874][1^^1] = prime! [875][1^^2] = prime! [876][1^^1] = prime! [877][1^^3] = prime! [878][1^^2] = prime! [879][1^^2] = prime! [880][1^^45] = prime! 880111111111111111111111111111111111111111111111 is prime [881][1^^12] = prime! = [88][1^^13] [882][1^^1] = prime! [883][1^^1] = prime! [884][1^^2] = prime! [885][1^^4] = prime! [886][1^^1] = prime! [887][1^^9] = prime! [888][1^^2] = prime! [889][1^^10] = prime! [890][1^^3] = prime! [891][1^^5] = prime! = [89][1^^6] [892][1^^6] = prime! [893][1^^3] = prime! [894][1^^1] = prime! [895][1^^1] = prime! [896][1^^2] = prime! [897][1^^1] = prime! [898][1^^4] = prime! [899][1^^5] = prime! [900][1^^1] = prime! [901][1^^1] = prime! = [90][1^^2] [902][1^^1931] = prime! [903][1^^10] = prime! [904][1^^1] = prime! [905][1^^2] = prime! [906][1^^4] = prime! [907][1^^3] = prime! [908][1^^9] = prime! [909][1^^1] = prime! [910][1^^16] = prime! [911][1^^3] = prime! = [91][1^^4] = [9][1^^5] [912][1^^5] = prime! [913][1^^9] = prime! [914][1^^2] = prime! [915][1^^1] = prime! [916][1^^1] = prime! [917][1^^2] = prime! [918][1^^1] = prime! [919][1^^3] = prime! [920][1^^9] = prime! [921][1^^2] = prime! = [92][1^^3] [922][1^^1] = prime! [923][1^^2] = prime! [924][1^^1] = prime! [925][1^^10] = prime! [926][1^^3] = prime! [927][1^^4] = prime! [928][1^^1] = prime! [929][1^^6] = prime! [930][1^^5] = prime! [931][1^^1] = prime! = [93][1^^2] [932][1^^20] = prime! [933][1^^4] = prime! [934][1^^1] = prime! [935][1^^23] = prime! [936][1^^n] = always composite! set of six divisors (11, 7, 3, 37, 11, 3) that appear periodically [937][1^^1] = prime! [938][1^^2] = prime! [939][1^^1] = prime! [940][1^^18] = prime! [941][1^^2] = prime! = [94][1^^3] [942][1^^1] = prime! [943][1^^1] = prime! [944][1^^6] = prime! [945][1^^4] = prime! [946][1^^1] = prime! [947][1^^14] = prime! [948][1^^2] = prime! [949][1^^1] = prime! [950][1^^3] = prime! [951][1^^1] = prime! = [95][1^^2] [952][1^^1] = prime! [953][1^^2] = prime! [954][1^^46] = prime! 9541111111111111111111111111111111111111111111111 is prime [955][1^^1] = prime! [956][1^^6] = prime! [957][1^^5] = prime! [958][1^^6] = prime! [959][1^^2] = prime! [960][1^^1] = prime! [961][1^^6] = prime! = [96][1^^7] [962][1^^2] = prime! [963][1^^1] = prime! [964][1^^6] = prime! [965][1^^14] = prime! [966][1^^1] = prime! [967][1^^3] = prime! [968][1^^3] = prime! [969][1^^2] = prime! [970][1^^3] = prime! [971][1^^3] = prime! = [97][1^^4] [972][1^^1] = prime! [973][1^^1437] = prime! [974][1^^18] = prime! [975][1^^2] = prime! [976][1^^13] = prime! [977][1^^2] = prime! [978][1^^1] = prime! [979][1^^1] = prime! [980][1^^2] = prime! [981][1^^1] = prime! = [98][1^^2] [982][1^^6] = prime! [983][1^^6] = prime! [984][1^^2] = prime! [985][1^^1] = prime! [986][1^^8] = prime! [987][1^^1] = prime! [988][1^^3] = prime! [989][1^^2] = prime! [990][1^^1] = prime! [991][1^^6] = prime! = [99][1^^7] [992][1^^3] = prime! [993][1^^1] = prime! [994][1^^1] = prime! [995][1^^2100] = prime! [996][1^^2] = prime! [997][1^^3] = prime! [998][1^^3] = prime! [999][1^^7] = prime! [1000][1^^13] = prime! [1001][1^^9] = prime! = [100][1^^10] [1002][1^^4] = prime! [1003][1^^3] = prime! [1004][1^^2] = prime! [1005][1^^2] = prime! [1006][1^^1] = prime! [1007][1^^6] = prime! [1008][1^^2] = prime! [1009][1^^1] = prime! [1010][1^^6] = prime! [1011][1^^1] = prime! = [101][1^^2] = [10][1^^3] [1012][1^^9] = prime! [1013][1^^6] = prime! [1014][1^^1] = prime! [1015][1^^1] = prime! [1016][1^^2] = prime! [1017][1^^4] = prime! [1018][1^^1] = prime! [1019][1^^5] = prime! [1020][1^^7] = prime! [1021][1^^1] = prime! = [102][1^^2] [1022][1^^17] = prime! [1023][1^^n] = always composite! set of six divisors (13, 11, 3, 11, 7, 3) that appear periodically [1024][1^^18] = prime! [1025][1^^3] = prime! [1026][1^^2] = prime! [1027][1^^1] = prime! [1028][1^^2] = prime! [1029][1^^2] = prime! [1030][1^^1] = prime! [1031][1^^5] = prime! = [103][1^^6] [1032][1^^1] = prime! [1033][1^^1] = prime! [1034][1^^47] = prime! 103411111111111111111111111111111111111111111111111 is prime [1035][1^^2] = prime! [1036][1^^4] = prime! [1037][1^^18] = prime! [1038][1^^2] = prime! [1039][1^^1] = prime! [1040][1^^11] = prime! [1041][1^^43] = prime! = [104][1^^44] [1042][1^^25] = prime! [1043][1^^2] = prime! [1044][1^^86] = prime! [1045][1^^3] = prime! [1046][1^^426] = prime! [1047][1^^2] = prime! [1048][1^^7] = prime! [1049][1^^2] = prime! [1050][1^^1] = prime! [1051][1^^6] = prime! [1052][1^^2] = prime! [1053][1^^1] = prime! [1054][1^^99] = prime! [1055][1^^6] = prime! [1056][1^^13] = prime! [1057][1^^4] = prime! [1058][1^^14] = prime! [1059][1^^4] = prime! [1060][1^^1] = prime! [1061][1^^5] = prime! [1062][1^^287] = prime! [1063][1^^1] = prime! [1064][1^^2] = prime! [1065][1^^1] = prime! [1066][1^^3] = prime! [1067][1^^15] = prime! [1068][1^^506] = prime! [1069][1^^1] = prime! [1070][1^^14] = prime! [1071][1^^1] = prime! [1072][1^^6] = prime! [1073][1^^8] = prime! [1074][1^^4] = prime! [1075][1^^6] = prime! [1076][1^^3] = prime! [1077][1^^1] = prime! [1078][1^^1] = prime! [1079][1^^620] = prime! [1080][1^^2] = prime! [1081][1^^4] = prime! [1082][1^^2] = prime! [1083][1^^1] = prime! [1084][1^^18] = prime! [1085][1^^3] = prime! [1086][1^^1] = prime! [1087][1^^24] = prime! [1088][1^^5] = prime! [1089][1^^1] = prime! [1090][1^^66] = prime! [1091][1^^2] = prime! [1092][1^^2] = prime! [1093][1^^3] = prime! [1094][1^^5] = prime! [1095][1^^10] = prime! [1096][1^^12] = prime! [1097][1^^3] = prime! [1098][1^^22] = prime! [1099][1^^4] = prime! [1100][1^^8589] = prime! [1101][1^^16] = prime! [1102][1^^3] = prime! [1103][1^^2] = prime! [1104][1^^4] = prime! [1105][1^^4] = prime! [1106][1^^8] = prime! [1107][1^^1] = prime! [1108][1^^6] = prime! [1109][1^^8] = prime! [1110][1^^8] = prime! [1111][1^^15] = prime! [1112][1^^2] = prime! [1113][1^^1] = prime! [1114][1^^3] = prime! [1115][1^^6] = prime! [1116][1^^1] = prime! [1117][1^^1] = prime! [1118][1^^45] = prime! [1119][1^^56] = prime! [1120][1^^4] = prime! [1121][1^^2] = prime! [1122][1^^77] = prime! [1123][1^^4] = prime! [1124][1^^9] = prime! [1125][1^^1] = prime! [1126][1^^1] = prime! [1127][1^^3] = prime! [1128][1^^10] = prime! [1129][1^^3] = prime! [1130][1^^2] = prime! [1131][1^^1] = prime! [1132][1^^1] = prime! [1133][1^^59] = prime! [1134][1^^50] = prime! [1135][1^^1] = prime! [1136][1^^3] = prime! [1137][1^^5] = prime! [1138][1^^12] = prime! [1139][1^^911] = prime! [1140][1^^4] = prime! [1141][1^^1] = prime! [1142][1^^9] = prime! [1143][1^^2] = prime! [1144][1^^7] = prime! [1145][1^^20] = prime! [1146][1^^805] = prime! [1147][1^^1] = prime! [1148][1^^3] = prime! [1149][1^^1] = prime! [1150][1^^4] = prime! [1151][1^^5] = prime! [1152][1^^2] = prime! [1153][1^^4] = prime! [1154][1^^6] = prime! [1155][1^^1] = prime! [1156][1^^6] = prime! [1157][1^^3] = prime! [1158][1^^2] = prime! [1159][1^^7] = prime! [1160][1^^3] = prime! [1161][1^^8] = prime! [1162][1^^1] = prime! [1163][1^^3] = prime! [1164][1^^2] = prime! [1165][1^^4] = prime! [1166][1^^5] = prime! [1167][1^^18178] = PRP! [1168][1^^1] = prime! [1169][1^^2] = prime! [1170][1^^1] = prime! [1171][1^^3] = prime! [1172][1^^3] = prime! [1173][1^^1] = prime! [1174][1^^19] = prime! [1175][1^^2] = prime! [1176][1^^4] = prime! [1177][1^^1771] = prime! Nice! [1178][1^^2] = prime! [1179][1^^2] = prime! [1180][1^^1] = prime! [1181][1^^5] = prime! [1182][1^^1] = prime! [1183][1^^1] = prime! [1184][1^^2] = prime! [1185][1^^16] = prime! [1186][1^^3] = prime! [1187][1^^3] = prime! [1188][1^^5] = prime! [1189][1^^4] = prime! [1190][1^^8] = prime! [1191][1^^4] = prime! [1192][1^^9] = prime! [1193][1^^2] = prime! [1194][1^^1] = prime! [1195][1^^18] = prime! [1196][1^^2] = prime! [1197][1^^1] = prime! [1198][1^^1] = prime! [1199][1^^5] = prime! [1200][1^^2] = prime! [1201][1^^1] = prime! [1202][1^^5] = prime! [1203][1^^4] = prime! [1204][1^^1] = prime! [1205][1^^2] = prime! [1206][1^^4] = prime! [1207][1^^1] = prime! [1208][1^^2] = prime! [1209][1^^4] = prime! [1210][1^^1] = prime! [1211][1^^134] = prime! [1212][1^^14] = prime! [1213][1^^54] = prime! [1214][1^^6] = prime! [1215][1^^5] = prime! [1216][1^^1] = prime! [1217][1^^2] = prime! [1218][1^^4] = prime! [1219][1^^3] = prime! [1220][1^^2] = prime! [1221][1^^1] = prime! [1222][1^^n] = always composite! set of six divisors (11, 3, 11, 7, 3, 13) that appear periodically [1223][1^^624] = prime! [1224][1^^1] = prime! [1225][1^^1] = prime! [1226][1^^2] = prime! [1227][1^^14] = prime! [1228][1^^1] = prime! [1229][1^^35] = prime! [1230][1^^1] = prime! [1231][1^^18] = prime! [1232][1^^147] = prime! [1233][1^^2] = prime! [1234][1^^4] = prime! [1235][1^^201] = prime! [1236][1^^31] = prime! [1237][1^^9] = prime! [1238][1^^5] = prime! [1239][1^^1] = prime! [1240][1^^1] = prime! [1241][1^^5] = prime! [1242][1^^1] = prime! [1243][1^^3] = prime! ************************************************************************************************************************************************************************************ [1244][1^^n] = possible candidate ! n > 200000 ************************************************************************************************************************************************************************************ [1245][1^^1] = prime! [1246][1^^21] = prime! [1247][1^^6] = prime! [1248][1^^5] = prime! [1249][1^^1] = prime! [1250][1^^8] = prime! [1251][1^^1] = prime! [1252][1^^10] = prime! [1253][1^^2] = prime! [1254][1^^1] = prime! [1255][1^^4] = prime! [1256][1^^6] = prime! [1257][1^^2] = prime! [1258][1^^4] = prime! [1259][1^^396] = prime! [1260][1^^1] = prime! [1261][1^^1] = prime! [1262][1^^2] = prime! [1263][1^^2] = prime! [1264][1^^1] = prime! [1265][1^^3] = prime! [1266][1^^2] = prime! [1267][1^^1] = prime! [1268][1^^18] = prime! [1269][1^^11] = prime! [1270][1^^3] = prime! [1271][1^^3] = prime! [1272][1^^1] = prime! [1273][1^^10] = prime! [1274][1^^3] = prime! [1275][1^^49] = prime! [1276][1^^33] = prime! [1277][1^^2] = prime! [1278][1^^1] = prime! [1279][1^^1] = prime! [1280][1^^5] = prime! [1281][1^^2] = prime! [1282][1^^1] = prime! [1283][1^^2] = prime! [1284][1^^1] = prime! [1285][1^^3] = prime! [1286][1^^17] = prime! [1287][1^^29] = prime! [1288][1^^16] = prime! [1289][1^^3] = prime! [1290][1^^2] = prime! [1291][1^^1] = prime! [1292][1^^6] = prime! [1293][1^^4] = prime! [1294][1^^1] = prime! [1295][1^^158] = prime! [1296][1^^16] = prime! [1297][1^^4] = prime! [1298][1^^3] = prime! [1299][1^^26] = prime! [1300][1^^1] = prime! [1301][1^^12] = prime! [1302][1^^2] = prime! [1303][1^^9] = prime! [1304][1^^2] = prime! [1305][1^^11] = prime! [1306][1^^9] = prime! [1307][1^^5] = prime! [1308][1^^2] = prime! [1309][1^^207] = prime! [1310][1^^2] = prime! [1311][1^^2] = prime! [1312][1^^1] = prime! [1313][1^^2] = prime! [1314][1^^265] = prime! [1315][1^^1] = prime! [1316][1^^2] = prime! [1317][1^^1] = prime! [1318][1^^10] = prime! [1319][1^^17] = prime! [1320][1^^5] = prime! [1321][1^^4] = prime! [1322][1^^12] = prime! [1323][1^^16] = prime! [1324][1^^1] = prime! [1325][1^^2] = prime! [1326][1^^2] = prime! [1327][1^^3] = prime! [1328][1^^3] = prime! [1329][1^^1] = prime! [1330][1^^3] = prime! [1331][1^^2889] = prime! [1332][1^^4] = prime! [1333][1^^1] = prime! [1334][1^^3] = prime! [1335][1^^5] = prime! [1336][1^^6] = prime! [1337][1^^2] = prime! [1338][1^^1] = prime! [1339][1^^3] = prime! [1340][1^^32] = prime! [1341][1^^1] = prime! [1342][1^^1] = prime! [1343][1^^6] = prime! [1344][1^^1] = prime! [1345][1^^1] = prime! [1346][1^^17] = prime! [1347][1^^8] = prime! [1348][1^^3] = prime! [1349][1^^17] = prime! [1350][1^^8] = prime! [1351][1^^3] = prime! [1352][1^^2] = prime! [1353][1^^n] = always composite! set of six divisors (7, 11, 3, 11, 13, 3) that appear periodically [1354][1^^52] = prime! [1355][1^^2] = prime! [1356][1^^52] = prime! [1357][1^^7] = prime! [1358][1^^3] = prime! [1359][1^^1] = prime! [1360][1^^4] = prime! [1361][1^^2] = prime! [1362][1^^5] = prime! [1363][1^^6] = prime! [1364][1^^17] = prime! [1365][1^^2] = prime! [1366][1^^6] = prime! [1367][1^^2] = prime! [1368][1^^1] = prime! [1369][1^^1] = prime! [1370][1^^3] = prime! [1371][1^^1] = prime! [1372][1^^1] = prime! [1373][1^^14] = prime! [1374][1^^11] = prime! [1375][1^^1] = prime! [1376][1^^14] = prime! [1377][1^^22] = prime! [1378][1^^1] = prime! [1379][1^^2] = prime! [1380][1^^50] = prime! [1381][1^^3] = prime! [1382][1^^9] = prime! [1383][1^^1] = prime! [1384][1^^1] = prime! [1385][1^^2] = prime! [1386][1^^7] = prime! [1387][1^^6] = prime! [1388][1^^5] = prime! [1389][1^^25] = prime! [1390][1^^1] = prime! [1391][1^^23] = prime! [1392][1^^1] = prime! [1393][1^^1] = prime! [1394][1^^1934] = prime! Nice! [1395][1^^2] = prime! [1396][1^^15] = prime! [1397][1^^15] = prime! [1398][1^^4] = prime! [1399][1^^6] = prime! [1400][1^^15] = prime! [1401][1^^1] = prime! [1402][1^^42] = prime! [1403][1^^5] = prime! [1404][1^^2] = prime! [1405][1^^1] = prime! [1406][1^^2] = prime! [1407][1^^1] = prime! [1408][1^^1] = prime! [1409][1^^6] = prime! [1410][1^^13] = prime! [1411][1^^7] = prime! [1412][1^^5] = prime! [1413][1^^2] = prime! [1414][1^^7] = prime! [1415][1^^2] = prime! [1416][1^^4] = prime! [1417][1^^99] = prime! [1418][1^^2] = prime! [1419][1^^181] = prime! [1420][1^^4] = prime! [1421][1^^2] = prime! [1422][1^^1] = prime! [1423][1^^3] = prime! [1424][1^^6] = prime! [1425][1^^1] = prime! [1426][1^^3] = prime! [1427][1^^2] = prime! [1428][1^^1] = prime! [1429][1^^4] = prime! [1430][1^^9] = prime! [1431][1^^2] = prime! [1432][1^^1] = prime! [1433][1^^45] = prime! [1434][1^^1] = prime! [1435][1^^3] = prime! [1436][1^^3] = prime! [1437][1^^2] = prime! [1438][1^^4] = prime! [1439][1^^3] = prime! [1440][1^^1] = prime! [1441][1^^1] = prime! [1442][1^^614] = prime! [1443][1^^1] = prime! [1444][1^^3] = prime! [1445][1^^2] = prime! [1446][1^^1] = prime! [1447][1^^4] = prime! [1448][1^^5] = prime! [1449][1^^4] = prime! [1450][1^^13] = prime! [1451][1^^15] = prime! [1452][1^^5] = prime! [1453][1^^6] = prime! [1454][1^^12] = prime! [1455][1^^1] = prime! [1456][1^^1] = prime! [1457][1^^3] = prime! [1458][1^^4] = prime! [1459][1^^1] = prime! [1460][1^^2] = prime! [1461][1^^4] = prime! [1462][1^^1] = prime! [1463][1^^11] = prime! [1464][1^^8] = prime! [1465][1^^9] = prime! [1466][1^^3] = prime! [1467][1^^7] = prime! [1468][1^^4] = prime! [1469][1^^5] = prime! [1470][1^^2] = prime! [1471][1^^72] = prime! [1472][1^^2] = prime! [1473][1^^1] = prime! [1474][1^^1] = prime! [1475][1^^1206] = prime! [1476][1^^11] = prime! [1477][1^^1] = prime! [1478][1^^2] = prime! [1479][1^^4] = prime! [1480][1^^205] = prime! [1481][1^^15] = prime! [1482][1^^1] = prime! [1483][1^^1] = prime! [1484][1^^2] = prime! [1485][1^^1] = prime! [1486][1^^6] = prime! [1487][1^^2] = prime! [1488][1^^5] = prime! [1489][1^^1] = prime! [1490][1^^2] = prime! [1491][1^^2] = prime! [1492][1^^3] = prime! [1493][1^^8] = prime! [1494][1^^2] = prime! [1495][1^^1] = prime! [1496][1^^3] = prime! [1497][1^^2] = prime! [1498][1^^4] = prime! [1499][1^^2] = prime! [1500][1^^2] = prime! [1501][1^^6] = prime! [1502][1^^2] = prime! [1503][1^^1] = prime! [1504][1^^6] = prime! [1505][1^^3] = prime! [1506][1^^1] = prime! [1507][1^^3] = prime! [1508][1^^8] = prime! [1509][1^^1] = prime! [1510][1^^1] = prime! [1511][1^^20] = prime! [1512][1^^1] = prime! [1513][1^^1] = prime! [1514][1^^17] = prime! [1515][1^^58] = prime! [1516][1^^1] = prime! [1517][1^^47] = prime! [1518][1^^31] = prime! [1519][1^^n] = always composite! set of six divisors (11, 3, 11, 13, 3, 7) that appear periodically [1520][1^^8] = prime! [1521][1^^2] = prime! [1522][1^^3] = prime! [1523][1^^2] = prime! [1524][1^^1] = prime! [1525][1^^12] = prime! [1526][1^^32] = prime! [1527][1^^1] = prime! [1528][1^^6] = prime! [1529][1^^5] = prime! [1530][1^^66254] = PRP! [1531][1^^3] = prime! [1532][1^^14] = prime! [1533][1^^1] = prime! [1534][1^^4] = prime! [1535][1^^2] = prime! [1536][1^^1] = prime! [1537][1^^6] = prime! [1538][1^^3] = prime! [1539][1^^1] = prime! [1540][1^^1] = prime! [1541][1^^2] = prime! [1542][1^^2] = prime! [1543][1^^3] = prime! [1544][1^^12] = prime! [1545][1^^1] = prime! [1546][1^^1] = prime! [1547][1^^201] = prime! [1548][1^^8] = prime! [1549][1^^46] = prime! [1550][1^^5] = prime! [1551][1^^1] = prime! [1552][1^^6] = prime! [1553][1^^11] = prime! [1554][1^^1] = prime! [1555][1^^1] = prime! [1556][1^^18] = prime! [1557][1^^5] = prime! [1558][1^^1] = prime! [1559][1^^5] = prime! [1560][1^^1] = prime! [1561][1^^3] = prime! [1562][1^^3] = prime! [1563][1^^8] = prime! [1564][1^^1] = prime! [1565][1^^2] = prime! [1566][1^^1] = prime! [1567][1^^1] = prime! [1568][1^^9] = prime! [1569][1^^4] = prime! [1570][1^^15] = prime! [1571][1^^6] = prime! [1572][1^^2] = prime! [1573][1^^1] = prime! [1574][1^^2] = prime! [1575][1^^8] = prime! [1576][1^^1] = prime! [1577][1^^39] = prime! [1578][1^^14] = prime! [1579][1^^1] = prime! [1580][1^^18] = prime! [1581][1^^5] = prime! [1582][1^^4] = prime! [1583][1^^12] = prime! [1584][1^^107] = prime! [1585][1^^10] = prime! [1586][1^^2] = prime! [1587][1^^13] = prime! [1588][1^^1] = prime! [1589][1^^5] = prime! [1590][1^^1] = prime! [1591][1^^118] = prime! [1592][1^^3] = prime! [1593][1^^2] = prime! [1594][1^^3] = prime! [1595][1^^311] = prime! [1596][1^^4] = prime! [1597][1^^1] = prime! [1598][1^^2] = prime! [1599][1^^1] = prime! [1600][1^^1] = prime! [1601][1^^27] = prime! [1602][1^^11] = prime! [1603][1^^3] = prime! [1604][1^^3] = prime! [1605][1^^11] = prime! [1606][1^^1] = prime! [1607][1^^2] = prime! [1608][1^^4] = prime! [1609][1^^1] = prime! [1610][1^^14] = prime! [1611][1^^1] = prime! [1612][1^^3] = prime! [1613][1^^12] = prime! [1614][1^^1] = prime! [1615][1^^21] = prime! [1616][1^^2] = prime! [1617][1^^5] = prime! [1618][1^^16] = prime! [1619][1^^2] = prime! [1620][1^^2] = prime! [1621][1^^18] = prime! [1622][1^^11] = prime! [1623][1^^1] = prime! [1624][1^^3] = prime! [1625][1^^8] = prime! [1626][1^^2] = prime! [1627][1^^3] = prime! [1628][1^^5] = prime! [1629][1^^46] = prime! [1630][1^^1] = prime! [1631][1^^5] = prime! [1632][1^^2] = prime! [1633][1^^4] = prime! [1634][1^^2] = prime! [1635][1^^5] = prime! [1636][1^^1] = prime! [1637][1^^11] = prime! [1638][1^^1] = prime! [1639][1^^9] = prime! [1640][1^^2] = prime! [1641][1^^1] = prime! [1642][1^^1] = prime! [1643][1^^9] = prime! [1644][1^^4] = prime! [1645][1^^1] = prime! [1646][1^^3] = prime! [1647][1^^4] = prime! [1648][1^^1] = prime! [1649][1^^2] = prime! [1650][1^^5] = prime! [1651][1^^10] = prime! [1652][1^^2] = prime! [1653][1^^2] = prime! [1654][1^^3] = prime! [1655][1^^2] = prime! [1656][1^^1] = prime! [1657][1^^10] = prime! [1658][1^^2] = prime! [1659][1^^23] = prime! [1660][1^^3] = prime! [1661][1^^3] = prime! [1662][1^^20] = prime! [1663][1^^1] = prime! [1664][1^^141] = prime! [1665][1^^1] = prime! [1666][1^^1] = prime! [1667][1^^8] = prime! [1668][1^^4] = prime! [1669][1^^1] = prime! [1670][1^^6] = prime! [1671][1^^4] = prime! [1672][1^^9403] = PRP! [1673][1^^2] = prime! [1674][1^^1] = prime! [1675][1^^3] = prime! [1676][1^^2] = prime! [1677][1^^2] = prime! [1678][1^^3] = prime! [1679][1^^2] = prime! [1680][1^^5] = prime! [1681][1^^1] = prime! [1682][1^^2] = prime! [1683][1^^1] = prime! [1684][1^^132] = prime! [1685][1^^3] = prime! [1686][1^^4] = prime! [1687][1^^1] = prime! [1688][1^^8] = prime! [1689][1^^5] = prime! [1690][1^^1] = prime! [1691][1^^2] = prime! [1692][1^^1] = prime! [1693][1^^1] = prime! [1694][1^^167] = prime! [1695][1^^22] = prime! [1696][1^^6] = prime! [1697][1^^8] = prime! [1698][1^^1] = prime! [1699][1^^3] = prime! [1700][1^^5] = prime! [1701][1^^1] = prime! [1702][1^^1] = prime! [1703][1^^15] = prime! [1704][1^^1] = prime! [1705][1^^3] = prime! [1706][1^^144] = prime! [1707][1^^2] = prime! [1708][1^^13] = prime! [1709][1^^6] = prime! [1710][1^^5] = prime! [1711][1^^6] = prime! [1712][1^^8] = prime! [1713][1^^11] = prime! [1714][1^^7] = prime! [1715][1^^5] = prime! [1716][1^^7] = prime! [1717][1^^10] = prime! [1718][1^^2] = prime! [1719][1^^1] = prime! [1720][1^^6] = prime! [1721][1^^12] = prime! [1722][1^^23] = prime! [1723][1^^1] = prime! [1724][1^^2] = prime! [1725][1^^14] = prime! [1726][1^^115] = prime! [1727][1^^119] = prime! [1728][1^^8] = prime! [1729][1^^1] = prime! [1730][1^^12] = prime! [1731][1^^10] = prime! [1732][1^^1] = prime! [1733][1^^294] = prime! [1734][1^^1] = prime! [1735][1^^1] = prime! [1736][1^^59] = prime! [1737][1^^64] = prime! [1738][1^^81] = prime! [1739][1^^80] = prime! [1740][1^^1] = prime! [1741][1^^3] = prime! [1742][1^^5] = prime! [1743][1^^1] = prime! [1744][1^^3] = prime! [1745][1^^3] = prime! [1746][1^^8] = prime! [1747][1^^1] = prime! [1748][1^^12] = prime! [1749][1^^1] = prime! [1750][1^^n] = always composite! set of six divisors (11, 3, 11, 37, 3, 7) that appear periodically [1751][1^^15] = prime! [1752][1^^2] = prime! [1753][1^^9] = prime! [1754][1^^2] = prime! [1755][1^^1] = prime! [1756][1^^37] = prime! [1757][1^^20] = prime! [1758][1^^1] = prime! [1759][1^^4] = prime! [1760][1^^15] = prime! [1761][1^^n] = always composite! see [176][1^^n] [1762][1^^7] = prime! [1763][1^^8] = prime! [1764][1^^10] = prime! [1765][1^^6] = prime! [1766][1^^2] = prime! [1767][1^^2] = prime! [1768][1^^1] = prime! [1769][1^^3] = prime! [1770][1^^2] = prime! [1771][1^^21] = prime! [1772][1^^2] = prime! [1773][1^^5] = prime! [1774][1^^4] = prime! [1775][1^^2] = prime! [1776][1^^1] = prime! [1777][1^^10] = prime! [1778][1^^2] = prime! [1779][1^^1] = prime! [1780][1^^4] = prime! [1781][1^^9] = prime! [1782][1^^37] = prime! [1783][1^^12] = prime! [1784][1^^5] = prime! [1785][1^^1] = prime! [1786][1^^13] = prime! [1787][1^^12] = prime! [1788][1^^1] = prime! [1789][1^^1] = prime! [1790][1^^3] = prime! [1791][1^^1] = prime! [1792][1^^1] = prime! [1793][1^^6711] = PRP! [1794][1^^2] = prime! [1795][1^^16] = prime! [1796][1^^3] = prime! [1797][1^^1] = prime! [1798][1^^1] = prime! [1799][1^^5] = prime! [1800][1^^1042] = prime! [1801][1^^24] = prime! [1802][1^^2] = prime! [1803][1^^2] = prime! [1804][1^^1] = prime! [1805][1^^2] = prime! [1806][1^^1] = prime! [1807][1^^4] = prime! [1808][1^^2] = prime! [1809][1^^8] = prime! [1810][1^^7] = prime! [1811][1^^9] = prime! [1812][1^^1] = prime! [1813][1^^1] = prime! [1814][1^^6] = prime! [1815][1^^17] = prime! [1816][1^^4] = prime! [1817][1^^2] = prime! [1818][1^^1] = prime! [1819][1^^1] = prime! [1820][1^^2] = prime! [1821][1^^1] = prime! [1822][1^^28] = prime! [1823][1^^41] = prime! [1824][1^^20] = prime! [1825][1^^1] = prime! [1826][1^^17] = prime! [1827][1^^2] = prime! [1828][1^^4] = prime! [1829][1^^20] = prime! [1830][1^^1] = prime! [1831][1^^1] = prime! [1832][1^^5] = prime! [1833][1^^10] = prime! [1834][1^^1] = prime! [1835][1^^2] = prime! [1836][1^^2] = prime! [1837][1^^1] = prime! [1838][1^^18] = prime! [1839][1^^5] = prime! [1840][1^^1] = prime! [1841][1^^2] = prime! [1842][1^^2] = prime! [1843][1^^3] = prime! [1844][1^^3] = prime! [1845][1^^1] = prime! [1846][1^^1] = prime! [1847][1^^2] = prime! [1848][1^^1] = prime! [1849][1^^4] = prime! [1850][1^^23] = prime! [1851][1^^13] = prime! [1852][1^^1] = prime! [1853][1^^6] = prime! [1854][1^^1] = prime! [1855][1^^16] = prime! [1856][1^^446] = prime! [1857][1^^2] = prime! [1858][1^^19] = prime! [1859][1^^3] = prime! [1860][1^^28] = prime! ************************************************************************************************************************************************************************************ [1861][1^^n] = possible candidate ! n > 200000 ************************************************************************************************************************************************************************************ [1862][1^^2] = prime! [1863][1^^2] = prime! [1864][1^^3] = prime! [1865][1^^9] = prime! [1866][1^^1] = prime! [1867][1^^1] = prime! [1868][1^^11] = prime! [1869][1^^1] = prime! [1870][1^^1] = prime! [1871][1^^2] = prime! [1872][1^^2] = prime! [1873][1^^1] = prime! [1874][1^^3] = prime! [1875][1^^11] = prime! [1876][1^^16] = prime! [1877][1^^2] = prime! [1878][1^^35] = prime! [1879][1^^12] = prime! [1880][1^^2] = prime! [1881][1^^185] = prime! [1882][1^^4] = prime! [1883][1^^2] = prime! [1884][1^^13] = prime! [1885][1^^4] = prime! [1886][1^^8] = prime! [1887][1^^2] = prime! [1888][1^^33] = prime! [1889][1^^2] = prime! [1890][1^^2] = prime! [1891][1^^1] = prime! [1892][1^^35] = prime! [1893][1^^2] = prime! [1894][1^^9] = prime! [1895][1^^15] = prime! [1896][1^^5] = prime! [1897][1^^4] = prime! [1898][1^^1605] = prime! [1899][1^^80] = prime! [1900][1^^1] = prime! [1901][1^^24] = prime! [1902][1^^5] = prime! [1903][1^^1] = prime! [1904][1^^n] = always composite! set of six divisors (3, 13, 11, 3, 11, 7) that appear periodically [1905][1^^1] = prime! [1906][1^^16] = prime! [1907][1^^2] = prime! [1908][1^^1] = prime! [1909][1^^3] = prime! [1910][1^^41] = prime! [1911][1^^10] = prime! [1912][1^^1] = prime! [1913][1^^14] = prime! [1914][1^^1] = prime! [1915][1^^6] = prime! [1916][1^^48] = prime! [1917][1^^7] = prime! [1918][1^^1] = prime! [1919][1^^2] = prime! [1920][1^^46] = prime! [1921][1^^1] = prime! [1922][1^^3] = prime! [1923][1^^1] = prime! [1924][1^^10] = prime! [1925][1^^33] = prime! [1926][1^^2] = prime! [1927][1^^3] = prime! [1928][1^^2] = prime! [1929][1^^23] = prime! [1930][1^^1] = prime! [1931][1^^5] = prime! [1932][1^^4] = prime! [1933][1^^16] = prime! [1934][1^^29] = prime! [1935][1^^8] = prime! [1936][1^^3] = prime! [1937][1^^n] = always composite! set of six divisors (3, 7, 11, 3, 11, 13) that appear periodically [1938][1^^1] = prime! [1939][1^^1] = prime! [1940][1^^9] = prime! [1941][1^^5] = prime! [1942][1^^1] = prime! [1943][1^^12] = prime! [1944][1^^1] = prime! [1945][1^^16] = prime! [1946][1^^17] = prime! [1947][1^^1] = prime! [1948][1^^30] = prime! [1949][1^^2] = prime! [1950][1^^1] = prime! [1951][1^^15] = prime! [1952][1^^20] = prime! [1953][1^^1] = prime! [1954][1^^1] = prime! [1955][1^^2] = prime! [1956][1^^11] = prime! [1957][1^^1] = prime! [1958][1^^23] = prime! [1959][1^^4] = prime! [1960][1^^3] = prime! [1961][1^^2] = prime! [1962][1^^988] = prime! [1963][1^^3] = prime! [1964][1^^14] = prime! [1965][1^^7] = prime! [1966][1^^1] = prime! [1967][1^^9] = prime! [1968][1^^1] = prime! [1969][1^^3] = prime! [1970][1^^6] = prime! [1971][1^^11] = prime! [1972][1^^3] = prime! [1973][1^^2] = prime! [1974][1^^5] = prime! [1975][1^^1] = prime! [1976][1^^8] = prime! [1977][1^^2] = prime! [1978][1^^3] = prime! [1979][1^^5] = prime! [1980][1^^1] = prime! [1981][1^^100] = prime! = [198][1^^101] [1982][1^^3] = prime! [1983][1^^11] = prime! [1984][1^^1] = prime! [1985][1^^5] = prime! [1986][1^^1] = prime! [1987][1^^7] = prime! [1988][1^^2] = prime! [1989][1^^1] = prime! [1990][1^^3] = prime! [1991][1^^5] = prime! [1992][1^^2] = prime! [1993][1^^4] = prime! [1994][1^^2] = prime! [1995][1^^155] = prime! [1996][1^^1] = prime! [1997][1^^3] = prime! [1998][1^^2] = prime! [1999][1^^1] = prime! [2000][1^^6] = prime! [2001][1^^1] = prime! [2002][1^^1] = prime! [2003][1^^8] = prime! [2004][1^^5] = prime! [2005][1^^1] = prime! [2006][1^^3] = prime! [2007][1^^1] = prime! [2008][1^^10] = prime! [2009][1^^8] = prime! [2010][1^^1] = prime! [2011][1^^3] = prime! [2012][1^^2] = prime! [2013][1^^173] = prime! [2014][1^^4] = prime! [2015][1^^2] = prime! [2016][1^^1] = prime! [2017][1^^6] = prime! [2018][1^^3] = prime! [2019][1^^2] = prime! [2020][1^^1] = prime! [2021][1^^30] = prime! = [202][1^^31] [2022][1^^5] = prime! [2023][1^^1] = prime! [2024][1^^3] = prime! [2025][1^^8] = prime! [2026][1^^1] = prime! [2027][1^^3] = prime! [2028][1^^13] = prime! [2029][1^^25] = prime! [2030][1^^2] = prime! [2031][1^^4] = prime! [2032][1^^3] = prime! [2033][1^^2] = prime! [2034][1^^1] = prime! [2035][1^^13] = prime! [2036][1^^36] = prime! [2037][1^^41] = prime! [2038][1^^6] = prime! [2039][1^^2] = prime! [2040][1^^4] = prime! [2041][1^^1] = prime! [2042][1^^3] = prime! [2043][1^^1] = prime! [2044][1^^1] = prime! [2045][1^^2] = prime! [2046][1^^59] = prime! [2047][1^^6] = prime! [2048][1^^5] = prime! [2049][1^^4] = prime! [2050][1^^6] = prime! [2051][1^^2] = prime! [2052][1^^1] = prime! [2053][1^^3] = prime! [2054][1^^5] = prime! [2055][1^^1] = prime! [2056][1^^3] = prime! [2057][1^^1409] = prime! [2058][1^^236] = prime! [2059][1^^4] = prime! [2060][1^^5] = prime! [2061][1^^1] = prime! [2062][1^^9] = prime! [2063][1^^3] = prime! [2064][1^^1] = prime! [2065][1^^3] = prime! [2066][1^^3] = prime! [2067][1^^5] = prime! [2068][1^^1] = prime! [2069][1^^2] = prime! [2070][1^^5] = prime! [2071][1^^13] = prime! [2072][1^^38] = prime! [2073][1^^1] = prime! [2074][1^^12] = prime! [2075][1^^2] = prime! [2076][1^^5] = prime! [2077][1^^1] = prime! [2078][1^^2] = prime! [2079][1^^5] = prime! [2080][1^^10] = prime! [2081][1^^2] = prime! [2082][1^^7] = prime! [2083][1^^36] = prime! [2084][1^^3] = prime! [2085][1^^2] = prime! [2086][1^^3] = prime! [2087][1^^14] = prime! [2088][1^^4] = prime! [2089][1^^28] = prime! [2090][1^^3] = prime! [2091][1^^n] = always composite! see [209][1^^n] [2092][1^^1] = prime! [2093][1^^2] = prime! [2094][1^^14] = prime! [2095][1^^45] = prime! [2096][1^^3] = prime! [2097][1^^14] = prime! [2098][1^^1] = prime! [2099][1^^12] = prime! [2100][1^^1] = prime! [2101][1^^1] = prime! [2102][1^^6] = prime! [2103][1^^1] = prime! [2104][1^^3] = prime! [2105][1^^3] = prime! [2106][1^^1] = prime! [2107][1^^4] = prime! [2108][1^^2] = prime! [2109][1^^2] = prime! [2110][1^^1] = prime! [2111][1^^9] = prime! [2112][1^^1] = prime! [2113][1^^6] = prime! [2114][1^^5] = prime! [2115][1^^8] = prime! [2116][1^^21] = prime! [2117][1^^2] = prime! [2118][1^^2] = prime! [2119][1^^1] = prime! [2120][1^^8] = prime! [2121][1^^1] = prime! [2122][1^^1] = prime! [2123][1^^11] = prime! [2124][1^^2] = prime! [2125][1^^3] = prime! [2126][1^^48] = prime! [2127][1^^5] = prime! [2128][1^^4] = prime! [2129][1^^9] = prime! [2130][1^^26] = prime! [2131][1^^4] = prime! [2132][1^^8] = prime! [2133][1^^10] = prime! [2134][1^^1] = prime! [2135][1^^14] = prime! [2136][1^^2] = prime! [2137][1^^18] = prime! [2138][1^^108] = prime! [2139][1^^1] = prime! [2140][1^^1] = prime! [2141][1^^23] = prime! [2142][1^^2] = prime! [2143][1^^12] = prime! [2144][1^^9] = prime! [2145][1^^229] = prime! [2146][1^^n] = always composite! set of six divisors (11, 3, 11, 7, 11, 37) that appear periodically [2147][1^^39] = prime! [2148][1^^1] = prime! [2149][1^^1] = prime! [2150][1^^3] = prime! [2151][1^^652] = prime! = [215][1^^653] [2152][1^^1] = prime! [2153][1^^3] = prime! [2154][1^^5] = prime! [2155][1^^7] = prime! [2156][1^^3] = prime! [2157][1^^68] = prime! [2158][1^^4] = prime! [2159][1^^33] = prime! [2160][1^^1] = prime! [2161][1^^1] = prime! [2162][1^^2] = prime! [2163][1^^13] = prime! [2164][1^^3] = prime! [2165][1^^5] = prime! [2166][1^^1] = prime! [2167][1^^3] = prime! [2168][1^^12] = prime! [2169][1^^2] = prime! [2170][1^^1] = prime! [2171][1^^2] = prime! [2172][1^^14] = prime! [2173][1^^3] = prime! [2174][1^^2] = prime! [2175][1^^1] = prime! [2176][1^^7] = prime! [2177][1^^87] = prime! [2178][1^^55] = prime! [2179][1^^10] = prime! [2180][1^^3] = prime! [2181][1^^2] = prime! [2182][1^^1] = prime! [2183][1^^8] = prime! [2184][1^^1] = prime! [2185][1^^1] = prime! [2186][1^^2] = prime! [2187][1^^1] = prime! [2188][1^^1] = prime! [2189][1^^11] = prime! [2190][1^^4] = prime! [2191][1^^1] = prime! [2192][1^^3] = prime! [2193][1^^2] = prime! [2194][1^^42] = prime! [2195][1^^5] = prime! [2196][1^^1] = prime! [2197][1^^4] = prime! [2198][1^^8] = prime! [2199][1^^1] = prime! [2200][1^^57] = prime! [2201][1^^66] = prime! [2202][1^^11] = prime! [2203][1^^1] = prime! [2204][1^^2] = prime! [2205][1^^1] = prime! [2206][1^^10] = prime! [2207][1^^5] = prime! [2208][1^^2] = prime! [2209][1^^1] = prime! [2210][1^^21] = prime! [2211][1^^1] = prime! [2212][1^^100] = prime! [2213][1^^2] = prime! [2214][1^^2] = prime! [2215][1^^3] = prime! [2216][1^^9] = prime! [2217][1^^1] = prime! [2218][1^^34] = prime! [2219][1^^3] = prime! [2220][1^^2] = prime! [2221][1^^3] = prime! [2222][1^^9] = prime! [2223][1^^2] = prime! [2224][1^^7] = prime! [2225][1^^2] = prime! [2226][1^^4] = prime! [2227][1^^1] = prime! [2228][1^^8] = prime! [2229][1^^1] = prime! [2230][1^^30] = prime! [2231][1^^6] = prime! [2232][1^^2] = prime! [2233][1^^27] = prime! [2234][1^^18] = prime! [2235][1^^5] = prime! [2236][1^^3] = prime! [2237][1^^2] = prime! [2238][1^^1] = prime! [2239][1^^1] = prime! [2240][1^^2] = prime! [2241][1^^4] = prime! [2242][1^^3] = prime! [2243][1^^8] = prime! [2244][1^^1] = prime! [2245][1^^12] = prime! [2246][1^^2] = prime! [2247][1^^2] = prime! [2248][1^^1] = prime! [2249][1^^2] = prime! [2250][1^^1] = prime! [2251][1^^1] = prime! [2252][1^^63] = prime! [2253][1^^1] = prime! [2254][1^^1] = prime! [2255][1^^3] = prime! [2256][1^^2] = prime! [2257][1^^1] = prime! [2258][1^^3] = prime! [2259][1^^4] = prime! [2260][1^^6] = prime! [2261][1^^3] = prime! [2262][1^^1] = prime! [2263][1^^42] = prime! [2264][1^^9] = prime! [2265][1^^1] = prime! [2266][1^^9] = prime! [2267][1^^42] = prime! [2268][1^^113] = prime! [2269][1^^1] = prime! [2270][1^^2] = prime! [2271][1^^2] = prime! [2272][1^^1] = prime! [2273][1^^9] = prime! [2274][1^^1] = prime! [2275][1^^1] = prime! [2276][1^^2] = prime! ************************************************************************************************************************************************************************************ [2277][1^^n] = possible candidate ! n > 43000 ************************************************************************************************************************************************************************************ [2278][1^^4] = prime! [2279][1^^6] = prime! [2280][1^^58] = prime! [2281][1^^1] = prime! [2282][1^^2] = prime! [2283][1^^2] = prime! [2284][1^^4] = prime! [2285][1^^2] = prime! [2286][1^^1] = prime! [2287][1^^1] = prime! [2288][1^^359] = prime! [2289][1^^2] = prime! [2290][1^^1] = prime! [2291][1^^38] = prime! [2292][1^^1] = prime! [2293][1^^3] = prime! ************************************************************************************************************************************************************************************ [2294][1^^n] = possible candidate ! n > 38000 ************************************************************************************************************************************************************************************ [2295][1^^4] = prime! [2296][1^^1] = prime! [2297][1^^2] = prime! [2298][1^^14] = prime! [2299][1^^3] = prime! [2300][1^^60] = prime! [2301][1^^1] = prime! [2302][1^^1] = prime! [2303][1^^2] = prime! [2304][1^^1] = prime! [2305][1^^3] = prime! [2306][1^^2] = prime! [2307][1^^1] = prime! [2308][1^^1] = prime! [2309][1^^12] = prime! [2310][1^^47] = prime! [2311][1^^16] = prime! [2312][1^^8] = prime! [2313][1^^1] = prime! [2314][1^^2727] = prime! [2315][1^^6] = prime! [2316][1^^2] = prime! [2317][1^^15] = prime! [2318][1^^3] = prime! [2319][1^^5] = prime! [2320][1^^1] = prime! [2321][1^^683] = prime! [2322][1^^22] = prime! [2323][1^^226] = prime! [2324][1^^2] = prime! [2325][1^^1] = prime! [2326][1^^6] = prime! [2327][1^^2] = prime! [2328][1^^2] = prime! [2329][1^^1] = prime! [2330][1^^8] = prime! [2331][1^^1] = prime! [2332][1^^1] = prime! [2333][1^^660] = prime! [2334][1^^13] = prime! [2335][1^^3] = prime! [2336][1^^3] = prime! [2337][1^^1] = prime! [2338][1^^1051] = prime! [2339][1^^2] = prime! [2340][1^^5] = prime! [2341][1^^3] = prime! [2342][1^^2] = prime! [2343][1^^1] = prime! [2344][1^^10] = prime! [2345][1^^2] = prime! [2346][1^^4] = prime! [2347][1^^4] = prime! [2348][1^^2] = prime! [2349][1^^14] = prime! [2350][1^^3] = prime! [2351][1^^2] = prime! [2352][1^^2] = prime! [2353][1^^1] = prime! [2354][1^^3] = prime! [2355][1^^4] = prime! [2356][1^^1] = prime! [2357][1^^12] = prime! [2358][1^^1] = prime! [2359][1^^3] = prime! [2360][1^^14] = prime! [2361][1^^2] = prime! [2362][1^^3] = prime! [2363][1^^17] = prime! [2364][1^^19] = prime! [2365][1^^4051] = PRP! [2366][1^^14] = prime! [2367][1^^1] = prime! [2368][1^^4] = prime! [2369][1^^138] = prime! [2370][1^^2] = prime! [2371][1^^3] = prime! [2372][1^^5] = prime! [2373][1^^20] = prime! [2374][1^^1] = prime! [2375][1^^3] = prime! [2376][1^^1] = prime! [2377][1^^12] = prime! [2378][1^^3] = prime! [2379][1^^2] = prime! [2380][1^^1] = prime! [2381][1^^18] = prime! [2382][1^^4] = prime! [2383][1^^1] = prime! [2384][1^^8] = prime! [2385][1^^5] = prime! [2386][1^^4] = prime! [2387][1^^3] = prime! [2388][1^^10] = prime! [2389][1^^6] = prime! [2390][1^^3] = prime! [2391][1^^1] = prime! [2392][1^^9] = prime! [2393][1^^6] = prime! [2394][1^^4] = prime! [2395][1^^15] = prime! [2396][1^^2] = prime! [2397][1^^1] = prime! [2398][1^^1] = prime! [2399][1^^24] = prime! [2400][1^^1] = prime! [2401][1^^3] = prime! [2402][1^^6] = prime! [2403][1^^11] = prime! [2404][1^^3] = prime! [2405][1^^8] = prime! [2406][1^^1] = prime! [2407][1^^1] = prime! [2408][1^^2] = prime! [2409][1^^1] = prime! [2410][1^^10] = prime! [2411][1^^3] = prime! [2412][1^^1] = prime! [2413][1^^3] = prime! [2414][1^^5] = prime! [2415][1^^1] = prime! [2416][1^^12] = prime! [2417][1^^2] = prime! [2418][1^^1] = prime! [2419][1^^7] = prime! [2420][1^^3] = prime! [2421][1^^32] = prime! [2422][1^^3] = prime! [2423][1^^8] = prime! [2424][1^^22] = prime! [2425][1^^1] = prime! [2426][1^^12] = prime! [2427][1^^35] = prime! [2428][1^^1] = prime! [2429][1^^2] = prime! [2430][1^^2] = prime! [2431][1^^477] = prime! [2432][1^^6] = prime! [2433][1^^2] = prime! [2434][1^^12] = prime! [2435][1^^41] = prime! [2436][1^^5] = prime! [2437][1^^1] = prime! [2438][1^^6] = prime! [2439][1^^1] = prime! [2440][1^^3] = prime! [2441][1^^3] = prime! [2442][1^^1] = prime! [2443][1^^4] = prime! [2444][1^^2] = prime! [2445][1^^4] = prime! [2446][1^^30] = prime! [2447][1^^2] = prime! [2448][1^^1] = prime! [2449][1^^4] = prime! [2450][1^^11] = prime! [2451][1^^31] = prime! [2452][1^^3] = prime! [2453][1^^5] = prime! [2454][1^^2] = prime! [2455][1^^1] = prime! [2456][1^^6] = prime! [2457][1^^1] = prime! [2458][1^^826] = prime! [2459][1^^2] = prime! [2460][1^^2] = prime! [2461][1^^1] = prime! [2462][1^^5] = prime! [2463][1^^1] = prime! [2464][1^^757] = prime! [2465][1^^2] = prime! [2466][1^^2] = prime! [2467][1^^1] = prime! [2468][1^^2] = prime! [2469][1^^1] = prime! [2470][1^^7] = prime! [2471][1^^27] = prime! [2472][1^^28] = prime! [2473][1^^6] = prime! [2474][1^^6] = prime! [2475][1^^5] = prime! [2476][1^^4] = prime! [2477][1^^2] = prime! [2478][1^^1] = prime! [2479][1^^4] = prime! [2480][1^^18] = prime! [2481][1^^5] = prime! [2482][1^^1] = prime! [2483][1^^29] = prime! [2484][1^^1] = prime! [2485][1^^1] = prime! [2486][1^^381] = prime! [2487][1^^4] = prime! [2488][1^^3] = prime! [2489][1^^3] = prime! [2490][1^^29] = prime! [2491][1^^4] = prime! [2492][1^^2] = prime! [2493][1^^2] = prime! [2494][1^^6] = prime! [2495][1^^17] = prime! [2496][1^^17] = prime! [2497][1^^1] = prime! [2498][1^^2] = prime! [2499][1^^2] = prime! [2500][1^^4] = prime! [2501][1^^216] = prime! [2502][1^^13] = prime! [2503][1^^1] = prime! [2504][1^^5] = prime! [2505][1^^5] = prime! [2506][1^^40] = prime! [2507][1^^6] = prime! [2508][1^^11] = prime! [2509][1^^34] = prime! [2510][1^^3] = prime! [2511][1^^1] = prime! [2512][1^^1] = prime! [2513][1^^23] = prime! [2514][1^^34] = prime! [2515][1^^9] = prime! [2516][1^^2] = prime! [2517][1^^1] = prime! [2518][1^^4] = prime! [2519][1^^17] = prime! [2520][1^^32] = prime! [2521][1^^3] = prime! [2522][1^^11] = prime! [2523][1^^334] = prime! [2524][1^^19] = prime! [2525][1^^6] = prime! [2526][1^^1] = prime! [2527][1^^3] = prime! [2528][1^^990] = prime! [2529][1^^2] = prime! [2530][1^^1] = prime! [2531][1^^8] = prime! [2532][1^^1] = prime! [2533][1^^12] = prime! [2534][1^^3] = prime! [2535][1^^7] = prime! [2536][1^^16] = prime! [2537][1^^3] = prime! [2538][1^^2] = prime! [2539][1^^1] = prime! [2540][1^^8] = prime! [2541][1^^1] = prime! [2542][1^^4] = prime! [2543][1^^3] = prime! [2544][1^^16] = prime! [2545][1^^33] = prime! [2546][1^^9] = prime! [2547][1^^1] = prime! [2548][1^^3] = prime! [2549][1^^2] = prime! [2550][1^^5] = prime! [2551][1^^7] = prime! [2552][1^^3] = prime! [2553][1^^4] = prime! [2554][1^^1] = prime! [2555][1^^2] = prime! [2556][1^^1] = prime! [2557][1^^3] = prime! [2558][1^^6] = prime! [2559][1^^5] = prime! [2560][1^^1] = prime! [2561][1^^5] = prime! [2562][1^^1] = prime! [2563][1^^15] = prime! [2564][1^^24] = prime! [2565][1^^4] = prime! [2566][1^^19] = prime! [2567][1^^3] = prime! [2568][1^^5] = prime! [2569][1^^49] = prime! [2570][1^^9] = prime! [2571][1^^8] = prime! [2572][1^^7] = prime! [2573][1^^2] = prime! [2574][1^^1] = prime! [2575][1^^12] = prime! [2576][1^^2] = prime! [2577][1^^1] = prime! [2578][1^^3] = prime! [2579][1^^3] = prime! [2580][1^^1] = prime! [2581][1^^4] = prime! [2582][1^^2] = prime! [2583][1^^8] = prime! [2584][1^^1] = prime! [2585][1^^3] = prime! [2586][1^^2] = prime! ************************************************************************************************************************************************************************************ [2587][1^^n] = possible candidate ! n > 30000 ************************************************************************************************************************************************************************************ [2588][1^^51] = prime! [2589][1^^43] = prime! [2590][1^^40] = prime! [2591][1^^9] = prime! [2592][1^^2] = prime! [2593][1^^1] = prime! [2594][1^^2] = prime! [2595][1^^1] = prime! [2596][1^^n] = always composite! set of six divisors (13, 11, 7, 11, 3, 11) that appear periodically [2597][1^^518] = prime! [2598][1^^1] = prime! [2599][1^^3] = prime! [2600][1^^2] = prime! [2601][1^^2] = prime! [2602][1^^1] = prime! [2603][1^^12] = prime! [2604][1^^1] = prime! [2605][1^^6] = prime! [2606][1^^5] = prime! [2607][1^^73] = prime! [2608][1^^6] = prime! [2609][1^^6] = prime! [2610][1^^2] = prime! [2611][1^^1] = prime! [2612][1^^38] = prime! [2613][1^^4] = prime! [2614][1^^1] = prime! [2615][1^^3] = prime! [2616][1^^1] = prime! [2617][1^^1] = prime! [2618][1^^3] = prime! [2619][1^^124] = prime! [2620][1^^4] = prime! [2621][1^^2] = prime! [2622][1^^20] = prime! [2623][1^^3] = prime! [2624][1^^2] = prime! [2625][1^^1] = prime! [2626][1^^1] = prime! [2627][1^^20] = prime! [2628][1^^343] = prime! [2629][1^^9] = prime! [2630][1^^12192] = PRP! [2631][1^^2] = prime! [2632][1^^1] = prime! [2633][1^^8] = prime! [2634][1^^2] = prime! [2635][1^^39] = prime! [2636][1^^2] = prime! [2637][1^^1] = prime! [2638][1^^12] = prime! [2639][1^^2] = prime! [2640][1^^7] = prime! [2641][1^^6] = prime! [2642][1^^2] = prime! [2643][1^^1] = prime! [2644][1^^22] = prime! [2645][1^^5] = prime! [2646][1^^8] = prime! [2647][1^^3] = prime! [2648][1^^2] = prime! [2649][1^^5] = prime! [2650][1^^1] = prime! [2651][1^^3] = prime! [2652][1^^548] = prime! [2653][1^^3] = prime! [2654][1^^3] = prime! [2655][1^^2] = prime! [2656][1^^1] = prime! [2657][1^^2] = prime! [2658][1^^5] = prime! [2659][1^^1] = prime! [2660][1^^14] = prime! [2661][1^^2] = prime! [2662][1^^309] = prime! [2663][1^^12] = prime! [2664][1^^1] = prime! [2665][1^^4] = prime! [2666][1^^318] = prime! [2667][1^^2] = prime! [2668][1^^1] = prime! [2669][1^^3] = prime! [2670][1^^1] = prime! [2671][1^^1] = prime! [2672][1^^5] = prime! [2673][1^^1] = prime! [2674][1^^34] = prime! [2675][1^^2] = prime! [2676][1^^2] = prime! [2677][1^^15] = prime! [2678][1^^2] = prime! [2679][1^^31] = prime! [2680][1^^1] = prime! [2681][1^^5] = prime! [2682][1^^1] = prime! [2683][1^^4] = prime! [2684][1^^53] = prime! [2685][1^^32] = prime! [2686][1^^1] = prime! [2687][1^^5] = prime! [2688][1^^1] = prime! [2689][1^^1] = prime! [2690][1^^3] = prime! [2691][1^^4] = prime! [2692][1^^1] = prime! [2693][1^^3] = prime! [2694][1^^70] = prime! [2695][1^^1] = prime! [2696][1^^42] = prime! [2697][1^^16] = prime! [2698][1^^1] = prime! [2699][1^^3] = prime! [2700][1^^389] = prime! [2701][1^^1] = prime! ************************************************************************************************************************************************************************************ [2702][1^^n] = possible candidate ! n > 34000 ************************************************************************************************************************************************************************************ [2703][1^^1] = prime! [2704][1^^3] = prime! [2705][1^^3] = prime! [2706][1^^1] = prime! [2707][1^^16] = prime! [2708][1^^6] = prime! [2709][1^^1] = prime! [2710][1^^3] = prime! [2711][1^^26] = prime! [2712][1^^2] = prime! [2713][1^^3] = prime! [2714][1^^3] = prime! [2715][1^^5] = prime! [2716][1^^4] = prime! [2717][1^^15] = prime! [2718][1^^2] = prime! [2719][1^^1] = prime! [2720][1^^2] = prime! [2721][1^^1] = prime! [2722][1^^67] = prime! [2723][1^^81] = prime! [2724][1^^1] = prime! [2725][1^^16] = prime! [2726][1^^6] = prime! [2727][1^^1] = prime! [2728][1^^1] = prime! [2729][1^^2] = prime! [2730][1^^5] = prime! [2731][1^^3] = prime! [2732][1^^6] = prime! [2733][1^^2] = prime! [2734][1^^9] = prime! [2735][1^^11] = prime! [2736][1^^1] = prime! [2737][1^^4] = prime! [2738][1^^20] = prime! [2739][1^^n] = always composite! set of six divisors (7, 11, 3, 11, 37, 11) that appear periodically [2740][1^^10] = prime! [2741][1^^17] = prime! [2742][1^^7] = prime! [2743][1^^1] = prime! [2744][1^^3] = prime! [2745][1^^4] = prime! [2746][1^^3] = prime! [2747][1^^2] = prime! [2748][1^^1] = prime! [2749][1^^2019] = prime! [2750][1^^107] = prime! [2751][1^^20] = prime! [2752][1^^6] = prime! [2753][1^^3] = prime! [2754][1^^1] = prime! [2755][1^^1] = prime! [2756][1^^3] = prime! [2757][1^^2] = prime! [2758][1^^1] = prime! [2759][1^^2] = prime! [2760][1^^2] = prime! [2761][1^^1] = prime! [2762][1^^72] = prime! [2763][1^^1] = prime! [2764][1^^4] = prime! [2765][1^^20] = prime! [2766][1^^19] = prime! [2767][1^^3] = prime! [2768][1^^12] = prime! [2769][1^^1] = prime! [2770][1^^1] = prime! [2771][1^^5] = prime! [2772][1^^83] = prime! [2773][1^^126] = prime! [2774][1^^2] = prime! [2775][1^^1] = prime! [2776][1^^6] = prime! [2777][1^^3] = prime! [2778][1^^188] = prime! [2779][1^^1] = prime! [2780][1^^21] = prime! [2781][1^^2] = prime! [2782][1^^3] = prime! [2783][1^^3] = prime! [2784][1^^1462] = prime! [2785][1^^1] = prime! [2786][1^^2] = prime! [2787][1^^13] = prime! [2788][1^^46] = prime! [2789][1^^2] = prime! [2790][1^^1] = prime! [2791][1^^12] = prime! [2792][1^^2] = prime! [2793][1^^2] = prime! [2794][1^^1] = prime! [2795][1^^2] = prime! [2796][1^^1] = prime! [2797][1^^25] = prime! [2798][1^^6] = prime! [2799][1^^7] = prime! [2800][1^^1] = prime! [2801][1^^3] = prime! [2802][1^^5] = prime! [2803][1^^1] = prime! [2804][1^^2] = prime! [2805][1^^1] = prime! [2806][1^^6] = prime! [2807][1^^2] = prime! [2808][1^^1] = prime! [2809][1^^6] = prime! [2810][1^^6] = prime! [2811][1^^1] = prime! [2812][1^^73] = prime! [2813][1^^24] = prime! [2814][1^^5] = prime! [2815][1^^1] = prime! [2816][1^^5] = prime! [2817][1^^4] = prime! [2818][1^^1] = prime! [2819][1^^9] = prime! [2820][1^^1] = prime! [2821][1^^1] = prime! [2822][1^^9] = prime! [2823][1^^2] = prime! [2824][1^^49] = prime! [2825][1^^15] = prime! [2826][1^^7] = prime! [2827][1^^7] = prime! [2828][1^^15998] = PRP! [2829][1^^2] = prime! [2830][1^^6] = prime! [2831][1^^2] = prime! [2832][1^^2] = prime! [2833][1^^3] = prime! [2834][1^^2] = prime! [2835][1^^1] = prime! [2836][1^^6] = prime! [2837][1^^3] = prime! [2838][1^^59] = prime! [2839][1^^120] = prime! [2840][1^^5] = prime! [2841][1^^1] = prime! [2842][1^^10] = prime! [2843][1^^2] = prime! [2844][1^^11] = prime! [2845][1^^6] = prime! [2846][1^^3] = prime! [2847][1^^4] = prime! [2848][1^^12] = prime! [2849][1^^23] = prime! [2850][1^^64] = prime! [2851][1^^3] = prime! [2852][1^^11] = prime! [2853][1^^11] = prime! [2854][1^^1] = prime! [2855][1^^8] = prime! [2856][1^^2] = prime! [2857][1^^1] = prime! [2858][1^^5] = prime! [2859][1^^1] = prime! [2860][1^^99] = prime! [2861][1^^30] = prime! [2862][1^^1] = prime! [2863][1^^1] = prime! [2864][1^^2] = prime! [2865][1^^8] = prime! [2866][1^^1] = prime! [2867][1^^2] = prime! [2868][1^^5] = prime! [2869][1^^10] = prime! [2870][1^^11] = prime! [2871][1^^1] = prime! [2872][1^^18] = prime! [2873][1^^17] = prime! [2874][1^^7] = prime! [2875][1^^1] = prime! [2876][1^^2] = prime! [2877][1^^1] = prime! [2878][1^^6] = prime! [2879][1^^3] = prime! [2880][1^^25] = prime! [2881][1^^49] = prime! [2882][1^^3] = prime! [2883][1^^16] = prime! [2884][1^^7] = prime! [2885][1^^3] = prime! [2886][1^^11] = prime! [2887][1^^1] = prime! [2888][1^^8] = prime! [2889][1^^4] = prime! [2890][1^^1] = prime! [2891][1^^2] = prime! [2892][1^^1] = prime! [2893][1^^n] = always composite! set of six divisors (7, 11, 13, 11, 3, 11) that appear periodically [2894][1^^6] = prime! [2895][1^^2] = prime! [2896][1^^1] = prime! [2897][1^^5] = prime! [2898][1^^4] = prime! [2899][1^^10] = prime! [2900][1^^2] = prime! [2901][1^^5] = prime! [2902][1^^1] = prime! [2903][1^^3] = prime! [2904][1^^5] = prime! [2905][1^^4] = prime! [2906][1^^2] = prime! [2907][1^^2] = prime! [2908][1^^34] = prime! [2909][1^^9] = prime! [2910][1^^1] = prime! [2911][1^^4] = prime! [2912][1^^5] = prime! [2913][1^^1] = prime! [2914][1^^3] = prime! [2915][1^^3] = prime! [2916][1^^206] = prime! [2917][1^^7] = prime! [2918][1^^204] = prime! [2919][1^^1] = prime! [2920][1^^1] = prime! [2921][1^^3] = prime! [2922][1^^1] = prime! [2923][1^^1] = prime! [2924][1^^3] = prime! [2925][1^^1] = prime! [2926][1^^3] = prime! [2927][1^^2] = prime! [2928][1^^4] = prime! [2929][1^^3] = prime! [2930][1^^8] = prime! [2931][1^^1] = prime! [2932][1^^4] = prime! [2933][1^^2] = prime! [2934][1^^170] = prime! [2935][1^^4] = prime! [2936][1^^5] = prime! [2937][1^^43] = prime! [2938][1^^142] = prime! [2939][1^^8] = prime! [2940][1^^1] = prime! [2941][1^^1] = prime! [2942][1^^2] = prime! [2943][1^^2] = prime! [2944][1^^15] = prime! [2945][1^^6] = prime! [2946][1^^11] = prime! [2947][1^^3] = prime! [2948][1^^9] = prime! [2949][1^^2] = prime! [2950][1^^1] = prime! [2951][1^^2] = prime! [2952][1^^49] = prime! [2953][1^^1] = prime! [2954][1^^2] = prime! [2955][1^^13] = prime! [2956][1^^3] = prime! [2957][1^^3] = prime! [2958][1^^1] = prime! [2959][1^^7] = prime! [2960][1^^2] = prime! [2961][1^^1] = prime! [2962][1^^3] = prime! [2963][1^^5] = prime! [2964][1^^1] = prime! [2965][1^^3] = prime! [2966][1^^5] = prime! [2967][1^^1] = prime! [2968][1^^3] = prime! [2969][1^^2] = prime! [2970][1^^323] = prime! [2971][1^^36] = prime! [2972][1^^17] = prime! [2973][1^^22] = prime! [2974][1^^1] = prime! [2975][1^^3] = prime! [2976][1^^1] = prime! [2977][1^^111] = prime! [2978][1^^2] = prime! [2979][1^^2] = prime! [2980][1^^4] = prime! [2981][1^^23] = prime! [2982][1^^2] = prime! [2983][1^^3] = prime! [2984][1^^2] = prime! [2985][1^^1] = prime! [2986][1^^3] = prime! [2987][1^^5] = prime! [2988][1^^1] = prime! [2989][1^^27] = prime! [2990][1^^2] = prime! [2991][1^^14] = prime! [2992][1^^1] = prime! [2993][1^^2] = prime! [2994][1^^13] = prime! [2995][1^^16] = prime! [2996][1^^15] = prime! [2997][1^^2] = prime! [2998][1^^3] = prime! [2999][1^^6] = prime! [3000][1^^35] = prime! [3001][1^^1] = prime! [3002][1^^6] = prime! [3003][1^^11] = prime! [3004][1^^4] = prime! [3005][1^^2] = prime! [3006][1^^4] = prime! [3007][1^^1] = prime! [3008][1^^17] = prime! [3009][1^^1] = prime! [3010][1^^313] = prime! [3011][1^^26] = prime! [3012][1^^2] = prime! [3013][1^^6] = prime! [3014][1^^5] = prime! [3015][1^^10] = prime! [3016][1^^1] = prime! [3017][1^^2] = prime! [3018][1^^1] = prime! [3019][1^^3] = prime! [3020][1^^5] = prime! [3021][1^^1] = prime! [3022][1^^13] = prime! [3023][1^^5] = prime! [3024][1^^1] = prime! [3025][1^^3] = prime! [3026][1^^18] = prime! [3027][1^^1] = prime! [3028][1^^7] = prime! [3029][1^^5] = prime! [3030][1^^2] = prime! [3031][1^^10] = prime! [3032][1^^9] = prime! [3033][1^^5] = prime! [3034][1^^1] = prime! [3035][1^^27] = prime! [3036][1^^5] = prime! [3037][1^^70] = prime! [3038][1^^3] = prime! [3039][1^^1] = prime! [3040][1^^3] = prime! [3041][1^^3] = prime! [3042][1^^2] = prime! [3043][1^^1] = prime! [3044][1^^2] = prime! [3045][1^^2] = prime! [3046][1^^6] = prime! [3047][1^^11] = prime! [3048][1^^10] = prime! [3049][1^^1] = prime! [3050][1^^5] = prime! [3051][1^^2] = prime! [3052][1^^10] = prime! [3053][1^^6] = prime! [3054][1^^2] = prime! [3055][1^^27] = prime! [3056][1^^2] = prime! [3057][1^^4] = prime! [3058][1^^7] = prime! [3059][1^^8] = prime! [3060][1^^2] = prime! [3061][1^^3] = prime! [3062][1^^5] = prime! [3063][1^^1] = prime! [3064][1^^4] = prime! [3065][1^^2] = prime! [3066][1^^1] = prime! [3067][1^^1] = prime! [3068][1^^3] = prime! [3069][1^^85] = prime! [3070][1^^12] = prime! [3071][1^^179] = prime! [3072][1^^4] = prime! [3073][1^^3] = prime! [3074][1^^6] = prime! [3075][1^^2] = prime! [3076][1^^3] = prime! [3077][1^^2] = prime! [3078][1^^1] = prime! [3079][1^^7] = prime! [3080][1^^17] = prime! [3081][1^^22] = prime! [3082][1^^6] = prime! [3083][1^^2] = prime! [3084][1^^1] = prime! [3085][1^^1] = prime! [3086][1^^5] = prime! [3087][1^^1] = prime! [3088][1^^1] = prime! [3089][1^^15] = prime! [3090][1^^2] = prime! [3091][1^^1] = prime! ************************************************************************************************************************************************************************************ [3092][1^^n] = possible candidate ! n > 32000 ************************************************************************************************************************************************************************************ [3093][1^^1] = prime! [3094][1^^1] = prime! [3095][1^^3] = prime! [3096][1^^10] = prime! [3097][1^^1] = prime! [3098][1^^2] = prime! [3099][1^^53] = prime! [3100][1^^4] = prime! [3101][1^^2] = prime! [3102][1^^235] = prime! [3103][1^^18] = prime! [3104][1^^14] = prime! [3105][1^^1] = prime! [3106][1^^3] = prime! [3107][1^^2] = prime! [3108][1^^1] = prime! [3109][1^^1] = prime! [3110][1^^6] = prime! [3111][1^^2] = prime! [3112][1^^1] = prime! [3113][1^^3] = prime! [3114][1^^16] = prime! [3115][1^^1] = prime! [3116][1^^3] = prime! [3117][1^^2] = prime! [3118][1^^1] = prime! [3119][1^^3] = prime! [3120][1^^5] = prime! [3121][1^^6] = prime! [3122][1^^2] = prime! [3123][1^^1] = prime! [3124][1^^651] = prime! [3125][1^^38] = prime! [3313][1^^279] = prime! [3688][1^^280] = prime! [3895][1^^264] = prime! [6789][1^^1] = prime! [8394][1^^268] = prime! [8957][1^^266] = prime! [11342][1^^366] = prime! [12837][1^^263] = prime! [13013][1^^275] = prime! [13574][1^^267] = prime! [15422][1^^273] = prime! [17799][1^^274] = prime! [22915][1^^276] = prime! [24354][1^^271] = prime! [25245][1^^269] = prime! [26763][1^^281] = prime! [31683][1^^278] = prime! [33650][1^^270] = prime! [34273][1^^2016] = prime! Note that 34273 is also prime! [49078][1^^2017] = prime! [49420][1^^277] = prime! [129889][1^^3000] = prime! [133453][1^^666] = prime! [235533][1^^2000] = prime! [267923][1^^2015] = prime! [2144039][1^^20000] = prime!