Appending 1's to number n until prime WONPLATE_197 ---------------------------------------------------------------------- Still searching for 603*10^n+R(n) n >= 300000 1244*10^n+R(n) n >= 200000 1861*10^n+R(n) n >= 200000 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- [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 × 1058854399362990511245392179859 × 2343509638161628145225929956310157547974760516143237740348954466076287 [12](1_130) = 61 × 36369136999488198605614748630621486653942384326441069497849 × 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! but 136 > 35 [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 na deelbaar door 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 na deelbaar door 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 na deelbaat door 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 na deelbaar door 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 n = 28 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! 45*10^772+R(772) = 3-PRP! 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! but 772 > 9 [54](1_1) = prime! [55](1_31) = prime! but 772 > 31 ____________________________________________________________________________________________________________________________________________________________________________________ [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! 56*10^18470+R(18470) = 3-PRP! a new delayed prime record nr 7 ____________________________________________________________________________________________________________________________________________________________________________________ [57](1_1) = prime! [58](1_3) = prime! [59](1_18) = prime! but 18470 > 18 [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! but 18470 > 210 67*10^210+R(210) = 3-PRP! [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! but 18470 > 149 87*10^149+R(149) = 3-PRP! [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! but 18470 > 44 [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! but 18470 > 2890 133*10^2890+R(2890) = 3-PRP! [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! but 18470 > 119 159*10^119+R(119) = 3-PRP! [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! but 18470 > 186 159*10^119+R(119) is 3-PRP! [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! 198*10^101+R(101) is 3-PRP! [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! but 18470 > 653 215*10^653+R(653) is 3-PRP! [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! but 18470 > 684 232*10^684+R(684) is 3-PRP! [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! but 18470 > 478 243*10^478+R(478) is 3-PRP! [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! but 18470 > 217 250*10^217+R(217) is 3-PRP! [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 307*10^180+R(180) is 3-PRP! [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! but 18470 > 864 320*10^864+R(864) is 3-PRP! [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! 373*10^64+R(64) is 3-PRP! [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! 403*10^91+R(91) is 3-PRP! [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! 429*10^137+R(137) is 3-PRP! [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! 451*10^771+R(771) is 3-PRP! but 18470 > 771 [452](1_6) = prime! [453](1_1943) = prime! 453*10^1943+R(1943) is 3-PRP! but 18470 > 1943 next [453](1_n) is n > 10000 [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! 482*10^1704+R(1704) is 3-PRP! but 18470 > 1704 [483](1_1) = prime! [484](1_3) = prime! [485](1_14) = prime! [486](1_1) = prime! [487](1_1) = prime! [488](1_101) = prime! 488*10^101+R(101) is 3-PRP! [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! 496*10^108+R(108) is 3-PRP! [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! 519*10^145+R(145) is 3-PRP! [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! 529*10^2778+R(2778) is 3-PRP! but 18470 > 2778 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! 592*10^67+R(67) is 3-PRP! [593](1_3) = prime! [594](1_35) = prime! 59411111111111111111111111111111111111 is prime [595](1_88) = prime! 595*10^88+R(88) is 3-PRP! and 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_?) >= 300000 a new delayed prime record nr 8 alle {3 +3} deelbaar door 3 alle {5 +6} (always odd) deelbaar door 7 alle {1 +3} deelbaar door 37 alle {2 +5} deelbaar door 41 ENKEL {8 +6} levert mogelijke kandidaten voor priemgetallen ! [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! 617*10^5760+R(5760) is 3-PRP! but [603](1_n) > 5760 [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! 628*10^82+R(82) is 3-PRP! 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! 638*10^753+R(753) is 3-PRP! [639](1_8) = prime! [640](1_15) = prime! [641](1_11) = prime! =[64](1_12) [642](1_1) = prime! [643](1_390) = prime! 643*10^390+R(390) is 3-PRP! [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) 661*10^192+R(192) is 3-PRP! [662](1_3) = prime! [663](1_5) = prime! [664](1_594) = prime! 664*10^594+R(594) is 3-PRP! [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) 671*10^209+R(209) is 3-PRP! [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! 682*10^133+R(133) is 3-PRP! [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) = prime! 708*10^37156+R(37156) is 3-PRP! [603](1_n) > 37156 [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! 738*10^118+R(118) is 3-PRP! [739](1_3) = prime! [740](1_1955) = prime! 740*10^1955+R(1955) is 3-PRP! [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) = prime! 749*10^22850+R(22850) is 3-PRP! but [603](1_n) > 22850 [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! 793*10^124+R(124) is 3-PRP! [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) = aways 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! 818*10^74+R(74) is 3-PRP! [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! 825*10^161+R(161) is 3-PRP! [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! 847*10^249+R(249) is 3-PRP! [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! 862*10^1221+R(1221) is 3-PRP! [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! 869*10^1569+R(1569) is 3-PRP! [870](1_2) = prime! [871](1_148) = prime! =[87](1_149) 871*10^148+R(148) is 3-PRP! [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! 902*10^1931+R(1931) is 3-PRP! [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! 973*10^1437+R(1437) is 3-PRP! [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! 995*10^2100+R(2100) is 3-PRP! [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! 1134*10^50+R(50) is 3-PRP! [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) = prime! [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! 1213*10^54+R(54) is 3-PRP! [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 ! >= 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! 1275*10^49+R(49) is 3-PRP! [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! 1299*10^26+R(26) is 3-PRP! [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! 1354*10^52+R(52) is 3-PRP! [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! 1402*10^42+r(42) is 3-PRP! [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) = prime! 3,5,7-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! 1601*10^27+R(27) is 3-PRP! [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) = prime! [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! 1756*10^37+R(37) is 3-PRP! [1757](1_20) = prime! [1758](1_1) = prime! [1759](1_4) = prime! [1760](1_15) = prime! ____________________________________________________________________________________________________________________________________________________________________________________ [1761](1_n) = always composite zie [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) = prime! [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! 1823*10^41+R(41) is 3-PRP! [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 ! >= 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! 2036*10^36+R(36) is 3-PRP! [2037](1_41) = prime! [2178](1_55) = prime! 2178*10^55+R(55) is 3-PRP! [2506](1_40) = prime! 2506*10^40+R(40) is 3-PRP! [2588](1_51)= prime! 2588*10^51+R(51) is 3-PRP! [2589](1_43) = prime! 2589*10^43+R(43) is 3-PRP! [2684](1_53) = prime! 2684*10^53+R(53) is 3-PRP! [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! 11342*10^366+R(366) is 3-PRP! [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! 34273*10^2016+R(2016) is 3-PRP! Note that 34273 is also prime! [49078](1_2017) = prime! [49420](1_277) = prime! [129889](1_3000) = prime! is 3-PRP! [133453](1_666) = prime! 133453*10^666+R(666) is 3-PRP! [235533](1_2000) = prime! [267923](1_2015) = prime! 267923*10^2015+R(2015) is 3-PRP! [2144039](1_20000) = prime! 2144039*10^20000+R(20000) is 3-PRP!