Generalized Cullen and Woodall primes can be twins
Generalized Cullen Primes are defined as the primes of the form n.bn+1 with n+2 > b, while generalized Woodall Primes as the form n.bn-1 with n+2 > b. If we loose the restraint of n+2 > b to a plain n > 2, with every b>1, except for n = k^c and mod(n, c)=0,there is a conjuncture
There is always an integer of b>1 that makes n.bn-1and n.bn+1a pair of twin primes.
Found terms as following:
2 3 1 3 4 2 -- -- -- 5 570 14 6 1820 20 7 1464 23 8 54 14 9 60 16 10 14025 42 11 1932 37 12 3029 42 13 7194 51 14 15 17 15 3612 54 -- -- -- 17 4746 63 18 3154 64 19 540 53 20 150 44 21 7060 82 22 138 48 23 80094 114 24 6160 92 25 33480 114 26 93135 130 -- -- -- 28 366618 157 29 26058 129 30 13516 125 31 90510 155 32 16836 136 33 9824 133 34 418875 192 35 57246 168 -- -- -- 37 182394 196 38 64077 184 39 14178 163 40 943410 241 41 36078 189 42 78389 208 43 314520 239 44 15870 187 45 194942 240 46 15044700 332 47 241944 255 48 3871 174 49 308730 271 50 11604 205 51 89492 255 52 4745196 349 53 388626 298 54 3905 196 55 60648 265 56 26625 250 57 44240 267 58 198240 310 59 178290 312 60 937143 361 61 403488 344 62 19605 268 63 19716 273 -- -- -- 65 10098 263 66 2029430 419 67 420174 379 68 423 181 69 1177568 421 70 772764 415 71 580338 412 72 1285530 442 73 2978310 475 74 885120 442 75 68280 365 76 158655 398 77 1726236 483 78 84826329 621 79 1413132 488 80 27852 358 81 25092 359 82 1611528 511 83 413856 469 84 45 141 85 247272 461 86 1232580 526 87 26550 387 88 52847043 682 89 527892 512 90 1416870 556 91 448380 517 92 79209 453 93 204470 496 94 448020 534 95 228144 512 96 666875 562 97 215154 520 98 71727 478 99 3162208 646 -- -- -- 101 274560 552 102 7119669 701 103 232464 555 104 2007420 658 105 186298 556 106 484443570 923 107 2822406 693 108 16130583 781 109 591780 632 110 68748 535 111 162498 581 112 6032505 762 113 171546 594 114 56215 544 115 323520 636 116 6801570 795 117 555676 675 118 1679421 737 119 701982 698 120 58266208 934 121 228858 651 122 409011 687 123 158620 642 124 1553460 770 125 1145286 760 126 27835860 941 127 1552446 789 128 546417 737 129 170172 677 130 74235735 1026 131 1259052 802 132 1329566 811 133 127584 682 134 999180 807 135 242580 730 136 >1E9 -- 137 10893030 967 138 81732139 1095 139 220122 745 140 148491 721 141 8406692 979 142 744168 836 143 1352616 879 -- -- -- 145 7313424 998 146 797505 864 147 66890 712 148 21504723 1088 149 1754178 933 150 17103770 1088 151 11806812 1071 152 -- -- 153 -- -- 154 -- -- 155 -- -- 156 -- -- 157 -- -- 158 422547 933 159 158632 892 160 573291 924 161 284418 881 162 -- -- 163 539016 937 164 -- -- 165 169256 865 166 -- -- 167 1054716 1009 168 581204 971 169 -- -- 170 1474092 1051 171 712508 1004 172 -- -- 173 603744 1003 174 -- -- 175 -- -- 176 -- -- 177 -- -- 178 -- -- 179 440418 1013 180 -- -- 181 1012620 1090 182 497169 1040 183 388934 1026 184 -- -- 185 1580046 1150 186 99465 932 187 -- -- 188 -- -- 189 -- -- 190 -- -- 191 -- -- 192 -- -- 193 -- -- 194 1701405 1212 195 -- -- 196 -- -- 197 -- -- 198 -- -- 199 -- -- 200 49839 942 201 -- -- 202 -- -- 203 859146 1207 204 -- -- 205 239604 1106
The dashes in the first column means that that item does not exist theoretically. The other dashes means not-yet-found terms. Currently processed to 200.
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