All n must be ≥1.

k-values with at least one of the following conditions are excluded from the conjectures:

1. All n-values have a single trivial factor.
2. Make a full covering set with all or partial algebraic factors.
3. Make generalized Fermat numbers (GFN), i.e. q^m*b^n+1 where b is the base, m≥0, and q is a root of the base.

k-values that are a multiple of base (b) and where k+1 (Sierpinski) or k−1 (Riesel) is composite are included in the conjectures but excluded from testing. Such k-values will have the same prime as k / b.

## Sierpinski bases

### 1 k bases

 base conjectured k remain k 9 1434 1218 X 5387 452X 15 1E2 184 1X 3X5X 2E74 23 38X 292 37 1380 11X 58 1X 15 63 2446 914 72 24 8 73 1XX 28 94 203X E94 99 1320 X2X 9X 59 40 X2 34 2X X8 38 34 E8 3X 8 104 2707 1449 10E 12 4 126 6 4 132 1E 8 135 28 X 148 3E 34 150 69 4 161 10X6 950 162 62 15 16E 18 16 172 8 4 190 39 23 194 859 593 195 38 34 197 100 54 19E X 8 1X0 46 35 206 9E 51 214 X1 50 225 44 38 226 100 75 228 8X 81 234 40 23 23E 8 4 244 219 147 255 14 8 271 X0 90 277 186 110 295 58 18 296 78 51 2X9 48 X 2E6 52 8 2E8 X 8 2EX 10E79 8X49 304 154 39 316 X2 73 325 8 2 32E 8 4 330 14X 81 332 112 28 338 44 24 340 32 10 350 72 59 355 14 8 368 16 5 370 EX X2 374 6EX 269 386 8X 88 39X 97 7X 3EX 20 14 403 72 6 406 46 28 418 148 E4 425 84 5X 452 5X 28 461 100 54 484 589 427 486 143 8X 492 172 98 4X6 63 33 4XE 4X 34 500 88 11 504 150 9 50X 123 70 514 E1 10 518 12 11 532 X 8 54X 154 117 551 380 26X 554 110 107 555 XX 8 559 178 80 566 137 29 56E 14 4 572 1X4 E8 580 247 109 585 E4 68 590 10 8 596 11X 75 598 28 2 5XX 269 190 5E1 150 8X 600 126 62 602 14 8 60E 62 4 617 230 56 642 4 2 645 14 2 656 18 8 65E 12 X 675 44 8 688 14 E 698 92 21 69E 34 8 6E2 32 10 6E8 4 2 701 214 100

### 2 k bases

 base conjectured k remain k 22 165 55, 10E 24 2776 607, 2774 26 603 1E2, 410 41 1854 99X, X14 8E X2 32, 58 15X 123 73, 8X 178 68 45, 57 20X 133 56, 120 223 E4X 39X, 598 238 32 4, 14 23X 56 4, 43 265 214 2, 128 274 42X 186, 20X 278 X8 54, 71 28X 113 X9, E4 28E X 4, 8 2X2 E4 87, 92 301 246 9X, 1X0 310 12E 3X, 93 313 150 72, 104 327 830 434, 754 334 73 19, 57 366 162 49, 143 382 4X 12, 44 385 74 32, 54 392 28 2, 11 3E0 96 58, 67 415 X 4, 8 438 1X 10, 11 44X X6 63, 8X 490 72 2X, 35 494 89 46, 87 4X7 38X 256, 336 529 100 10, 80 53X 177 4X, 166 542 194 8, E 546 51 6, 17 55X 169 X7, 114 568 74 51, 6X 589 128 4X, 54 594 59 30, 57 595 E8 28, 8X 597 336 7X, 1E0 5E7 336 E4, 18X 61E 32 14, 2X 67X 2X4 40, 263 6X9 30 6, 8

### 3 k bases

 base conjectured k remain k 31 1610 7X, 8X0, 1354 5X 64E1 32E4, 5413, 605X 84 1519 301, 64X, 12X9 86 205 X2, 12X, 178 E1 1160 74, 7XX, 934 111 940 490, 81X, 864 119 187X 884, X3X, 105X 13E 212 44, 58, 124 170 7E6 138, 233, 643 189 588 304, 490, 4XX 202 82 61, 74, 77 256 E9 10, 63, E2 268 34 8, 10, 2X 2X4 E0 30, 54, 99 2E2 3X 8, 11, 15 30E 134 8, 1X, 7X 360 149 67, 7X, 98 363 7E2 278, 4X6, 6X0 388 12X 11, 63, 69 3X6 197 8, 133, 146 3E9 150 8X, E0, 14X 402 58 15, 27, 32 45E X4 2, 62, 84 4E2 68 8, 3E, 44 4E8 17X 8X, X1, 11X 52X 211 83, 113, 147 535 X8 14, 28, 78 53E 68 4, 14, 44 558 34 12, 14, 32 577 3X0 190, 316, 38X 5X2 58 11, 17, 27 608 82 17, 3X, 58 609 154 98, 106, 152 612 1E 2, 11, 15 624 137 3X, 79, 107 635 9X 52, 58, 74 64X 1E9 26, E6, 15X 666 152 34, E5, E7 669 282 136, 208, 228 66E 68 2, 2X, 58 6X0 144 X9, 114, 142 6X1 630 37X, 476, 53X

## Riesel bases

### 1 k bases

 base conjectured k remain k 6 41013 E11 X 5X80 2685 1X 26E9 2148 1E 338 298 23 570 4XX 27 65E66 28326 79 430 2E4 7X 33 25 87 806 650 91 100 70 X3 10X 20 E1 2170 652 114 133 98 117 270 192 125 24 1X 131 210 120 159 386 206 15X 38 E 165 32 28 175 12 X 176 3X 6 191 1128 10X6 1XE 1X 4 226 100 X2 229 1X 8 232 92 42 234 40 8 238 32 16 239 35X 14 23X 56 12 24E 24 1X 256 E9 5E 266 1279 1017 268 34 30 271 62 16 288 62 7 292 8 7 295 58 32 296 78 28 2X4 59 6 2X8 E8 47 2E5 5X 54 322 14 E 331 370 2E2 332 112 E5 351 122 78 354 452 49 360 149 7X 361 4E6 58 370 EX 73 385 74 62 398 11 7 399 2X 6 39E 1X X 3XE 3X 24 3E9 150 6 405 82 2 406 46 44 42X 529 176 42E 9X X 433 2X 10 437 160 6 43X 76 66 450 23 9 462 8 4 472 12 7 475 32 8 478 12 E 487 136 126 490 3X 33 494 89 9 49E 24 22 4X6 63 28 4E4 135 3E 507 186 8 50X 123 122 50E 52 2X 514 606 3X8 51E 28 12 535 X8 28 545 38 32 552 24 12 553 212 88 554 110 98 55X 169 40 568 74 8 578 11 4 579 136 X2 57E 14 8 595 E8 88 598 28 8 5XX 269 165 600 126 96 603 78 8 613 2X 20 617 230 142 620 59 54 635 108 1X 67X 126 8 687 2X0 182 688 14 4 6XE 6X 18 70E 4 2 714 69 25 715 18 8 719 88 22

### 2 k bases

 base conjectured k remain k 51 7978 56E6, 6150 94 2283 E66, 1E13 112 44 25, 38 116 1X77 1286, 1789 13E 198 150, 192 161 2868 968, 1642 162 62 45, 4E 1E5 234 32, 222 200 431 243, 365 228 8X 61, 87 241 276 32, 166 29X 415 198, 209 2X1 386 1E8, 248 304 459 116, 248 313 104 66, 9X 327 478 160, 258 355 6X 12, 48 366 162 114, 14X 384 3E9 110, 150 386 8X 25, 4E 3E0 96 33, 72 410 7X 3, 14 422 58 4X, 56 44X X6 18, 25 457 210 96, 152 477 596 200, 248 492 172 28, 78 49X 1E3 80, 1X0 4X0 200 108, 169 515 34 12, 1X 522 2X 12, 21 546 51 21, 26 550 1E9 91, X2 559 178 X0, X6 56E 58 12, 44 572 1X4 X5, 15X 57X 118 38, X8 590 100 54, 58 609 154 7X, 96 61E 32 1X, 22 657 2360 10X6, 2258 665 112 78, 94 669 282 36, 212 696 129 10, 7X 698 92 X, 27 6X4 210 3E, 79 6E7 290 190, 226 71E 38 4, 8

### 3 k bases

 base conjectured k remain k 57 19X0 8X2, 1358, 1792 5X 36X8 1040, 1336, 31E8 68 191 X, 27, 15X 124 892 163, 283, 7E0 20X 98 23, 78, 89 223 630 54, 294, 3X0 227 X72 432, 950, X56 233 4X0 32, 150, 26X 26X 383 138, 169, 299 278 X8 32, 42, 67 2X2 E4 3E, 4X, 54 2E4 59 16, 19, 38 307 100 38, 80, X0 312 62 11, 47, 56 318 4E E, 37, 44 333 526 100, 212, 2X0 358 11X 32, 45, 6X 374 7X0 230, 400, 772 37X 630 X5, 1X9, 446 412 144 82, 91, 108 421 582 210, 342, 520 460 179 19, 136, 138 500 88 18, 23, 6E 580 247 16, 95, 150 624 139 40, 80, 122 625 104 1X, 38, 7X 648 87 45, 51, 64 6X0 144 83, 9E, 13E 6X3 122 4X, 7X, 9X 6E5 814 5X, 122, 6XX