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Williams primes of the form (b-1)bn+1, remaining data

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Description

Here are all remaining data given not yet available as separate page for Williams primes of the form (b-1)bn+1 for b < 1025.

  • The highest n-value for all listed bases is n = 1000, otherwise the search range is given in brackets.

The data file can be found here.

Base n-value
111 1, 2, 8, 12, 21, 146, 161, 618, 963
112 1, 28, 948
114 3, 10, 22, 24, 45, 772, 886
115 2, 52, 81, 134, 767
116 16, 814
117 3, 99, 137, 219, 335, 392, 896
118 1, 2, 10, 29, 161, 244, 318, 352, 634, 748
119 46, 56, 88, 204
120 1, 2, 38, 40, 42, 56
124 2, 62
125 16, 26, 72, 242
126 4, 188, 209, 224, 509, 860
127 165, 183, 228, 452
129 5, 22, 148, 171
130 64
131 14, 18, 42, 172, 426, 774
132 1, 32, 39, 368
133 2, 5, 9, 14, 126
134 50, 90
135 2, 20, 424
136 279, 374
137 12, 960
138 2, 8, 81
139 1, 3, 6, 21, 22
140 2, 30, 40, 228
141 6, 16, 29, 50, 95, 314
142 1, 11, 159
143 4, 64, 438
144 1, 24, 208, 837
145 3, 11, 100, 202, 232
146 4, 16, 372
147 4, 9, 788
148 1, 2, 14, 30, 40, 281
149 2, 116
150 14
152 8, 48
153 4, 9, 170, 944
154 1, 3, 4, 914
155 6
156 1, 12, 18, 113, 119, 207, 243, 352, 588, 944
157 29, 44, 695
159 16, 21, 780
160 5, 18, 52, 95, 270
161 2, 10, 16, 54, 292
162 1, 3, 24, 227
164 20, 48, 62, 182, 514
165 1, 9, 10, 12, 40, 216, 730
166 5, 194, 576, 806
167 24
168 1
169 1, 5, 10, 107, 338
170 2, 10, 16, 180, 324, 610, 900
171 52, 80, 348
172 99
173 2, 70, 114
174 1, 3, 6, 10, 34, 78, 394, 978
175 15, 46, 101, 114, 122, 147, 648
176 4, 6, 10, 132, 594
177 1, 9, 896
178 8, 9, 50
179 46, 550, 832
181 2, 5, 16, 105, 176, 260, 286, 321, 527
182 396
183 22, 141, 189, 245, 513, 880
184 3, 8, 10, 279, 399
185 208
186 3, 6, 78, 156, 399
187 8, 17, 47, 536, 635
188 10, 52, 54, 450
189 1, 8, 17, 18, 77
190 1, 2, 4
191 2, 14, 38
192 15, 21, 41, 167, 536
193 1, 178, 886
194 2, 14
195 1, 2, 4, 8, 9, 11, 33, 111, 207, 327, 330
196 60, 856
197 520
198 4, 5, 8, 46, 316, 557, 770
199 8, 28, 45
200 60, 294
201 2, 5, 11, 39, 95
203 2, 32, 178, 190, 648
204 1, 2, 122, 597
205 2, 16, 140, 214, 276, 353, 755
206 2, 14, 414
207 1, 3, 4, 135, 220, 351
208 9, 29, 326
209 2, 4, 136, 500
210 1, 197
211 2, 4, 596
212 4
213 4, 28, 53, 172, 478, 657
214 118, 154, 456
215 2
216 1, 2, 3, 24, 30, 143
217 5, 164, 668
218 44, 80, 178, 346
219 1, 50, 63, 198
220 5, 6, 24, 30, 38, 41, 45, 65, 192, 432
221 24, 30, 202, 642, 874
222 3, 40, 44, 140, 432, 543
223 14
224 2, 4, 44
225 5, 8, 17, 32, 46, 56, 333, 563
226 2, 21, 30
227 16, 36, 276
228 24, 45, 48, 78, 225, 510
229 41, 243
230 2, 70
231 4, 6, 45, 46, 126, 282
232 1, 76, 87, 96
233 16, 52
234 10, 26, 90, 119, 290, 750
235 15, 111, 138
236 4, 62, 748
237 1, 4, 5, 81, 232
238 40
239 50, 84, 208
240 3, 5, 8, 16, 104, 114, 144, 160, 216, 614, 905
242 4, 228
243 6, 22, 57, 116
244 14, 17, 27, 34, 153
245 4, 34, 62
246 1, 3, 47, 137
247 1, 45, 197, 460
248 604
250 3, 11, 28, 99
252 11, 15, 105
253 2, 8, 16, 24, 72, 682
254 2, 152
255 4, 6, 11, 17, 88, 150, 192
258 2, 14, 132, 142, 232
259 2, 4, 28, 34, 78, 82, 384
260 2, 4, 10
261 5, 8, 112
262 4, 63
263 10
264 5, 17
265 3, 8, 12, 29, 40, 83
266 2, 42, 324, 340
267 1, 15, 17
268 6, 212
270 3, 6, 82, 102
271 12, 297, 802
273 1, 10, 20, 153, 684
274 2, 3, 29, 206, 254
275 980
276 3, 10, 14, 23, 90, 459
277 24, 57
278 2, 30, 122
279 1, 2, 18, 34, 86, 152, 179
280 1, 3, 17, 21, 36, 53
281 2, 32, 210, 524
282 276
283 14, 164, 198
284 36
285 2, 3, 5, 10, 15, 22, 52, 57, 58, 93, 298
286 2, 10
287 4, 8, 80
288 1, 12, 57, 84, 293, 320
289 1, 12, 40, 71, 514, 536
290 24, 94, 154, 200
291 1, 306
292 5, 12, 228, 240
293 44, 222, 516
294 1, 2, 8, 17, 45, 105, 238
295 6, 8, 46
296 4, 62, 264
299 4, 68, 344
300 2, 4, 6, 36
301 2, 9, 16, 51, 113, 323
302 16, 256
303 5, 28, 33, 390
304 70, 154
305 52, 378, 582
306 8, 10, 16, 18, 50, 548, 694
307 203
308 8
309 2, 4, 88
310 1, 26, 51, 302, 591
311 2, 16
312 4, 40, 220
313 4, 101, 476
314 12, 20, 84
315 1, 4, 17, 297, 896
316 5, 10, 21, 48, 69, 328
317 128, 308
318 2, 4, 14, 17, 65
319 564
320 2, 48
321 2, 3, 16, 872
322 17, 56
323 2, 12, 24, 36, 78, 126, 708
324 6, 9, 21, 27, 32, 125, 231, 777
325 2, 3
327 24
329 480
330 1, 2, 9, 15
331 4, 6, 54, 84, 722
332 112, 208
333 1, 249, 316
334 2, 20, 56, 578
335 4, 34, 42, 50, 80, 710, 836, 862
336 2, 4, 21, 22, 873
337 1, 3, 17, 75
338 272
339 10, 54, 81, 89, 99, 569
340 324
341 84, 170
343 1, 8, 12, 22, 32, 86, 609
344 2, 34
345 1, 3, 10, 26, 102, 112, 129, 822
346 4, 6, 98, 164
348 2, 4, 12, 154
349 1, 2, 12, 34, 100, 132, 642, 970
350 270
351 5, 8, 60, 203, 802
352 1, 4, 711, 921
353 2, 4, 10, 20, 170, 262
354 21, 33
355 2, 16, 27, 36
356 528
357 3
358 1, 2, 28, 68, 92
359 104
360 4, 8, 9, 12, 17, 34, 35, 92, 150, 340, 461
361 6, 9, 558, 616
364 3, 4, 5, 60, 220, 268
365 2, 92, 122, 330
366 2
367 5, 84, 123, 837
368 36, 456, 460, 504, 568, 814
369 8, 10, 11, 16, 470, 543
370 1, 2, 6, 167, 209, 454, 666
371 22, 312, 378, 862
372 3, 39, 904
373 2, 4, 5, 36, 38, 66, 144
374 52
375 6, 10, 12, 24, 219, 334, 570
376 8, 47
377 16, 96, 196
378 5, 42, 102, 244, 273, 641
379 1, 2, 142
380 2, 118, 658
381 3, 5, 16, 22, 34, 81, 105, 207, 356, 413
382 1, 273
383 4, 6, 86
384 1
385 9, 22, 98, 729, 940
386 2, 28, 66
387 4, 23
388 41
389 70, 196, 280, 490
390 2, 4, 46, 218, 335, 412, 490, 510, 574, 736, 856
391 3, 6, 42, 46, 47, 51, 84, 466, 477
392 4, 20, 64
393 1, 2, 144, 974
394 3, 369
395 2, 6, 20, 22, 242
396 1, 3, 10, 78, 196
397 44
398 56, 58, 82, 86, 248, 284
399 1, 2, 5, 24, 44, 57
400 2, 14, 318, 636, 833
401 16, 72
402 112
403 1, 129
404 2, 4, 924
405 1, 9, 16
406 1, 5, 10, 12, 14, 44, 106, 210, 255, 700, 804
407 500
408 76, 77, 269, 302
409 3, 8, 11, 16
410 42
411 2, 6, 323, 722
412 9, 11, 105, 213
413 4, 18, 22, 36
414 2, 4, 26, 50, 214
415 1, 8, 14
416 180
417 1, 93, 177
418 9, 14, 118, 442
420 10, 122, 573
421 9, 22, 26, 77
423 2, 4, 9, 38, 57, 992
424 4, 136
425 2, 6
426 3, 17, 77, 122
427 1, 71, 89
428 2, 164, 768
429 6, 69, 87, 255, 303, 602
430 3, 5, 8, 17, 80, 264
431 76
432 99, 117
433 2, 105, 148, 333, 509, 669
434 882
435 1, 3
436 1, 4, 86, 122, 170
437 108, 128
439 15, 46, 586
440 4, 28, 86, 106, 564
441 2, 102, 189
442 16, 132
443 4, 82, 754
444 2, 5, 11, 110, 526
445 3, 12, 18, 81, 480
446 2, 14, 184
447 3, 4, 21, 65, 299
448 1, 12, 34
449 14, 18, 30
450 20, 26, 143, 286, 406, 832
451 2, 4, 18
453 6
454 1, 2, 11
456 1, 5, 122, 530
457 1, 15, 64, 220, 387
458 2, 252
459 3, 4, 10, 90
460 5, 14, 94, 353, 969
461 26, 730
462 80, 159
463 10, 220
464 36, 74, 86, 144, 266, 362
465 2, 10, 17, 36, 684
466 4, 22, 40, 54, 528
467 40, 216
468 18, 42, 44, 45, 70
469 9, 10, 35, 46, 113
470 24, 140
471 263, 404
472 45, 101, 789
473 72
474 2, 27, 106, 136, 154, 198, 695
475 4, 160, 326
476 60, 924
477 1, 3, 15, 24, 65, 136
478 9, 17, 18, 461
480 15
481 5
482 4, 880
483 2, 8, 122, 146, 321, 617
484 2, 376, 728
485 20
486 4, 150
488 10, 80, 270, 740
489 2, 131, 678
490 1, 204
491 2, 74, 300, 570
492 27, 64, 171
493 5, 28, 29, 36, 148, 516
494 144, 214
495 2, 3, 63, 104, 158, 795, 831, 855, 959
496 1, 12, 28, 622
499 20, 165, 258
500 2, 4, 26, 218, 316, 600, 926
501 1, 6, 58
502 3, 12, 17, 29, 141, 344, 364
503 892
504 9, 10, 461, 965
505 2, 3, 4, 28, 36, 57, 142, 671
506 2, 6, 92, 996
507 3, 5, 99, 723
508 4, 42
509 194, 236
510 3, 16, 30, 32
511 15, 18, 30
513 1, 22
514 2, 8, 10, 75, 124
515 6, 10
516 6, 51, 275
517 8, 33
518 2, 24
519 1, 2, 3, 9, 10, 12, 180, 238, 664
520 24, 29, 59
521 8, 14, 18, 34, 60
522 105, 916
523 2, 5, 28, 34, 94, 534
524 814
525 2, 28, 142, 412, 560, 984
526 1, 10, 15, 18, 28, 124, 280
527 328
528 2, 5
529 6, 118
530 4, 8, 182, 248, 574, 824
531 1, 2, 5, 60
532 1, 11, 195, 519
533 6, 28
534 1, 147, 188, 375
535 45
537 56, 376
538 1, 6, 8, 12
539 2, 334
540 12, 290
541 1, 2, 44, 53, 117
544 10, 21, 52, 65, 153, 209
546 131, 190, 266, 291, 386
547 11, 861, 880
548 16
549 23, 107, 587
550 4, 6, 162
551 248
552 1, 27, 303
553 752
554 22, 48, 502
555 1, 5, 100, 116, 185, 726
556 6, 8, 28, 81, 243, 402
557 60
558 32, 64, 189, 590, 824
559 9, 20, 188, 304
560 2
561 1, 2, 10, 11, 24
562 5, 23, 232, 412, 488
563 6, 58, 270, 464
565 2, 3, 156, 243, 783
566 2, 38
567 1, 3
568 1, 32
569 148, 172, 710, 902
570 160
571 10
573 1, 6, 9, 46, 150
574 17, 288
575 34
576 3, 6, 12, 16, 117, 291, 484, 740, 819
577 3, 4, 35, 915
579 2, 6, 9, 16, 132
580 1, 2, 18, 77, 219
581 44, 226
582 4, 119
583 1, 2
584 2, 6
585 1, 117, 153, 231
586 2, 10, 14, 15, 105, 279, 821, 911
587 916
588 106, 140, 284, 464, 713, 884
589 4, 12, 261, 564
590 26, 94, 104, 132, 830, 966
591 10, 80, 220, 263, 268, 484
592 99, 120
594 2, 20, 33, 51, 124, 233, 694
595 11, 46, 68, 90, 538
596 370
597 15, 29
598 4, 14
600 5, 11, 122, 315, 562, 878
601 17, 44, 60, 832
603 9
604 1, 4, 41, 94
605 6, 8, 20, 30
606 1, 30
607 3, 4, 20, 108, 200, 884
608 2, 4
609 5, 41, 47, 149, 249, 335
610 1, 2, 6, 20, 60, 122, 728
611 274
612 5, 35, 45, 220
613 1, 357
614 30, 520
615 3, 5, 20, 41, 70, 72, 84, 875, 930
616 2, 6, 58, 239, 333, 916
617 16, 32, 36
618 18, 238, 572
619 2, 4, 35
620 972
621 3, 9, 10, 34, 99
622 1, 4, 11
623 2
624 18, 24, 233, 315
625 1, 4, 9, 81, 358, 516, 548
626 8, 46, 48
627 1, 9
628 8, 42, 52, 68, 597, 645, 728
629 2, 100
630 5, 10, 104, 154, 209, 350, 492, 574
631 3, 5, 141, 264
632 4, 144
633 5, 173, 240
635 74, 698
636 1, 10, 20, 45, 95, 105, 303, 536, 680, 695
637 11
638 6, 10, 30, 90, 168
639 3, 9, 27, 305
640 9, 12, 44, 59, 102, 188, 274
641 4
642 3, 4, 11, 113
643 1, 2, 24, 48, 50, 504
644 14, 18, 222, 422
645 1, 20
646 5, 8, 20, 83, 173, 753
647 24
648 6, 129
649 34, 96
650 22
651 131, 213, 449
652 71, 772
653 6, 484, 580
654 2, 5, 6, 10, 62, 566
655 142
656 236
657 4, 5, 111, 141
658 786
659 4, 22, 666
660 3, 10, 15, 17, 22, 32, 76, 107
661 237, 269
662 28
663 2, 12, 69, 170, 302, 404
664 60, 179, 282, 299, 460, 500, 537, 939
665 70
666 2, 3, 110
667 3, 23, 272
668 58, 158
669 1, 18
670 2, 9, 26, 98, 485, 648, 728
671 12, 50, 184, 280, 754
672 1, 4
673 24, 164
675 9, 60, 141, 214, 652
676 3, 15, 27, 219
677 320
678 1, 2, 20, 34
679 2, 4, 14, 149, 930
680 40
681 2, 287, 362, 491, 574, 771
682 616
683 738
684 3, 18, 20, 29, 77, 406
685 6, 24, 32, 120, 465
686 64, 380
687 1, 5, 12, 28, 196, 381, 437
688 172, 417, 701
689 4, 16
690 3
691 314
692 4, 788
693 5, 28
694 227, 990
695 2, 40, 140, 738
696 4, 130, 824
697 1, 3, 36
698 10, 48, 136, 280, 912
699 23, 86
700 23, 60, 316, 431
702 1, 9
703 6, 8
704 12, 172
705 197
706 70, 80
707 12
708 6, 18, 30
709 9, 17, 26, 112, 172, 430
710 2, 22, 28
711 21, 39, 219, 726, 909
712 4, 8
713 14
714 2, 3, 6, 10, 82, 968
715 3, 4, 8, 9, 41, 53, 93
716 8, 18, 134
717 59
718 144, 324
719 16
720 3, 18, 56, 161
721 1, 2, 3, 46, 335, 824
722 972
723 2, 38, 40, 297
724 3, 4, 5, 26, 140
725 4, 654
726 6, 15, 57, 822
727 1
728 16, 232, 264
729 1, 10, 60
730 4, 50
731 14, 72
733 5, 825
734 2, 48
735 3, 14, 18, 50, 285
736 1, 2, 32, 46, 84, 149, 310
737 12, 152, 232
738 86, 969
739 12, 18, 82, 112, 222
740 766, 906
741 4, 21
742 11, 41, 189
743 238
744 1, 34, 112, 120, 280, 587
745 71, 582, 599
746 40, 190
747 20, 48, 65, 980
748 1, 17, 94, 268, 962
749 6, 10
750 2, 8, 83, 962
751 870
752 4, 48
753 40, 160, 756
754 2, 40, 72, 100, 112, 596
755 2, 50, 234
756 1, 3, 20
759 802
760 267, 370
761 4, 8
762 1, 381
763 1, 12, 934
764 2, 392
765 2, 5, 11, 35
766 81, 117
768 65, 184
769 1, 2, 17, 95, 143, 178, 227, 400
770 116, 288
771 6, 182, 456
772 3, 677
773 2, 34, 350
774 1, 30, 136, 184, 834
775 3, 4, 11, 39, 93, 389, 924
776 6, 30, 44, 420
777 3, 296, 484, 911, 912
778 4, 34, 69, 844
780 5, 99
781 4, 12, 192, 412
783 1, 4, 6, 17, 18
784 6
785 2, 32
786 1, 6, 12, 232, 515
787 20, 45
789 2, 518
790 5, 60, 306
791 26, 60
792 12, 20, 51, 363
793 1, 8, 10, 197, 420
794 962
795 52, 370
796 9, 21, 119, 366
798 5, 6
799 1, 5, 11, 53, 550
800 12, 52, 168
801 53, 135, 431, 905
802 1
803 2, 78, 468
804 3, 35, 130, 155, 274
805 16, 18, 59
806 2, 46, 50, 724
807 36, 135, 225, 351, 468
808 2, 84, 141
809 10
811 99, 148, 184, 264, 527
812 44, 136
813 1, 18, 21
814 3, 8, 27, 47, 57, 104
815 2, 6, 30, 164, 750
816 6, 42, 249, 934
818 2, 112, 354
819 1, 2, 20, 33, 89, 137, 210
820 1, 5, 6, 8, 45, 50, 191, 453, 796
821 14, 554
822 3, 41
824 2, 184
825 5, 20, 35, 66, 94, 275
826 1, 5, 56, 364
828 1, 60, 742, 982
829 4, 26, 86, 982
831 6, 282, 341, 446
832 65, 327
833 18, 104
834 4, 8, 24, 75, 195, 694, 723
835 24, 93
837 1
838 104, 116
840 1, 12, 15, 46, 95, 112
841 12, 29, 231, 506, 540, 648, 695
842 52, 576
843 4, 9, 26
844 9, 34, 144, 202
845 10, 70, 194
846 18, 171, 284
847 1, 9, 112
848 2, 940
849 3, 16, 22, 23, 77, 279, 707
850 5, 17, 59, 119, 132
851 12, 264
852 45, 161, 200
853 2, 6, 406, 866
854 2, 22, 26, 66, 432
855 2, 87, 107
856 1, 5, 74, 144, 288
857 12, 516
858 1, 24, 264
859 2, 10, 80
860 4, 120
861 1, 2, 4, 5, 32, 146, 444, 474, 740
862 11, 176, 184
863 4, 12, 46
864 322
865 1, 9, 10
866 14
867 65, 285, 628
868 5, 16, 45, 120, 988
870 4, 11, 87, 201, 580
871 3, 20, 89
873 2, 4, 21, 22, 262, 554, 777
874 3, 45, 46, 66, 266, 624, 728
875 58, 176, 584
876 1, 3, 102
877 4, 183
878 114, 436
879 1, 33, 40, 108
880 2, 10, 22, 33, 105, 695
881 2, 600
882 3, 4, 9, 24, 396
883 2, 41, 341, 834
884 2, 36
885 4, 14, 15, 42, 78
886 33
887 32
888 5, 18, 220, 658
889 3, 34, 333, 389
891 1, 2, 3, 18, 112, 158
892 596
894 11, 17, 40
895 1, 16, 17, 110, 370
896 4, 16, 34, 260, 780
897 27, 123
898 1
899 2, 152
900 1, 3, 4, 81
901 23, 629
902 16
903 302, 728
904 3, 4, 20, 78, 80, 93, 147, 749, 999
905 4, 14, 30, 40
906 4, 93, 166, 292, 356
907 327
908 2, 96, 256, 482
909 3, 15, 29, 60
910 2, 11, 45, 52, 387
911 4, 8, 160
912 1, 36
913 36, 126, 154
914 18, 106, 120
915 3, 12, 238, 438
916 1, 39, 65, 540
917 44, 408
918 653
919 1, 4, 23, 863
920 142
921 1, 4, 118, 294
922 41
924 17, 53, 90, 95, 232
925 2, 87
926 10, 22
927 96
928 1, 90
929 28, 562
930 4, 6
931 3, 16, 70
933 4, 29, 766
934 51, 66, 436
935 84
936 26, 129, 201, 287, 723
937 56
938 12, 20, 62, 540, 696
939 15, 120, 579
940 42, 137, 244, 510
941 24, 46, 964
942 243
943 5, 170, 794
944 4, 188, 268, 350
945 36, 84
946 2, 17, 186, 545, 561
947 120
948 36, 38, 130
949 9
951 1, 3, 4, 20, 44, 108, 227, 717
952 41, 604, 808
954 2, 8, 21, 30
955 173
956 714
957 17
958 10, 520
959 10, 74, 190, 254, 324
960 1, 4, 6, 111, 674
961 1, 3, 6, 22, 44, 974
962 64
963 81, 525
964 50
965 2, 8, 400, 584
966 6, 9, 10, 11, 576
967 12, 53, 165
968 6, 64, 88
969 2, 15, 75, 216
970 1, 6, 9, 10, 240, 514
971 6, 24, 94, 600
972 15, 28, 39, 40
973 30, 40
975 1, 3, 6, 80, 664, 671, 756
976 3, 933
977 48
978 26, 46, 64
979 4, 16, 62, 81, 465
980 2, 6, 8, 24, 30, 108
981 118, 146
982 1, 4, 32, 392
983 2, 24, 26, 194
984 33, 39, 60
985 3, 10, 12, 322, 988
986 4, 102
987 8, 101, 141, 203, 261
988 1, 8, 113, 470
989 68, 310
990 3, 272
991 1, 4, 9, 34, 87, 294, 484
993 1, 14, 40, 41, 390
994 1, 3, 4, 282, 492, 562, 608
995 110
996 5, 6, 20, 46, 56, 417, 705
998 34, 694
1000 8, 10, 27, 64, 75, 107
1001 28, 34, 128
1002 1, 8, 47, 113, 129, 147, 207
1003 1, 346
1006 3, 4, 17, 27, 152, 436, 610
1008 1, 2, 21, 56, 452, 976
1009 18, 20
1010 4, 6, 114
1011 2, 4, 9, 17, 131, 723
1012 1, 4
1013 6, 8, 240, 264
1014 2, 136, 906
1015 71, 141, 372
1016 14, 58, 316, 584, 656
1017 1, 248
1018 16, 20, 22
1019 444
1020 3, 11, 90, 100, 884
1021 1, 5, 86, 206
1023 1, 494
Williams primes