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
65 3, 5, 110, 155, 900
66 1, 2, 18
68 2
69 1, 2, 5, 9, 113, 429
72 120, 170
74 2, 12, 78, 272, 798
75 1
77 1
78 1, 5, 15, 42
80 1, 24, 33, 147, 222, 225, 426
81 8, 45, 252, 282, 746
84 9, 257, 348, 429, 662
86 2
87 2, 9, 24, 276, 366, 390
89 1, 2, 3, 8, 230, 873, 927
90 1, 23, 54, 158, 800
92 2, 9, 566
95 9, 339, 515, 567
96 14, 17, 122, 689
98 3, 11, 114
99 1, 11, 30
101 1, 2, 45, 116, 321
102 5, 14, 113, 194, 314, 921
104 5, 12, 77, 252
105 1, 23, 485, 878
108 398
110 1, 3, 21, 69
111 1, 2, 5, 14, 71, 159
114 3, 9, 11, 71, 89, 192
116 44, 53, 71, 126, 161, 876
117 1, 14
119 1, 18
120 2, 9, 30, 39, 56, 72, 101, 104, 126, 488
122 2, 8, 72, 128
123 2, 389
125 2, 45, 62, 92, 860
126 5, 6, 93, 465
129 54, 134, 552
131 1, 968
132 54, 168, 488
134 9, 36, 206, 501, 846
135 17, 146, 219, 815
137 20
138 1, 23, 159, 794
140 2, 6, 27, 38, 39, 45, 165, 180, 291, 389, 584
141 1, 29, 32, 38, 77, 224, 464, 873
143 1, 2, 962
144 3, 12, 219, 278, 429
146 3, 17, 99, 197
147 1, 2, 5, 6, 24, 33, 936
149 9, 27, 53, 189, 221
150 1, 3, 507
152 2, 8, 9, 68
153 1, 3, 201, 321
155 1, 5, 15, 180, 251, 459, 476
156 3, 6, 83, 168, 362, 720
159 32, 356, 975
161 1, 408, 822
162 1, 8, 312
164 1, 132, 186, 249, 267, 291
165 5, 311
167 1, 872
168 1, 14, 546, 569
170 2, 6, 8, 17, 30, 51
171
173 1, 5, 21, 35, 41, 327, 515
174 14, 21, 63, 71, 443
176 1, 18, 170
177 2, 9, 821
179 2, 30, 33, 83, 585
180 2, 3, 51
182 5, 9, 30, 33
183 3, 11, 14, 75, 93
185 12, 21, 156
186 6, 12, 21, 39, 126, 132, 186
188 1, 14, 147
189 1, 8, 68, 198, 284, 332, 651
191 2, 56, 297
192 1, 2, 42, 866
194 1, 38, 227, 251, 512
195 2, 5, 8, 11, 14
197 18, 120, 581
198 2, 5, 14, 105, 198, 323
200 9, 35, 65, 140
203 1, 2, 6, 207, 747
204 3, 9, 21, 24, 51
206 1, 6
207 8, 17, 33, 326, 497
209 1, 2, 23, 120, 414
210 27, 56, 116, 119, 258
212 6, 8, 14, 38
213 447, 674
215 1, 8, 998
216 8, 39
218 1, 54, 366
219 2, 6, 9, 14, 15, 38, 50, 51, 110, 140
221 5, 8, 14, 27, 32, 47, 413
224 2, 23
225 30
228 5, 14, 71
230 2, 3, 24, 41, 54, 156, 221, 303, 534
231 1, 6, 9, 18, 26, 62, 144, 309
233 6
234 2, 6, 12, 15, 141, 471, 633
236 1, 3, 5, 17, 201
237 30
239 2, 128, 272
240 12, 198, 768
242 9, 14
243 2, 201, 353
245 1, 2, 3, 5, 32
246 1, 2, 8, 35, 81
248 3, 6, 230
249 17, 647
251 11, 24, 53, 414
252 53, 108, 216, 908
254 2, 24, 39, 78, 159, 363
255 2, 8, 24, 110, 140, 531
257 662, 788
258 153
260 9, 27, 39, 87, 752
261 32, 56, 327, 492, 561, 945
263 2
264 2, 35, 224, 915
266 1, 2, 3, 80, 278
267 14, 56, 146, 569
270 5, 6, 23, 26, 134, 213, 261, 497
272 1, 2, 12, 105
273 102, 222
276 12, 27, 44, 45
278 1, 14
279 1, 2, 8, 9, 17, 29, 357
281 8, 14, 26, 170, 206, 404
282 32, 42
284 2, 11
285 2, 9, 39, 992
287 1, 18, 38, 150
288 1, 5, 11, 294
290 1, 27, 32, 386
291 3, 12, 26, 33, 41, 612, 920
293 1, 11, 38, 39
294 2, 6, 14
296 24, 30, 36, 210, 303, 584
297 2, 6, 18, 74, 200, 513, 525
299 26, 225
300 24
303 21
305 6, 72, 144, 294, 386, 989
306 2, 3, 23, 51, 62
308 2, 6, 23, 89
309 1, 5, 36
311 6, 9, 68
312 2, 6, 480, 824
314 1, 5, 6, 773
315 48, 110, 378, 734
317 2, 288, 708
318 30, 75, 171
320 5, 29, 230
321 38, 122
323 2, 15, 29, 230, 578
324 3, 26, 480
326 2, 24
329 1, 2, 96, 648
330 6, 27
332 1, 38, 126, 192
333 26, 29
335 2, 3, 200
336 1, 11, 15, 201, 234
338 5, 15, 345
341 2, 8, 9
342 1, 188
344 1, 2, 9, 44, 329
345 3, 6, 8, 18, 24, 54, 83, 312, 654
347 320, 564
348 1, 53, 131, 249, 731
350 3, 12, 21, 227
351 1
353 3, 18
354 26, 63, 125, 128, 249
356 5, 8, 81, 314, 521
357 1, 2, 8, 62, 585, 641
359 2, 5, 8, 11, 59, 120, 492
360 8, 62, 978
362 200, 369
363 2, 219
365 2, 84, 339, 654
366 5, 6, 18, 41, 77, 483
368 2, 18, 113, 338
369 1, 3, 45
371 5, 42, 155
372 333, 674
374 3, 21, 51, 54, 672, 936
375 2, 3, 116
377 50, 294
378 1, 2, 6, 41, 129, 227
380 24, 74, 239
381 1, 2, 14, 30, 219, 468
383 1, 3, 69
384 2, 5, 8, 128
386 2, 60, 200, 525
387 8, 45, 242, 281
389 2, 5, 27, 345
390 32, 320
392 1, 8, 54, 744
393 17, 57
395 1, 2, 378
396 24, 132, 140, 183, 774
398 1, 2, 3, 179, 278
399 6, 8, 11, 12
401 26, 62
402 1, 6, 20, 44
404 1, 8, 9, 29, 194, 215, 245
405 1, 9, 12, 44, 231
407 2, 54, 81, 168, 173, 981
408 5, 15, 30
410 3, 8, 483
411 35
413 15
414 1, 8, 29, 80, 174
416 1, 44
417 17, 66, 68, 134, 264
419 5, 69, 102, 530
420 9
422 8, 77, 93, 842
423 6
426 1, 15, 21, 27, 356, 861, 866
428 2
429 243
431 18, 71, 810
432 2
434 1, 5, 11, 402
435 1, 125
437 8, 26, 30
438 3
440 2, 3, 9, 21, 99, 387, 893
441 12, 51, 102, 486
443 3, 9, 11, 18, 23, 65, 74, 138, 165, 435
444 12
446 20, 327
447 1, 662
449 696
450 2, 6, 20, 144, 201, 456
452 90
453 1, 2, 33
455 1, 3, 6, 21, 54
456 1, 15, 20, 53, 221
458 3, 15, 434
459 9, 14
461 2, 3, 195, 422, 507, 989
462 14, 30
464 18, 210, 903
465 12, 20, 39
467 2, 542
468 9, 51, 227, 335
470 20, 32, 72, 417, 977
471 2, 309
474 5, 333
476 1, 2, 104, 315
477 12, 41, 558
479 3
480 2, 3, 5, 33
482 2, 17, 62, 488, 504
483 3, 6, 179
485 12, 44, 158
486 38, 476, 612
488 3, 14
489 1, 3, 42, 81
491 17, 20, 21, 41, 195
492 26
494 56, 126, 212
495 1, 2, 17, 29, 899
497 5, 9, 18
498 15, 62, 131, 591
500 1, 63, 86
501 8, 36, 171, 180
503 2
504 36
506 6, 11, 198, 270, 554, 620
507 200, 528
509 20, 101, 200
510 3, 5, 9, 68, 260
513 3, 9, 69, 137, 774
515 6, 8, 27, 249
516 9, 44, 80, 219, 603
518 1, 2, 3, 150, 165
519 38, 479
521 498
522 92
524 20, 170
525 1, 9, 87
527 17, 48, 420
528 2
530 1, 2, 86, 95, 98, 345, 735
531 1, 65, 155, 377, 387, 639, 942
533 1, 255
534 6, 63, 270, 846
536 2, 260
537 1
539 6, 51
540 1, 2
543 2, 5, 41, 42, 75, 101, 837
545 11, 20
546 2, 15, 114, 200
548 21
549 8, 30
551 1, 2, 3, 140
552 36, 110, 138
554 1, 3, 5, 54, 305, 377, 974
555 2, 3, 677, 830
557 18, 270
558 11
560 1, 14, 36, 851
561 156, 455, 753
563 3, 15, 273
564 2, 14, 690
566 1, 15, 51, 68
567 1, 45, 50
569 96, 411
570 393
572 1, 41
573 50, 186
575 14, 120, 170, 347, 870
576 5, 68, 297
578 450
579 1, 15
581 11
582 1, 12, 30
584 1, 2, 6, 81
585 32, 39, 65, 390, 779, 828
587 8, 213
588 3, 53
590 2, 3, 14, 878
591 2, 36, 267, 474
593 2, 27
594 3, 45, 177
596 5, 11, 54
597 2, 29, 278, 876
599 36, 90, 110, 152, 740
600 8, 201
602 380
603 1, 161, 734
605 1, 2, 36, 360
606 2, 3
608 9, 17
609 1, 3, 6, 8, 213
611 6, 956
612 1, 9
614 11, 14, 423, 602
615 2, 41, 975
617 338, 588
618 2
620 6, 8, 12, 69, 621
621 1, 3, 5, 15, 650
623 3, 131
624 1, 6, 8, 72, 81, 92, 390, 540
626 1, 9, 20, 27, 45
627 6, 14, 161
629 8, 78, 764
630 2, 6
632 18, 48
635 1, 8
636 18, 47
638 11, 30, 65, 741
639 3, 5, 77
641 6
642 1, 21, 149, 189
644 1
645 5, 17, 77
647 504
648 114, 254, 257
650 3, 5, 41, 131, 204, 537, 575
651 2, 3, 63, 110
653 6, 50, 111
654 3, 62, 236
656 2, 17, 45, 425, 605
657 14
659 2, 23, 26, 120, 212, 408
660 261
662 50, 110, 365
663 143, 257, 573
665 5, 20, 426
666 3
668 1, 9, 14, 126
669 32
671 1, 3, 312, 608
672 21, 366
674 2
675 2, 117
677 1, 26
678 215, 438
680 2, 6, 18, 29, 41
681 12, 29, 326
684 2, 32, 95
686 1, 89, 489
687 2, 41, 98
689 2, 8
690 39, 104, 120
692 2, 528
693 11, 15, 23, 126, 698, 815
695 3, 6, 51, 438
696 1, 6, 8
698 3
699 23
701 1, 318, 392
702 9, 29, 113
704 8, 33, 320
705 38, 101, 153
707 2, 56, 197, 285
708 2, 50
711 3, 9, 224
713 2, 23, 78, 123
714 2, 24, 293, 380
716 78
720 1, 15, 282
722 8
723 6, 9, 17, 107
725 6, 12, 18
726 1, 8
728 1
729 5, 33, 54, 101, 663, 689
731 3, 15, 60, 650
732 50
734 5, 6, 18, 48, 96, 98
735 1, 8, 423
737 36, 62, 338
738 15, 87, 422, 675
740 2, 35, 177, 467, 891
741 2, 5, 86, 242, 359, 948
743 1, 5, 6, 197, 569
744 3, 11
746 2, 17
747 1, 8, 14
749 2, 14, 128, 270, 669
750 2, 869
752 2, 18, 186, 194, 393
753 2, 122
755 1, 2, 3, 12, 50, 852
756 5, 8, 69, 369
758 2, 3, 5, 6, 114
759 2, 26
761 1, 2, 15, 155, 482
762 1, 5, 8, 17
764 20, 156
765 3, 5, 110, 113, 293, 410, 890, 998
767 2, 9, 41, 516
768 1, 39, 669
770 191, 584
771 2, 6, 44, 176, 218, 494
773 1, 3
774 35, 95
776 51, 74, 527
777 2, 21, 197
779 3, 21
780 6, 21, 354
782 1, 32, 57, 188
783 2, 5
785 1, 6, 11, 27, 303
786 5, 77, 357
788 39, 42
789 248, 249
791 27, 162
792 1, 18, 86
794 30, 38, 312, 615
795 5, 23, 30, 56, 296, 915
797 21, 861
798 1, 3, 77, 165
800 8, 38, 221, 228
801 1, 39, 687
803 2, 3, 17, 303
804 6, 86
806 9, 462, 485
807 5, 156
809 5
810 2, 14, 101
812 1, 8, 176, 461
815 2, 590, 717
816 275
818 1, 2, 6, 74, 141, 245
819 1, 8, 350
821 81, 120
822 2, 6, 26, 80, 168, 360
824 8, 221
825 1, 9, 14, 492, 594, 663
827 1, 54, 56, 188, 198, 228, 353
828 3, 9
830 6, 8, 23, 458, 608
831 9, 59, 63, 716
833 17, 354, 987
834 71, 263
836 1, 2, 9, 675
837 2, 6, 54, 84, 249
839 1, 5, 23
840 29
842 69, 194
843 2, 3, 21, 30, 362
845 2
846 1, 20, 125
848 273, 569
849 9, 35, 134, 192, 581, 642
851 9, 36, 53, 284
852 8, 158, 257, 260
854 3, 14, 24, 587
855 1, 14, 431
857 1, 8, 18, 78, 188
860 1, 54, 119, 632, 732
861 2, 27, 38, 138
864 1, 6
866 2, 8, 51
867 2, 32
869 2, 11
870 3, 6, 20, 21, 41, 803
872 12, 26, 29, 138
873 5, 15, 107, 437
875 1, 6, 20, 74
876 414, 455
878 1
879 11, 177, 597, 815
881 47, 134, 171
882 5, 14
884 5, 51, 138
885 2, 138
887 5, 8, 557
890 1, 12, 14, 30, 449, 752
891 816
893 246, 273
894 1, 3
896 8, 48, 281, 488
897 1, 38
899 1, 9, 75, 174
900 2, 18, 503, 971
902 14, 24, 510, 654
903 29
905 6, 39, 204
906 6, 104
908 5
909 164, 401
911 1, 62, 84
914 12, 164
915 1, 93
917 2, 6, 8, 74, 326
918 1, 246
920 1, 9
921 137, 869
923 11, 41, 239, 413, 473
924 12, 152, 752
926 6, 9, 11, 26
927 1
930 24
932 6, 30, 281
933 2, 798, 963
935 6, 231, 269
936 62, 86, 791
938 17
939 66
941 26, 128
942 5, 14, 948
944 2, 6
945 170, 357
948 33, 75, 138
950 1
951 12, 21, 23, 36, 312
953 2, 5, 15, 63
954 2, 14, 71, 392
956 2, 3, 12, 891
957 2, 830
959 1, 3, 15, 672
960 1, 5, 162
963 357
965 17
966 6, 27
968 5, 29, 69
969 1, 8, 116, 543
971 2, 3, 9, 17
972 26, 42, 56, 89
974 1, 26, 171, 209, 611
975 2, 5, 18
977 24
978 2, 3, 41
980 17, 23
981 1, 6, 12, 18, 819
984 17
986 78, 597, 647
987 1, 2, 5, 12
989 2, 11, 15, 26, 84, 95
990 1, 3, 15
992 1, 2, 21, 278
993 1, 6, 47, 51, 113
995 6, 36, 48, 83
996 416
998 2, 6, 41
1001 1, 2, 11, 429
1002 1, 5, 176, 222, 266
1004 2, 62
1005 8, 11, 23, 44, 224, 302, 494
1007 1
1011 1, 2, 6, 27, 32, 810
1013 3, 5, 15, 38
1014 3, 6
1016 1, 201
1019 89, 627, 855
1020 1, 2, 26, 320
1022 1, 57, 672
1023 6, 59