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

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, 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
174	14, 21, 63, 71, 443
176	1, 18, 170
177	2, 9, 821
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

Williams primes

Main	Williams prime

Type MM: (b-1)•bn-1

Category Table (214) least n-values remaining data wanted values

Type MP: (b-1)•bn+1

Category Table (189) least n-values remaining data wanted values

Type PM: (b+1)•bn-1

Category Table (128) least n-values remaining data wanted values

Type PP: (b+1)•bn+1

Category Table (110) least n-values remaining data wanted values