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, 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

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