Williams prime MM remaining

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 < 2050.

• 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	2, 12, 14, 25, 33, 62, 119, 186
112	7, 43, 51, 103, 153
114	2
115	1, 3, 6, 20, 191, 193, 846
116	1, 3, 51, 91, 93, 145, 277, 855
117	2, 6, 9, 30, 45, 395, 729
118	2, 3, 27, 47, 144, 212, 218, 503, 768
119	3, 43, 281, 527, 859
120	2, 12, 47, 93, 96, 117, 162, 753
121	1, 2, 14, 161, 517
122	3, 17, 27, 417
123	6, 38, 115, 594, 734
124	33, 535
125	8739 [9000]
126	1
127	1, 2, 7, 11, 75, 149
129	2, 43, 320, 380, 480
130	8, 25, 60, 62
131	1, 15, 67, 369
132	1, 18, 25, 37, 75, 215, 249
133	2, 3, 11, 36, 151, 587, 902
134	3, 23, 59, 95, 163, 269, 387, 517
135	1, 37, 889
136	5, 37, 210, 277, 360, 864
137	25, 909
138	2, 3, 6, 11, 123, 147, 588, 870
139	1, 8, 30, 38, 120, 437
140	23, 35, 193, 993
141	1, 5, 7, 560
142	1, 13
143	7
144	2, 51, 468, 704
145	1, 5
146	1, 3, 45, 89, 333, 709
147	5, 14, 23, 62
148	3, 84, 138
149	1, 209
150	1, 8, 11, 31, 51
151	3, 5, 9, 277
152	3, 15, 55, 143, 355
153	2, 3, 6, 618
154	1, 3, 30, 31, 89, 367
155	1, 61, 77, 259
156	1, 37, 61, 74, 85
157	3
159	1, 15, 163, 351, 541, 618, 811
160	1, 2, 7, 8, 32, 50, 235, 296, 549
161	1, 7, 17, 45, 149
162	2, 6, 102, 194, 215, 337, 513
163	14, 211, 479
164	1, 3, 105, 181, 365
165	1, 19, 24, 120, 143, 505, 793
166	3, 5, 11, 37
167	3, 39, 57, 69, 101
168	3, 7, 11, 134
169	3, 33, 47, 72, 75, 632
170	1, 145
171	2, 53, 62
172	1, 11, 258, 519
173	23
174	2, 7, 23, 161, 505
175	1, 2, 9, 380, 758
176	23, 681
177	1, 86, 311
178	6, 62
179	15, 809
180	233, 313
181	1, 5, 39, 45, 145
182	1, 115, 409, 485, 559, 799
183	7, 516, 680, 807
184	83, 169
185	1, 11, 55
186	2, 17, 65
187	1, 2, 7, 42, 111
189	1, 12, 139, 738
190	7, 8, 33, 87, 140, 179, 193, 217
191	263
192	1, 19, 39, 41
193	3, 887
194	1, 5, 7, 607
195	2, 27, 32, 105, 476, 942
196	1, 12, 18, 978
197	1, 3, 7, 11, 51
198	55
199	2, 5, 7, 11, 50, 107, 464, 644, 911
200	1, 15, 19
201	43
202	2, 18
203	3, 271
204	1, 2, 5, 6, 18, 47, 505, 787
205	8
206	9, 15, 23, 35, 59, 99, 103
207	1, 3, 11
208	3, 107, 671
209	9, 13, 81, 191, 201, 541
210	1, 3, 7, 25, 557, 779
211	23, 365, 596
212	23, 53, 131, 643
213	20
214	8, 13, 59, 110, 216
215	95, 349
216	1, 25, 455
217	5, 55, 169, 626
218	11, 103, 539
219	1, 37
220	1, 2, 15, 20, 31, 43, 91, 545, 763
221	1, 15, 25, 41, 87
222	2, 11, 39
223	2, 11, 14, 51, 539
224	3, 13, 47, 137
225	6, 266
226	1, 17, 127
227	515
228	3695 [5000]
229	5, 23, 138, 295
230	73, 159
231	1, 2, 3, 134, 331, 344
232	1, 7, 9, 13, 21, 41, 137, 393, 527
234	1, 23, 43, 181
235	63
236	5, 19, 59, 351, 581
237	1, 27
238	12, 284
239	3, 67, 89, 107, 915
240	5, 47, 113, 433
241	1, 6, 13, 14, 913
242	1, 3, 63, 983
243	2, 3, 6, 38, 395
244	3, 24, 83, 99, 209, 866
245	1, 831
246	2, 15, 49, 132, 557
247	1, 53, 119
248	3, 11
249	1, 7, 69, 265, 401
250	8, 482
251	79
252	2, 3, 6, 150, 198, 806, 915
253	23, 66, 71, 655
254	541
255	25, 27, 68, 87, 175, 197, 403, 417, 499, 591
257	13, 37, 89
258	15, 126
259	1, 20, 25, 41, 753, 810
260	1, 17, 45, 81, 227, 677, 977
261	17
262	123, 134
263	75
264	1, 6, 9, 15, 24, 54, 135
265	1, 2, 3, 83
266	1, 181, 253, 611
267	11, 26, 818
269	1, 9, 91, 383
270	8, 9, 13, 48, 139, 237, 257, 333, 645, 909
271	89, 95
272	3, 257, 837
273	2, 3, 7, 48, 359
274	57, 793
275	349
276	2, 3, 9, 61, 78, 258, 267, 955
277	5, 23, 42, 873
278	7, 15, 963
279	2, 199, 673
280	3, 75, 96, 663
281	79
282	1, 14, 85
283	768
284	7, 19, 73, 103, 117, 419, 433, 507, 587
285	3, 21, 543, 870, 906
286	1, 6, 7, 13, 15, 144, 258, 582
287	247
288	3, 311
289	1, 7, 11, 275, 464
290	373
291	1, 5, 23, 60, 230, 236
292	6
294	14, 23, 50, 57, 60, 743
295	1, 2, 6, 7, 36, 50, 97, 366, 455
296	7, 391
297	1, 13, 17, 270, 643, 735
298	2, 32, 50, 906
299	1, 5, 9, 123, 445, 573
300	9, 15, 51, 53, 227
301	7, 9, 18, 57, 67, 434
302	1, 99, 111
303	2, 343, 451
304	1, 362, 564
305	17, 65, 155, 249, 515, 913
306	1, 3, 43, 114, 135, 194, 203, 333, 668
307	1, 2, 5, 62, 93, 578, 938
308	47
309	3, 7, 9, 20, 35, 39, 80, 463
310	1, 119, 503
311	17, 19, 139, 351, 443, 585
312	3, 7
313	8, 44, 464, 651
314	3, 51, 65, 77, 515, 919
315	1, 5, 9, 41
316	29, 177
317	5, 37, 85
318	12, 19, 20, 103, 203, 863
319	96, 260
320	1, 7, 27, 53, 87, 909
321	97, 121, 385, 467, 603, 656
322	23, 173, 303, 383
323	15, 475
324	1
325	3, 447
326	5, 9, 17, 69
327	5, 33, 110, 366, 438, 858
328	2, 6, 18, 56, 776
329	17, 51, 55, 199
330	134
331	1, 7, 19, 20, 77, 85
332	1, 7, 9, 39
333	204
334	2, 3, 5, 73, 80, 92, 113, 272, 447
335	3, 9, 21, 49, 71
336	1, 37, 312, 450, 615
337	14, 398
338	407
339	3, 7, 9, 19, 65, 67, 79, 114, 176, 223, 278, 540
340	1, 2, 11, 33, 42, 253, 531
341	33, 131, 241
342	2, 62, 177, 301
343	31, 87
344	1
345	2
346	3, 8, 15, 25, 29, 159, 211, 515
347	4461 [5000]
348	2, 6, 14, 35, 194, 336
349	42, 44, 77
350	1, 5, 21, 75, 205, 353
351	1, 14, 271, 551
352	1, 5, 25, 55, 977
353	3, 203, 675
354	3, 8, 493, 662, 674
355	1, 7, 439, 543, 974
356	9, 765
357	1319 [1400]
358	23, 79, 147
359	1, 119
360	5, 20
361	1, 2, 14, 42, 152, 527, 769
362	1, 3, 75, 147, 211, 651
363	3, 8, 42, 68, 111
364	23, 78, 390, 847, 901
365	1, 43, 127
366	2
367	14, 530
368	3, 31
369	56, 929
370	5, 18, 225, 530, 570, 701
371	517
372	2, 6, 353, 389, 459
373	223, 926
374	1, 53, 943
375	1, 3, 24, 227, 361, 504
376	2, 3, 6, 327
377	5, 11, 91, 111, 381, 547, 733
378	2, 7
379	1, 3, 5, 9, 14, 19, 31, 54, 71, 133, 151, 869, 875
380	19, 29, 115
381	1, 2, 331
382	15, 105, 319, 343
384	104, 831
385	5, 54, 85, 105, 137
386	1, 495, 603
387	1, 13, 31
388	6, 260
389	9, 169
390	3, 6, 14, 113, 450, 788
391	3, 8, 23, 25, 27, 141, 260, 575
392	1
393	2, 26, 36, 115, 167, 507
394	1, 326, 956
395	3, 23, 151
396	1, 17, 287
397	1, 2, 3, 6, 66
398	63, 139
399	9, 11, 29, 81, 116
400	2, 7
402	1, 19, 62, 158, 421
403	2, 15
404	7, 15
405	3, 21
406	1, 2, 17, 191, 288, 331, 495
407	3, 25, 43, 67, 103, 117, 179, 335, 639
408	7, 575
409	1, 2, 18, 205, 217
410	3, 7, 11, 13, 21, 75, 103
411	9, 572
412	18, 38
413	87, 179
414	31, 61, 89, 116, 219, 258
415	23, 344, 602
416	521
418	2, 6, 8
419	1, 3, 15, 237
420	1, 3, 9, 11, 15, 55, 96
421	1, 8
422	335, 997
423	23, 24, 38
424	1, 2, 3, 5, 6, 177, 407, 498
425	9
426	2, 3, 12, 457, 920
427	7, 11, 29, 54, 93
428	19
429	1, 2, 122
430	18, 23, 35, 47, 61, 77, 629
431	247
432	1, 2, 117, 138, 597
433	3, 54
434	1, 53
435	2, 6, 19, 81
436	2, 8, 116
437	5, 9, 105, 143
438	3, 8, 15, 71
439	5, 6, 17
440	79, 183, 813
441	5, 8
442	3, 7, 71, 133
443	1691 [2000]
444	33, 54, 239, 323
445	6, 11, 56, 99, 251, 511
446	1, 21, 119
447	2, 7, 15, 54, 75, 199, 459
448	427, 876
449	1, 289, 395, 553, 589
450	1, 2, 301
451	1, 8, 15, 32, 98, 812
452	7, 221, 697, 841
453	104
454	1, 11, 12, 755
455	5, 223
456	1, 6, 15, 29
457	1, 13, 17, 71, 121, 197, 206
459	2, 20, 24, 32, 44
460	2, 13, 74, 128, 139, 158
461	17, 57, 65, 121, 905
462	1, 3, 14, 59, 259
463	2, 11, 18, 27
464	1, 5, 25, 35, 53
465	2, 7, 8, 15, 115, 153, 186, 345
466	9
467	3, 339, 613
468	2, 26, 776
469	1, 85, 126, 164, 398
470	9, 19, 159
471	2, 17, 53, 85
472	1, 2, 191
473	3
474	1, 5, 12, 90, 318, 794
475	1, 3, 578, 597
476	1, 3, 233, 677
477	165
479	1, 3, 5, 33
480	2, 8, 9, 624
481	7, 9, 35, 37
482	1, 157, 283, 857
483	6, 7, 38, 119, 254
484	41, 468
485	13
486	3, 31, 289, 291, 407, 527
487	1, 17
489	86, 123
490	3, 575
501	1, 30, 93, 119
502	1, 15, 125
503	3
504	2, 5, 7, 15, 72, 137, 320
505	1, 7, 25, 36, 967
506	19, 31, 89
507	1, 9, 93, 237
508	2, 144, 272
509	9, 11, 47, 63, 119
510	2, 15, 120
511	1, 60
513	14
514	43, 85, 175, 525
515	3, 75, 315
516	1, 3, 35, 36, 327, 456
517	9, 121
519	1, 7, 45, 133
520	1, 2, 5, 11, 49
521	23, 33, 159
522	3, 6, 49, 78, 79, 135, 395
523	18, 139, 391, 679, 680
524	15, 195, 561
525	2, 3, 5, 7, 17, 83, 114
526	2, 77, 116, 176
528	3, 38
529	1, 67
530	103
531	1, 5, 13, 31
532	23, 277, 685
534	2450 [3000]
535	2, 51
536	53
537	23, 33, 43, 81, 263
538	3, 7, 239
539	7, 9, 11, 129
540	15, 33, 108
541	2, 55, 98
542	1, 3, 117, 223, 243
543	12, 312
544	5, 6, 43, 150, 284
545	1
546	11, 51
547	13, 29, 95, 117
548	7
549	1, 2, 8, 25, 87, 115, 205, 224
550	1, 33, 38, 105
551	1, 5, 39, 969
552	1, 7, 9
553	20, 26, 391, 711, 735, 986
555	23
556	2, 20, 511, 518
557	1445, 2167 [2500]
558	2, 7, 19, 323, 330
559	3, 42, 43, 121, 143
560	81
561	1, 5, 11, 18, 57, 74, 489
562	1, 5, 11, 19, 61
563	67, 103
564	6, 8, 247, 769
565	2, 14, 32, 55, 264
566	85
567	2, 3, 33
568	6, 7, 11
569	29
570	1, 17, 23, 36, 53
571	7, 23, 422
572	1, 61, 145
573	75, 198, 470
574	1, 3, 6, 71, 75, 327, 407, 455
575	5
576	259
577	243
578	11, 223
579	1, 30, 240
580	86, 306, 955
581	23, 59, 385
582	1, 2, 5, 9, 26, 71, 135, 145, 209, 227
583	332, 560, 668
584	57, 173, 371
585	11, 17, 129, 368, 606
586	11, 19, 87, 553
587	29, 39, 55
588	3
589	1, 1125 [1500]
590	1, 19
591	14, 573, 919
592	1, 3, 75, 918
593	7
594	2, 231, 266, 403, 503, 738
595	1, 2, 3, 5, 25, 27, 524
596	1, 11, 13, 33, 451
597	1, 2, 5, 59, 161, 913
598	3, 90
599	1, 3, 281
600	3, 37, 447, 453, 698
601	6
603	3, 6
604	7
605	1, 7, 19, 43, 51
606	3, 9, 377, 656
607	1, 2, 9, 426
609	33
610	3, 221, 551, 983
611	1, 457, 703
612	2, 7, 27
613	2, 8, 83, 678
614	113
615	3, 6, 101, 122, 133, 152, 273, 560
616	9, 15, 26, 38, 479
617	1, 11, 271, 549
618	59, 347, 776
619	1, 11, 15, 17, 55, 169, 297, 895
620	23, 49, 189
621	5, 6, 24
622	3899 [4000]
623	7, 31
624	7, 163, 320
625	1, 2, 89, 98, 199
626	1, 1005 [1500]
627	73, 470
628	15, 48, 90
629	17
630	1, 7, 25, 66
631	9, 18, 20, 35, 95, 117, 179
632	239, 385
633	38, 102
634	1, 2, 26, 285
635	9, 193
636	2, 47, 93, 587, 822
637	9, 27, 33, 125, 131
639	59
640	1, 3, 6, 114, 243, 595, 786
641	1, 3
642	45
643	126, 738
644	9, 33, 123
645	1, 24, 87, 96, 101, 176, 367
646	7, 14, 25, 343
647	1, 5, 65, 123, 437, 473
648	131, 427
649	1, 3
650	3, 5, 19, 37, 79, 189, 359, 581, 939
651	2, 42, 57, 77, 177, 653
652	1, 163, 486
653	3127 [4000]
654	3, 11, 24, 55
655	1, 9, 157
656	1, 25
657	9, 103, 333, 433, 535
658	31
659	3, 7, 39
660	1, 2, 8, 31, 53, 127
661	3, 8, 45, 164, 299, 300
662	13, 19, 65, 433, 955
664	15, 37, 117, 897
666	3, 5, 96, 188, 825
667	2, 7, 50
668	287
669	1, 7, 61, 215, 584
670	14, 30, 56, 306, 648
671	1, 811
672	9, 13, 73, 506, 613
673	24, 174, 296
674	1, 175
675	9
676	8, 15, 23
677	1, 25, 219, 233
678	14, 38, 68
679	3, 14, 39, 49, 134
680	43
681	11, 73, 77, 139, 395
682	2, 11, 223
683	35
684	1, 19, 36, 296, 379, 392
685	3, 14, 18, 83
686	47
687	1, 6
688	2
689	5
690	2, 32, 577, 725, 780
691	5
692	1
693	11, 23, 492
694	1, 2, 24, 56, 169, 362, 391, 573
695	5, 11, 17, 505, 763
696	1, 2, 3, 578, 969
697	19
699	5, 7, 108
700	1, 5, 27, 35, 516, 667
701	2257, 2313 [3000]
702	2, 5, 737
703	2, 14
704	13, 145, 155, 167
705	2, 3, 8, 12, 133, 499, 674, 843
706	1, 4735 [5000]
707	1, 9, 255, 825, 845
708	18, 35, 62
709	1, 19, 116
710	1, 21, 373, 537, 543
711	2, 18, 158, 264, 297, 625
712	5, 23, 69, 114, 925, 965
713	7
714	5, 12, 23, 43, 71, 156, 159, 164, 369
715	3, 8, 23, 39, 57, 67, 101, 186, 254, 889
716	1, 7
717	1, 3, 111, 522
718	14, 210, 519
719	1199 [1500]
720	13, 26, 126
721	1, 2, 126
722	27
723	24535 [82000]
724	11, 335
725	1, 3, 45, 237
726	25, 44, 68, 380, 579
727	7, 65, 75, 185, 218
728	3, 411
729	1, 2, 6, 8, 125, 229, 293
730	97, 169, 913
731	83
732	2, 23, 839, 959
733	2, 122
734	5, 17, 237
735	3, 8, 55
736	2, 3, 14, 19, 72, 150
737	1409 [2000]
738	2, 3492 [4000]
739	6, 21, 53, 569
740	1, 5, 135, 137, 553, 745
741	8
742	35, 86
743	3, 15, 195
744	1, 2, 14, 217, 350, 686
745	2, 5, 8, 62, 206, 438
746	13
747	1, 5
748	51
749	3
750	9, 19, 35, 79, 141, 147, 383, 645, 683
751	1, 23, 25, 223
752	3, 257
753	15
754	1, 3, 29
755	1, 15, 27, 245
756	15, 78, 155, 158
757	337
759	2, 25, 38, 77, 92, 337, 354, 423
760	6, 31, 54, 213, 294
761	45
762	1, 2, 39, 199
763	2, 24, 195, 320, 482
764	1
765	13, 32, 80, 367, 427
766	1, 2, 32, 174, 349, 617, 816
767	9, 37, 213, 269
768	20, 23, 164
769	8, 14, 47, 98, 205, 415, 667
770	1, 9, 11, 39, 605
771	7, 38, 45, 103, 151, 528
772	14
773	23, 163, 187
774	14, 253, 332, 528
775	9, 56, 65, 265, 288, 309, 348, 450, 589
776	7, 13
777	1, 4998 [5000]
778	12, 607
780	1, 2, 150, 626
781	1, 3, 35, 66, 84, 407
782	1, 3
783	6, 8, 31, 122, 295
784	3, 17
785	8993 [9000]
786	113
787	1, 2, 3, 55
788	15
789	2, 1316 [1500]
790	2, 3, 5, 13, 19, 50, 121, 189, 302, 409
791	5, 45
792	2, 6
793	14, 959
794	5
795	1, 5, 78
796	2, 13, 33, 279
797	5
798	2, 11, 32, 246, 287, 360
799	1, 45
800	817
801	6, 26, 143, 758
802	15, 575, 869
803	7, 295
804	1, 3, 8, 11, 41, 135, 431
805	1, 2, 19, 223, 247, 265, 434, 446
806	1983 [2000]
807	23, 413
808	6, 138
809	37, 41
810	1, 2, 14, 26, 31, 39, 81, 95, 764
811	6, 17
812	2327 [3000]
813	14, 35
814	1154 [1500]
815	1, 1473 [1500]
816	1, 3, 8, 75
817	1, 71, 102, 443
818	3, 7, 67, 775
819	265
820	529
821	317
822	3, 9, 62, 107
823	8, 38, 50, 290, 455, 998
824	41, 81, 295
825	26, 66, 837
826	1, 95
827	211, 227
828	8, 155, 215, 851
829	38, 140, 165, 242, 459, 792
830	3, 29
831	2, 69, 108, 612, 815
832	2, 11, 207, 350
834	1, 2, 18, 201, 297
835	2, 23, 62, 433
836	13, 87, 159, 279, 417
837	7, 13, 33, 51, 62
838	42, 78
839	1, 49
840	5, 104
841	11, 26, 56, 213, 246
842	47, 53
843	6, 7, 31, 36, 471
844	2, 8, 9, 79, 168, 492, 505
845	57, 225, 377
846	1, 2, 7, 79, 176, 941
847	21, 109, 402
848	583
849	1, 2, 7
850	23, 78, 110, 881
851	967
852	21, 158, 163
853	8, 872
854	49, 201
855	2, 89
856	8, 11, 20, 235
857	1, 25, 27, 65
858	24, 71, 80
859	2, 13
860	15, 51
861	19, 311
862	2, 18, 153, 695
864	1, 5, 6, 210, 549
865	2, 38, 67, 167, 265, 450, 500
866	1045, 2189, 14337 [20000]
867	11, 26, 27, 50, 265, 607, 685
868	8, 30, 55
869	3, 5, 31, 51
870	11, 62, 239, 314
871	2, 35, 128, 333, 407, 629
872	27, 51
873	3, 7, 8, 19, 79, 690
874	1, 45, 209, 485, 708
875	3, 7, 15, 121, 421
876	12, 17, 150, 174
877	2, 146
879	7, 198
880	32, 767, 781
881	3
882	1, 3, 59, 697, 875
883	306
884	37, 49, 149, 205, 299
885	1, 3, 5, 8, 401
886	1, 5, 73, 143, 467
887	2009, 2315 [3000]
888	6, 66
889	311, 342
890	1, 29
891	1
892	25, 30, 137
893	31
894	109, 303
895	977
896	55
897	3, 5, 45, 50, 57, 366
898	2, 14, 674, 986
899	3
900	108, 470, 561
901	31
902	1, 19
903	2, 2738 [3000]
904	13429 [20000]
905	19, 527
906	13, 23
907	1, 3
908	11
909	552
910	6, 13, 223, 749
911	3, 5, 11, 21, 23, 317
912	701
913	3, 8, 12, 95, 271, 762
914	23, 171, 901, 975
915	2, 25, 113, 241
916	1, 3888 [4000]
917	69
919	20
920	637
921	5, 13, 63, 363, 663
922	1, 3, 15, 45, 405
923	131
924	1, 2, 9, 15, 120, 313
925	2, 17, 23, 63, 255
926	1, 85, 157
927	21
928	12, 92
929	13, 803
930	3, 9, 27, 43, 519, 619
931	1, 2, 21, 32, 50, 114, 397
933	2, 152
934	56, 260, 296
935	51, 245
936	15, 29
937	7, 131
939	5
940	1, 8, 35, 73
942	1, 2, 25, 30
943	36
944	9, 73, 943
945	1, 3, 57, 450, 711
946	2, 3, 7, 9, 30
947	1, 31
948	2, 3, 119, 271, 487, 515
949	5, 7, 8, 27, 43, 54, 171
951	1, 6, 25, 51
952	7, 26, 81
953	7, 67
954	25, 277
955	14, 25, 29
956	1, 97, 457
957	1, 9, 17, 31, 103, 997
958	6, 74, 199
959	7, 9, 63
960	7, 18, 126
961	2, 110
962	3, 15, 109
963	7, 18
964	1, 42, 78, 282, 651
965	23, 57
966	1, 2, 6, 18, 81, 128, 199, 657
967	1, 15, 31, 99
968	79
969	1, 6, 23, 635
970	2, 105, 203
971	897
972	3, 9, 38, 42
973	60
974	119
975	1, 7, 8, 26
976	2, 8, 38, 197
977	1, 33, 265
978	26, 56, 114, 116, 140
979	3, 5, 11, 31, 840
980	45
981	2, 5, 23, 564, 762
982	1, 2485 [3000]
983	3
984	8, 169, 224, 786
985	1, 2, 7, 11, 25, 49
986	47, 81, 147
987	2, 7
988	3, 63
989	7, 211, 613
990	1, 2, 7, 189, 639, 644, 683
991	12, 120
992	3, 7, 87
993	2, 12, 66
994	38, 54
995	1, 15, 183, 381, 825, 895, 903
996	5, 143
997	1, 5, 174, 579, 786
998	3, 43
999	1, 3, 6, 8, 43, 56, 95, 103
1000	2, 39, 174, 217, 495
1001	1, 19, 67
1002	1, 9, 693
1003	251
1004	3, 71, 81
1005	3, 138, 673, 687
1006	1, 9, 21, 93, 103, 410
1007	1, 43, 57
1008	4091, 4566 [5000]
1009	2, 17, 44, 95, 105
1011	14, 25, 203, 350, 680
1013	43, 115, 451, 511
1014	1, 17, 19, 25, 26
1015	1, 3, 18, 25, 977
1016	1307 [1500]
1017	1, 301
1018	38, 72, 500, 986
1019	47, 147
1020	7, 8, 348, 446, 457
1021	12, 33, 543
1022	5, 779
1023	6, 71, 90
1025	1, 123, 127
1026	1, 51, 97, 147, 290, 362, 698
1027	2, 14, 77
1028	2491 [28600]
1029	5, 63, 116
1030	636
1031	707
1032	14, 43, 467
1033	14, 103, 720, 991
1035	1, 2, 3, 6, 19, 48, 90, 353, 359, 445, 795
1036	2, 59, 288
1037	7, 9, 947
1038	607
1039	5, 9, 251, 275
1040	1, 9, 51, 141
1041	24, 25, 30, 296
1042	3, 5, 265
1043	15, 27
1044	2, 5, 23, 25, 59
1045	1, 5, 8, 37, 41, 103, 197
1046	1
1047	1, 7, 9, 829
1048	2, 6, 32, 36, 90, 131, 422
1049	3, 67, 889
1050	149, 444, 816
1051	1, 5, 9
1052	1
1053	2
1054	1, 3, 12, 29, 32, 153
1055	3, 5, 9, 35, 55, 159
1056	126, 361
1057	5
1058	187, 507
1059	2, 14, 29, 155, 236, 314
1060	50
1061	1, 11, 171, 645
1062	1, 31, 99
1063	6, 26
1064	9
1065	1, 87, 133, 157, 857
1066	7, 8, 359
1067	51, 439, 771
1068	98, 231
1069	6, 86, 182
1070	1, 25, 507, 727
1071	9, 13, 145, 384, 589
1072	1, 81, 985
1073	155, 199, 575
1074	59, 272
1075	150
1076	1, 9, 21, 51, 665
1077	3, 9, 11, 63, 763
1078	24, 348, 399, 926
1079	129
1080	2159 [2170]
1081	3
1082	35, 39, 99
1083	3, 6
1084	681
1085	9, 21
1086	8, 12, 36, 39, 49, 92, 97, 152, 602
1087	17
1089	3, 5, 15, 171
1090	1, 3, 13, 21, 23, 31, 45
1091	1, 7, 13, 15, 35, 145, 375
1092	21, 59, 131, 553
1093	3128, 3710 [5000]
1094	1, 11, 511, 575
1095	1, 7, 73, 590, 750, 805
1096	18, 36
1097	965
1098	20, 116, 144
1099	1, 2, 3, 12, 25, 33, 69, 259, 525
1100	7, 39
1101	13, 14, 25, 38
1102	1, 2, 39, 45, 543, 855
1103	39, 71
1104	9, 43, 143, 147
1105	1, 5, 105, 379
1106	1, 3, 5, 7, 129
1107	9, 42, 539
1109	3, 45
1110	3, 14, 15, 422
1111	1, 7
1112	1, 43, 199
1113	14, 35, 126, 392
1114	13, 14, 55, 60, 189
1116	8, 93
1117	2, 9, 17, 33
1118	199
1119	15, 43
1120	1, 2, 31, 81, 115, 158, 702
1121	1, 3, 137, 181
1122	2, 13
1123	2, 3, 6
1124	7, 57, 143, 493
1125	1, 27, 367, 438
1126	23, 38, 300
1127	1
1128	2, 79, 131, 206, 342
1129	20, 529
1130	5, 9, 163, 975
1131	1, 2, 5, 303
1132	1, 15, 127, 182
1133	3
1134	2, 3, 5, 17, 23, 216
1135	12, 23, 266
1136	29, 151, 155, 455
1137	245, 263
1138	30
1139	1, 11, 15, 47, 79
1140	2, 5, 194, 629, 747
1141	164, 327, 329, 985
1143	7, 8
1144	1, 87, 414
1146	1, 9
1147	2, 71
1148	119, 199
1149	38, 113
1150	1, 17, 287, 883
1151	1, 7, 345
1152	7, 9, 69
1153	3, 107, 948
1154	3
1155	6, 9, 35
1156	15, 77, 163, 225, 410
1157	1295 [1500]
1158	3, 31, 260, 467
1159	3, 247
1161	17, 25, 33, 181, 192, 302
1162	25, 30
1165	1, 8, 161
1166	35, 185, 801
1167	185, 429
1168	12, 19, 888
1169	15, 43
1170	20, 25, 39, 192
1171	1
1172	1, 13, 255, 283, 335, 343
1173	6, 107
1174	13, 229, 324
1175	1, 51, 119
1176	8, 44, 151
1177	3, 351, 877
1178	11
1179	7, 227
1180	7, 9, 26
1181	5, 43
1182	5
1183	2, 8, 11, 351
1184	5
1185	2, 247, 278
1186	2, 6, 60
1187	47, 111, 167, 441, 521
1188	6, 12, 174, 659
1189	9, 24, 78, 96, 620
1190	111, 491, 891
1191	30, 41
1192	5, 37, 49, 55, 98
1193	291
1194	1, 8, 21, 36, 491
1195	6, 62, 96, 168, 301
1196	3, 25, 67, 93
1197	15
1198	3, 6, 175
1200	300, 387
1201	1, 2, 3, 6, 114, 211
1202	5, 211
1203	8, 12, 24, 199
1204	1, 8, 84, 113, 205, 655
1205	1, 13, 15, 709
1206	7, 800
1207	3, 13
1208	803
1209	3, 5, 6
1210	3, 6, 53, 55, 227, 801
1211	19
1212	13
1213	38, 146, 199
1214	1689 [2000]
1215	9
1216	20, 42, 578, 752
1217	1
1218	703
1219	1, 6, 67
1220	1
1221	3, 15, 17, 458
1222	6, 42, 54
1223	247
1224	3, 7, 17, 19, 366, 548, 809
1225	27, 37, 147, 207, 354
1226	1, 51, 81, 191, 283
1227	7, 47, 293, 733, 925
1228	38, 78
1229	3
1230	1, 17, 26, 71, 776, 863
1231	236, 327, 395, 749
1232	1, 3, 69, 115, 157
1233	15, 31
1234	2329 [3000]
1235	3, 41, 45, 89
1236	290
1237	50, 175, 345
1238	3, 7
1239	1, 2, 8, 15, 211
1240	27, 126, 459, 806
1241	1
1242	3, 61, 83
1243	67, 548
1244	1, 3, 5, 43, 79
1245	1, 9, 19, 32, 161, 986
1246	1, 15, 43, 66, 264
1247	3, 13, 29, 35
1248	8, 68
1249	38, 51
1250	2709 [3000]
1251	96
1252	1, 6, 39, 503
1254	6, 72
1255	278
1256	119, 493
1257	75, 171, 806
1258	7
1259	141
1260	1, 89, 140
1261	1, 7, 519
1262	35
1263	2, 102, 143, 254
1264	2, 17, 19, 74, 147
1265	9
1266	1, 2, 6, 20, 194, 548, 731
1267	1, 6, 657
1269	2, 23, 49
1270	5, 21, 145
1271	3, 7, 17
1272	1, 9, 11, 18, 54, 81
1273	24, 227
1274	3, 9, 73, 81
1275	1, 2, 6, 12, 19, 111, 187, 917
1276	3212 [4000]
1277	1, 7, 189
1278	3, 36, 251
1279	2, 7, 23, 407
1280	2023 [2070]
1281	9, 11, 18
1282	107, 207, 265
1284	5, 12
1285	8, 645
1286	1, 17, 143
1287	362
1288	128, 131
1289	1, 39, 307
1291	3, 5, 17, 18, 33, 50
1292	23, 475
1293	2, 11, 67, 835
1294	2, 37, 39
1295	3, 25
1296	1, 11, 199, 231
1297	13
1298	43
1299	6, 20, 87, 158, 501
1300	2, 3, 5, 6, 749
1301	21, 37, 193
1302	18, 235, 315
1303	8, 15
1304	1, 7, 937
1305	1, 21, 317, 480, 690
1306	9, 17, 36, 113
1307	3, 23, 43, 639
1308	24, 475
1309	1
1310	1, 21, 567, 851
1311	101
1312	1, 3, 303, 774
1313	555, 783
1314	21, 39
1315	638
1316	61, 75, 237
1317	2, 3, 6, 7, 39, 86
1318	2, 326, 410
1319	59, 727
1320	1, 87, 387, 476
1321	9, 14, 37, 434
1322	5, 15
1323	2, 11, 18, 116, 150
1324	29, 435, 449
1325	5
1326	99
1327	9, 21, 462
1329	6, 12, 14, 23, 61
1330	1, 11, 39, 306
1331	169, 409
1332	50
1333	36, 55
1334	1, 5, 13, 21, 41, 79
1335	8, 29
1336	71
1337	3, 115, 535, 969
1338	3255 [3280]
1339	13, 110, 613
1340	1403 [1500]
1341	2, 119, 201
1342	1, 5, 30, 33, 193
1343	7, 263
1344	1, 19, 63
1345	5, 6, 60, 918
1346	23, 179
1347	6, 210
1348	3, 7, 8, 11, 27
1349	1, 111
1350	45, 324
1351	1, 9
1352	15
1354	3, 5, 6, 344, 975
1355	1, 7, 55, 309
1356	1, 2, 8, 14, 25, 68, 73, 150, 182, 770
1357	373, 877
1358	11
1359	1, 13, 119, 721, 873
1360	3764 [4000]
1361	11657 [12000]
1362	2, 14, 29, 39, 57, 217, 953
1363	6, 104
1364	6717 [10000]
1365	1, 44, 459
1366	1, 91
1367	1, 5, 103
1368	39, 50
1369	6, 14, 81, 126, 473, 986
1370	1, 5, 7, 81
1371	49, 122
1372	14, 50
1373	3, 11
1374	23
1375	11, 15, 26, 42, 43, 56, 72, 261
1376	7, 177, 251
1377	38, 57, 79
1378	6
1379	17
1380	56, 86
1381	1, 5, 50, 68, 85, 140
1382	2789 [3000]
1383	6, 203, 242
1384	6, 12, 168, 191
1385	1, 75
1386	5, 8, 12, 18, 212
1387	2, 14, 65, 150, 213, 271
1389	3, 15, 42, 737
1390	535
1391	14809 [15000]
1392	11, 15, 63, 421, 495
1393	35, 167
1394	3, 59
1395	2, 104
1396	1, 3, 5, 38, 84, 319, 777
1397	1, 23, 553
1398	3, 18
1399	1, 2, 3, 26, 29
1400	727
1401	8, 9, 42, 109, 218
1402	43, 263
1403	87
1404	1, 2, 11, 37, 475
1405	7, 409, 809, 895
1406	3
1407	2, 15, 61, 278
1408	6, 66, 104
1409	1, 167, 391
1410	1, 2, 36, 218, 302
1411	2, 8, 284, 558, 575, 978
1412	145
1413	3, 690
1414	3, 170, 179, 872
1415	255, 315
1416	23
1417	2, 9, 477
1418	175
1419	2, 3, 757
1420	1, 13, 15, 21, 26, 42, 125
1421	7
1422	1, 21, 42
1423	7
1424	1, 103
1425	1, 3, 6, 8, 86, 138, 612
1426	17, 122, 519
1427	677
1428	3, 114, 139, 927
1429	3, 68, 337
1431	3, 9, 24, 77, 107, 255
1432	1, 2, 5, 11, 38, 55
1433	59, 107, 311
1434	7
1435	29
1436	57
1437	1070 [1500]
1438	6, 35, 78, 212
1439	81
1440	149, 332, 393
1441	42, 60
1442	53, 75, 327
1443	6, 32, 602
1445	7, 9, 59
1446	9, 26, 93, 194, 413, 905
1447	2, 6, 50, 435
1448	11, 375
1449	13, 20, 25, 43, 84, 512
1450	9, 11, 26, 80
1451	7
1452	17, 277, 303
1453	2, 228
1454	7, 29, 33, 53, 87
1455	2, 3, 8, 182, 197, 566, 953
1456	48, 122, 498
1457	83
1458	32
1459	2, 216
1460	57, 125, 269, 835
1461	1, 3, 103, 522
1462	6, 165, 263, 638
1463	7, 31
1464	3
1465	1, 35, 145, 806
1466	3, 271, 301
1467	5
1468	3, 11, 20, 150
1469	1, 141
1470	2, 18, 29, 39, 297, 545, 764
1471	5, 7, 173, 233, 383, 606
1472	29, 35, 841
1473	7, 12, 95, 138, 271
1474	3, 41, 103, 188, 293
1475	9, 593
1476	6, 349
1477	1, 573
1478	875
1479	5, 41, 134, 485
1480	1, 6, 20, 75, 672
1481	9, 125, 197, 327
1482	7, 209
1483	6, 14, 75, 83, 770
1484	1, 9, 13, 811
1485	17, 26, 38, 62, 161
1486	1
1487	9, 17, 621
1488	6, 20, 119
1490	1, 313
1491	1, 11, 12, 323, 343, 393
1492	1, 155, 198, 529
1494	1, 3, 7, 20, 29, 77
1495	1, 2, 7, 92, 201
1496	1, 11, 17, 357
1497	367, 445
1498	7, 39
1499	1, 15, 99, 769
1500	5, 323
1501	11, 26, 101, 288, 360, 713
1502	1, 9, 11
1503	24, 55, 278, 375
1504	7, 37, 44, 377
1505	1
1506	5, 8, 75, 173
1507	5, 19, 23
1508	1503 [1590]
1509	12, 13, 216
1510	223
1511	5, 23, 569
1512	1, 3, 73, 98
1513	2, 3
1514	397
1515	26, 150
1516	15, 17, 327, 525, 614, 680, 871
1517	1, 5, 85, 177, 693
1518	6, 18
1519	8, 125, 162
1520	21
1521	2, 44
1523	175
1524	2, 72, 87, 98
1525	8, 25, 32, 60, 108, 260
1526	3, 5
1527	1, 2, 9, 18, 29, 465
1528	2, 11
1529	1, 33, 135, 149
1530	1, 18, 162, 282
1531	3, 12, 453
1532	25, 45, 93, 191, 305, 873
1533	134, 972
1534	21, 33, 91, 221, 251, 818
1535	7, 365, 641
1536	134, 237, 321
1537	210
1538	3, 203
1539	2, 5, 317
1540	2
1541	1, 3
1542	26, 235
1543	18, 488, 755
1544	287
1545	15, 19, 791
1546	1, 7, 405
1547	11, 365
1548	2, 3, 120, 283
1549	1, 5
1550	1, 5
1551	7, 23, 31, 973
1552	6, 23, 191, 859
1553	35, 319
1554	32
1555	463
1556	1
1557	1, 2, 5, 7, 31, 38, 86, 261
1560	5, 25, 419, 776
1561	37, 75, 84, 403
1562	1, 5, 9, 183, 217, 359, 995
1563	2, 7
1564	1, 2, 7, 9, 55, 122
1565	7, 133, 233, 379, 653
1566	9, 13
1567	1, 446
1569	2, 131, 445, 765
1570	875
1571	23
1572	98, 590
1573	15
1574	3, 7, 885
1575	1, 2, 6, 15, 234
1576	1, 5, 35, 63, 171, 721
1577	7, 43
1578	3, 123
1579	1, 2, 66, 235, 318
1580	1, 441
1581	6, 7, 65, 117
1582	2, 7, 53, 915
1583	583
1584	163
1585	2, 12, 23
1586	1, 5, 35, 73, 79, 941
1587	1, 39
1588	8, 422, 464
1589	51, 285
1590	2, 23
1591	1, 11
1592	5
1593	18, 258
1594	2, 33, 722
1595	1, 317
1596	1, 26, 57, 537
1597	9, 23, 35
1598	31, 671
1599	3, 33, 309
1600	6, 11
1601	3, 65
1602	5, 14, 41, 50, 66
1603	74
1604	417
1605	13, 37, 125
1606	31, 48, 50, 427
1607	1
1608	2, 8, 143
1609	1, 2, 9
1610	3, 9
1611	6, 54
1612	266
1613	7, 135
1614	3, 56, 738, 747
1615	31, 206, 768
1616	3
1617	5, 211
1618	59
1619	25, 191
1620	11, 30, 938
1621	3, 15, 30, 108, 285
1622	1
1623	203
1624	5, 120, 255, 414, 566
1625	3, 125, 819
1626	2, 95, 482
1627	42, 74, 81
1628	115
1629	1, 2, 32, 36
1630	2, 3, 8, 33, 45, 599
1631	185
1633	31
1634	5, 11, 29, 115, 209, 291, 415, 455
1635	1, 67, 389, 435, 731
1636	5, 390
1637	1
1638	2, 14, 19
1639	14, 65, 689, 840
1640	5
1641	1, 223, 407, 912
1642	2, 5, 86, 818, 839
1643	7, 23
1644	1, 146
1645	2, 51, 169
1646	7, 11, 347
1647	19, 175
1648	2, 54
1649	99, 205
1650	1, 6, 9, 25, 48, 59, 474, 606
1651	9, 102, 828
1652	1, 11, 23, 171
1654	1087 [1100]
1655	143, 371
1656	8, 13, 780
1657	1, 5, 81, 102, 179, 407, 709
1659	6, 500, 596
1660	1, 14, 15, 41, 156, 228, 602
1661	1, 7, 761
1662	5, 477
1663	3, 96, 324
1664	1
1665	8, 9, 429
1666	23, 59, 301
1667	17, 465
1668	20, 38, 98, 695
1669	53
1670	1, 621
1671	1, 2, 294
1672	1, 2, 158, 497
1673	31
1674	1, 3, 5
1675	44, 176, 265
1677	21, 681
1678	2, 6, 170
1679	1, 189, 251
1680	5, 6, 14, 315, 356
1681	1, 2, 12, 13, 14, 26
1682	5, 205
1684	1, 3, 13, 90, 575
1685	37, 107
1686	3, 23, 39, 149
1687	27, 87, 447
1688	11
1689	2, 11
1690	8, 21, 529, 549
1691	25, 85, 295
1692	6, 21, 26, 33, 62, 265
1693	24
1694	1, 5, 9, 729
1695	12, 27, 42
1697	43
1698	643
1699	1, 73, 493
1700	1, 5, 247, 601
1701	20, 72, 131, 987
1702	6, 174
1703	131
1704	1, 2, 3, 14, 17, 47, 207
1705	1, 45, 49, 57, 65, 128
1706	45
1707	1
1708	3, 11, 363, 799
1709	5
1710	73
1711	1, 9, 51, 110
1712	1, 851
1713	3, 30, 54, 75, 96, 306, 710
1714	3, 6, 53
1715	3, 21
1716	3, 6, 9, 17, 195, 374, 603, 861, 950
1717	2, 47, 398
1718	207
1719	539, 891
1720	3, 20, 54
1721	13, 113
1722	2, 21, 113, 530, 537, 849
1723	14, 39, 180, 212, 419
1724	5
1725	11, 39, 525, 668
1726	14, 23, 263, 269
1727	1, 3, 7, 13, 169, 399
1728	7, 50, 179
1729	8, 23, 193
1730	27
1731	2, 13, 410, 503
1732	221, 331
1734	8, 408
1735	2, 5, 14, 570, 839
1736	1, 165
1737	45, 71, 87, 131
1739	3, 21, 43, 95, 227, 257, 327
1740	347
1741	1, 12, 20, 139, 479, 636, 804
1742	359
1743	495
1744	2, 3, 80, 223, 321
1746	1489 [1500]
1747	1, 3, 11, 109, 413
1749	2, 21, 83
1750	1, 21, 49, 51, 69, 390, 920
1751	13, 61
1752	2, 19, 163, 890
1753	3
1754	593
1755	21, 212
1756	1, 5, 144, 171
1757	3, 75
1758	2
1759	1
1760	1, 17, 119
1761	1, 18, 57
1762	1, 9, 111, 426, 698
1763	3, 283
1764	2, 12, 53, 290
1765	1
1766	31
1767	2, 7, 98
1768	3, 7, 36, 90, 96, 122, 138, 158, 783
1769	1813 [1870]
1770	2, 17, 842
1771	47, 222, 253, 303
1773	23
1774	8, 14, 205, 401, 685
1775	409
1776	1, 38, 73, 156, 359
1777	13
1778	3707 [4000]
1779	3, 8, 15, 39, 228
1780	25, 703
1781	1, 31, 163
1782	203, 710
1783	26, 27
1784	3, 11, 53, 133
1785	3, 44
1786	3, 9, 24, 54, 545
1787	25
1788	452, 711
1789	1, 9, 162, 269
1790	253
1791	14, 108, 119, 506
1792	7, 9, 66
1794	5, 263
1795	6, 44, 909
1796	9, 21, 47, 479
1797	135, 755
1798	3, 6, 54, 375
1799	1, 19, 23, 103, 317, 407
1800	1, 2, 12
1802	1, 11, 153, 273, 499
1803	3672 [4000]
1804	6, 9, 41, 171, 228, 282
1805	35, 43, 93, 399
1806	1, 3, 44, 48, 66, 75, 221, 303
1807	1, 57
1809	1, 218
1810	90, 405, 549
1811	17, 677
1812	59, 965
1814	1, 519, 743, 801
1815	79
1816	1
1817	7
1818	3, 6, 11, 176, 714
1819	2, 9, 152
1821	1, 26, 36, 129, 198, 897
1822	17, 145
1823	263, 583
1824	9, 17, 21, 133, 511
1825	1, 6, 59, 222
1827	1, 7, 95
1828	114
1829	7, 35
1830	80, 144, 354, 410, 583
1831	1, 56, 804
1832	1, 15
1833	2, 32
1834	7, 20, 42, 45
1835	1, 7, 155
1836	1, 325, 451
1837	1, 6
1838	11
1839	7, 12
1840	30, 339
1841	15
1842	903
1843	8
1844	1, 295, 585
1845	14, 173
1846	73, 324
1847	5
1848	7, 44, 59, 164
1849	1, 2, 9, 35, 53
1850	1, 11, 13, 287, 683
1851	11, 30, 33, 89, 189, 242, 749
1852	23, 138
1853	43, 55
1854	1, 2, 9, 416
1855	2, 21, 27, 131
1856	25, 35, 219
1857	3601 [4000]
1858	696
1859	1, 17, 63
1860	6, 11, 24, 26
1861	1, 23, 38, 813, 849
1862	2889 [3000]
1863	19, 27
1864	31, 451
1865	5, 133, 287
1866	7
1867	5, 6
1868	531
1869	1, 3, 33, 373, 419, 585, 971
1870	3, 5, 7, 239, 546
1871	919
1872	1, 2, 5, 29, 91, 258
1874	3, 9, 23, 55
1875	8, 30, 531
1876	3, 26, 42, 50, 449
1877	2599 [3000]
1878	128
1879	2, 984
1880	11, 451
1881	102, 611
1882	1, 807
1883	27
1884	1, 23, 68, 241
1885	2, 7, 13, 85
1886	3, 5, 9, 21, 139, 155
1887	1, 9, 27, 105, 158
1888	8, 367
1889	35, 265
1890	3, 9, 42, 627
1891	47, 91, 290, 847
1892	1, 13, 997
1894	29, 63, 984
1895	3, 377, 895
1896	32, 175, 725
1897	3, 253, 446
1899	1, 2, 14, 68
1900	2, 183, 555, 935, 995,
1902	1, 17, 27, 29, 41, 210, 717
1903	3, 6, 110, 270
1904	35
1905	511, 619
1906	1, 2, 164
1907	95, 257, 997
1908	50
1909	383
1910	7
1911	2, 18, 29, 39, 56, 602
1912	1, 5, 25, 121, 203
1914	134, 221, 236
1915	5, 41
1916	595
1917	1, 66, 217
1918	3, 7
1919	9, 93, 205, 291, 353
1920	2, 128
1921	7, 8, 295
1923	11, 55, 87, 116
1924	3, 17
1925	3, 289
1926	5, 7, 8, 19, 233
1927	1, 98
1929	15
1930	833
1931	1665 [2000]
1932	745
1933	3, 15, 35, 47, 56, 207, 363
1934	7, 35
1935	6, 7, 8
1936	11, 21, 523, 668, 780, 991
1937	1, 9
1938	2, 27, 75, 308
1939	1, 30, 51, 57, 153, 369
1941	5, 113
1942	9, 17, 29
1943	59
1944	3
1945	1, 5, 6, 9, 15, 61, 141
1946	47, 253
1947	1, 7, 23, 642
1949	161
1950	1, 6, 12, 47
1951	2, 3, 38
1952	209
1953	60, 75, 603
1954	2, 6, 51, 637
1955	559, 673
1956	5, 7, 8, 61, 62, 215, 359, 590
1957	7, 25, 35, 73, 145, 159, 267
1958	115, 199
1959	15, 26, 68, 159, 175, 426
1960	1, 5, 53
1961	9, 31, 91
1962	2
1963	299
1964	1, 15, 33, 37
1965	1, 2, 197, 248, 849
1966	17, 147
1968	60, 231, 240
1969	7, 17, 77, 109, 403
1971	12, 49, 171
1972	13, 25, 98
1973	155
1974	3, 13, 150, 173
1975	35, 38, 135
1976	235
1977	235, 367
1978	14
1979	1, 71, 221
1980	3, 21, 57, 61, 189
1981	14, 25, 61
1982	1, 43
1983	2
1984	3, 9, 63, 722
1985	35, 311, 381
1986	1, 3, 13, 117, 933
1987	5, 27
1989	1, 30, 719
1990	1, 11, 53, 92
1991	3, 11
1992	7, 26, 275, 590
1993	2, 3, 6, 8, 44, 456, 583, 852
1994	1, 19
1995	8, 33, 55
1996	9
1997	415
1998	2, 222
1999	2, 59, 77
2000	149, 243
2001	1, 2, 87, 137, 159
2002	1, 2, 3, 17, 87
2003	119
2004	1, 38
2005	13, 27, 92
2006	1239 [1500]
2007	11, 121, 650
2008	12, 26, 98, 115, 995
2009	1
2010	5232 [5270]
2011	13, 131
2012	1, 43, 377
2013	775
2014	11, 81, 97, 233, 249
2015	1, 5, 7, 33, 221
2016	2, 60
2017	1267 [1500]
2019	8, 12, 17, 75, 140, 479
2020	32
2021	7, 13
2022	21, 78, 103
2023	2
2024	3
2025	5, 524, 905
2026	1, 27, 239
2027	1, 3, 29, 115
2028	44
2029	45, 141, 481
2030	79, 97
2031	24, 65, 265, 621, 702
2032	158
2033	23
2034	2, 9, 86, 193, 415, 869
2035	1, 92
2037	1, 3, 6, 13, 15, 433
2038	2, 3, 54, 738
2039	745
2040	8, 63, 143
2041	6, 15, 95, 227, 987
2042	1, 29, 91, 225, 525
2043	223
2044	3, 571
2045	1, 15, 191
2046	23
2047	1, 29, 138
2048	7, 139, 143
2049	2, 15, 25, 191

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