Description
Here are shown the least n-value ≥ 1 for any base b with 2 ≤ b ≤ 1024 which generates a Williams prime of the form (b+1)•bn+1.
Values of bases b ≡ 1 mod 3 are always divisible by 3, so not listed here.
History
- 2020-07-19: Found n = 135981 (b=327), (unknown), Conjectures 'R Us
- 2019-06-15: Found n = 3615 (b=929), Karsten Bonath
- 2019-06-15: Found n = 4917 (b=912), Karsten Bonath
- 2019-05-21: Found n = 13418 (b=719), Karsten Bonath
- 2019-05-21: Found n = 37506 (b=717), Karsten Bonath
- 2019-05-20: Found n = 24110 (b=710), Karsten Bonath
- 2019-05-15: Found n = 3521 (b=473), Karsten Bonath
- 2019-05-15: Found n = 1806 (b=542), Karsten Bonath
- 2019-05-15: Found n = 6774 (b=683), Karsten Bonath
- 2019-05-14: Found n = 11229 (b=425), Karsten Bonath
Wanted values
Notes:
Data
The data file can be found here.
| Base
|
n-value
|
| 2
|
1
|
| 3
|
1
|
| 5
|
1
|
| 6
|
1
|
| 8
|
1
|
| 9
|
2
|
| 11
|
2
|
| 12
|
1
|
| 14
|
1
|
| 15
|
1
|
| 17
|
1
|
| 18
|
9
|
| 20
|
1
|
| 21
|
1
|
| 23
|
2
|
| 24
|
1
|
| 26
|
2
|
| 27
|
1
|
| 29
|
5
|
| 30
|
2
|
| 32
|
5
|
| 33
|
1
|
| 35
|
2
|
| 36
|
3
|
| 38
|
1
|
| 39
|
3
|
| 41
|
1
|
| 42
|
2
|
| 44
|
2
|
| 45
|
2
|
| 47
|
2
|
| 48
|
6
|
| 50
|
1
|
| 51
|
183
|
| 53
|
2
|
| 54
|
1
|
| 56
|
2
|
| 57
|
1
|
| 59
|
1
|
| 60
|
21
|
| 62
|
1
|
| 63
|
185
|
| 65
|
3
|
| 66
|
1
|
| 68
|
2
|
| 69
|
1
|
| 71
|
1
|
| 72
|
120
|
| 74
|
2
|
| 75
|
1
|
| 77
|
1
|
| 78
|
1
|
| 80
|
1
|
| 81
|
8
|
| 83
|
5
|
| 84
|
9
|
| 86
|
2
|
| 87
|
2
|
| 89
|
1
|
| 90
|
1
|
| 92
|
2
|
| 93
|
3
|
| 95
|
9
|
| 96
|
14
|
| 98
|
3
|
| 99
|
1
|
| 101
|
1
|
| 102
|
5
|
| 104
|
5
|
| 105
|
1
|
| 107
|
80
|
| 108
|
398
|
| 110
|
1
|
| 111
|
1
|
| 113
|
3
|
| 114
|
3
|
| 116
|
44
|
| 117
|
1
|
| 119
|
1
|
| 120
|
2
|
| 122
|
2
|
| 123
|
2
|
| 125
|
2
|
| 126
|
5
|
| 128
|
3
|
| 129
|
54
|
| 131
|
1
|
| 132
|
54
|
| 134
|
9
|
| 135
|
17
|
| 137
|
20
|
| 138
|
1
|
| 140
|
2
|
| 141
|
1
|
| 143
|
1
|
| 144
|
3
|
| 146
|
3
|
| 147
|
1
|
| 149
|
9
|
| 150
|
1
|
| 152
|
2
|
| 153
|
1
|
| 155
|
1
|
| 156
|
3
|
| 158
|
141
|
| 159
|
32
|
| 161
|
1
|
| 162
|
1
|
| 164
|
1
|
| 165
|
5
|
| 167
|
1
|
| 168
|
1
|
| 170
|
2
|
| 171
|
1851
|
| 173
|
1
|
| 174
|
14
|
| 176
|
1
|
| 177
|
2
|
| 179
|
2
|
| 180
|
2
|
| 182
|
5
|
| 183
|
3
|
| 185
|
12
|
| 186
|
6
|
| 188
|
1
|
| 189
|
1
|
| 191
|
2
|
| 192
|
1
|
| 194
|
1
|
| 195
|
2
|
| 197
|
18
|
| 198
|
2
|
| 200
|
9
|
| 201
|
31274
|
| 203
|
1
|
| 204
|
3
|
| 206
|
1
|
| 207
|
8
|
| 209
|
1
|
| 210
|
27
|
| 212
|
6
|
| 213
|
447
|
| 215
|
1
|
| 216
|
8
|
| 218
|
1
|
| 219
|
2
|
| 221
|
5
|
| 222
|
52725
|
| 224
|
2
|
| 225
|
30
|
| 227
|
36321
|
| 228
|
5
|
| 230
|
2
|
| 231
|
1
|
| 233
|
6
|
| 234
|
2
|
| 236
|
1
|
| 237
|
30
|
| 239
|
2
|
| 240
|
12
|
| 242
|
9
|
| 243
|
2
|
| 245
|
1
|
| 246
|
1
|
| 248
|
3
|
| 249
|
17
|
| 251
|
11
|
| 252
|
53
|
| 254
|
2
|
| 255
|
2
|
| 257
|
662
|
| 258
|
153
|
| 260
|
9
|
| 261
|
32
|
| 263
|
2
|
| 264
|
2
|
| 266
|
1
|
| 267
|
14
|
| 269
|
1398
|
| 270
|
5
|
| 272
|
1
|
| 273
|
102
|
| 275
|
1911
|
| 276
|
12
|
| 278
|
1
|
| 279
|
1
|
| 281
|
8
|
| 282
|
32
|
| 284
|
2
|
| 285
|
2
|
| 287
|
1
|
| 288
|
1
|
| 290
|
1
|
| 291
|
3
|
| 293
|
1
|
| 294
|
2
|
| 296
|
24
|
| 297
|
2
|
| 299
|
26
|
| 300
|
24
|
| 302
|
1085
|
| 303
|
21
|
| 305
|
6
|
| 306
|
2
|
| 308
|
2
|
| 309
|
1
|
| 311
|
6
|
| 312
|
2
|
| 314
|
1
|
| 315
|
48
|
| 317
|
2
|
| 318
|
30
|
| 320
|
5
|
| 321
|
38
|
| 323
|
2
|
| 324
|
3
|
| 326
|
2
|
| 327
|
135981
|
| 329
|
1
|
| 330
|
6
|
| 332
|
1
|
| 333
|
26
|
| 335
|
2
|
| 336
|
1
|
| 338
|
5
|
| 339
|
1002
|
| 341
|
2
|
| 342
|
1
|
| 344
|
1
|
| 345
|
3
|
| 347
|
320
|
| 348
|
1
|
| 350
|
3
|
| 351
|
1
|
| 353
|
3
|
| 354
|
26
|
| 356
|
5
|
| 357
|
1
|
| 359
|
2
|
| 360
|
8
|
| 362
|
200
|
| 363
|
2
|
| 365
|
2
|
| 366
|
5
|
| 368
|
2
|
| 369
|
1
|
| 371
|
5
|
| 372
|
333
|
| 374
|
3
|
| 375
|
2
|
| 377
|
50
|
| 378
|
1
|
| 380
|
24
|
| 381
|
1
|
| 383
|
1
|
| 384
|
2
|
| 386
|
2
|
| 387
|
8
|
| 389
|
2
|
| 390
|
32
|
| 392
|
1
|
| 393
|
17
|
| 395
|
1
|
| 396
|
24
|
| 398
|
1
|
| 399
|
6
|
| 401
|
26
|
| 402
|
1
|
| 404
|
1
|
| 405
|
1
|
| 407
|
2
|
| 408
|
5
|
| 410
|
3
|
| 411
|
35
|
| 413
|
15
|
| 414
|
1
|
| 416
|
1
|
| 417
|
17
|
| 419
|
5
|
| 420
|
9
|
| 422
|
8
|
| 423
|
6
|
| 425
|
11229
|
| 426
|
1
|
| 428
|
2
|
| 429
|
243
|
| 431
|
18
|
| 432
|
2
|
| 434
|
1
|
| 435
|
1
|
| 437
|
8
|
| 438
|
3
|
| 440
|
2
|
| 441
|
12
|
| 443
|
3
|
| 444
|
12
|
| 446
|
20
|
| 447
|
1
|
| 449
|
696
|
| 450
|
2
|
| 452
|
90
|
| 453
|
1
|
| 455
|
1
|
| 456
|
1
|
| 458
|
3
|
| 459
|
9
|
| 461
|
2
|
| 462
|
14
|
| 464
|
18
|
| 465
|
12
|
| 467
|
2
|
| 468
|
9
|
| 470
|
20
|
| 471
|
2
|
| 473
|
3521
|
| 474
|
5
|
| 476
|
1
|
| 477
|
12
|
| 479
|
3
|
| 480
|
2
|
| 482
|
2
|
| 483
|
3
|
| 485
|
12
|
| 486
|
38
|
| 488
|
3
|
| 489
|
1
|
| 491
|
17
|
| 492
|
26
|
| 494
|
56
|
| 495
|
1
|
| 497
|
5
|
| 498
|
15
|
| 500
|
1
|
| 501
|
8
|
| 503
|
2
|
| 504
|
36
|
| 506
|
6
|
| 507
|
200
|
| 509
|
20
|
| 510
|
3
|
| 512
|
1
|
| 513
|
3
|
| 515
|
6
|
| 516
|
9
|
| 518
|
1
|
| 519
|
38
|
| 521
|
498
|
| 522
|
92
|
| 524
|
20
|
| 525
|
1
|
| 527
|
17
|
| 528
|
2
|
| 530
|
1
|
| 531
|
1
|
| 533
|
1
|
| 534
|
6
|
| 536
|
2
|
| 537
|
1
|
| 539
|
6
|
| 540
|
1
|
| 542
|
1806
|
| 543
|
2
|
| 545
|
11
|
| 546
|
2
|
| 548
|
21
|
| 549
|
8
|
| 551
|
1
|
| 552
|
36
|
| 554
|
1
|
| 555
|
2
|
| 557
|
18
|
| 558
|
11
|
| 560
|
1
|
| 561
|
156
|
| 563
|
3
|
| 564
|
2
|
| 566
|
1
|
| 567
|
1
|
| 569
|
96
|
| 570
|
393
|
| 572
|
1
|
| 573
|
50
|
| 575
|
14
|
| 576
|
5
|
| 578
|
450
|
| 579
|
1
|
| 581
|
11
|
| 582
|
1
|
| 584
|
1
|
| 585
|
32
|
| 587
|
8
|
| 588
|
3
|
| 590
|
2
|
| 591
|
2
|
| 593
|
2
|
| 594
|
3
|
| 596
|
5
|
| 597
|
2
|
| 599
|
36
|
| 600
|
8
|
| 602
|
380
|
| 603
|
1
|
| 605
|
1
|
| 606
|
2
|
| 608
|
9
|
| 609
|
1
|
| 611
|
6
|
| 612
|
1
|
| 614
|
11
|
| 615
|
2
|
| 617
|
338
|
| 618
|
2
|
| 620
|
6
|
| 621
|
1
|
| 623
|
3
|
| 624
|
1
|
| 626
|
1
|
| 627
|
6
|
| 629
|
8
|
| 630
|
2
|
| 632
|
18
|
| 633
|
5246
|
| 635
|
1
|
| 636
|
18
|
| 638
|
11
|
| 639
|
3
|
| 641
|
6
|
| 642
|
1
|
| 644
|
1
|
| 645
|
5
|
| 647
|
504
|
| 648
|
114
|
| 650
|
3
|
| 651
|
2
|
| 653
|
6
|
| 654
|
3
|
| 656
|
2
|
| 657
|
14
|
| 659
|
2
|
| 660
|
261
|
| 662
|
50
|
| 663
|
143
|
| 665
|
5
|
| 666
|
3
|
| 668
|
1
|
| 669
|
32
|
| 671
|
1
|
| 672
|
21
|
| 674
|
2
|
| 675
|
2
|
| 677
|
1
|
| 678
|
215
|
| 680
|
2
|
| 681
|
12
|
| 683
|
6774
|
| 684
|
2
|
| 686
|
1
|
| 687
|
2
|
| 689
|
2
|
| 690
|
39
|
| 692
|
2
|
| 693
|
11
|
| 695
|
3
|
| 696
|
1
|
| 698
|
3
|
| 699
|
23
|
| 701
|
1
|
| 702
|
9
|
| 704
|
8
|
| 705
|
38
|
| 707
|
2
|
| 708
|
2
|
| 710
|
24110
|
| 711
|
3
|
| 713
|
2
|
| 714
|
2
|
| 716
|
78
|
| 717
|
37506
|
| 719
|
13418
|
| 720
|
1
|
| 722
|
8
|
| 723
|
6
|
| 725
|
6
|
| 726
|
1
|
| 728
|
1
|
| 729
|
5
|
| 731
|
3
|
| 732
|
50
|
| 734
|
5
|
| 735
|
1
|
| 737
|
36
|
| 738
|
15
|
| 740
|
2
|
| 741
|
2
|
| 743
|
1
|
| 744
|
3
|
| 746
|
2
|
| 747
|
1
|
| 749
|
2
|
| 750
|
2
|
| 752
|
2
|
| 753
|
2
|
| 755
|
1
|
| 756
|
5
|
| 758
|
2
|
| 759
|
2
|
| 761
|
1
|
| 762
|
1
|
| 764
|
20
|
| 765
|
3
|
| 767
|
2
|
| 768
|
1
|
| 770
|
191
|
| 771
|
2
|
| 773
|
1
|
| 774
|
35
|
| 776
|
51
|
| 777
|
2
|
| 779
|
3
|
| 780
|
6
|
| 782
|
1
|
| 783
|
2
|
| 785
|
1
|
| 786
|
5
|
| 788
|
39
|
| 789
|
248
|
| 791
|
27
|
| 792
|
1
|
| 794
|
30
|
| 795
|
5
|
| 797
|
21
|
| 798
|
1
|
| 800
|
8
|
| 801
|
1
|
| 803
|
2
|
| 804
|
6
|
| 806
|
9
|
| 807
|
5
|
| 809
|
5
|
| 810
|
2
|
| 812
|
1
|
| 813
|
|
| 815
|
2
|
| 816
|
275
|
| 818
|
1
|
| 819
|
1
|
| 821
|
81
|
| 822
|
2
|
| 824
|
8
|
| 825
|
1
|
| 827
|
1
|
| 828
|
3
|
| 830
|
6
|
| 831
|
9
|
| 833
|
17
|
| 834
|
71
|
| 836
|
1
|
| 837
|
2
|
| 839
|
1
|
| 840
|
29
|
| 842
|
69
|
| 843
|
2
|
| 845
|
2
|
| 846
|
1
|
| 848
|
273
|
| 849
|
9
|
| 851
|
9
|
| 852
|
8
|
| 854
|
3
|
| 855
|
1
|
| 857
|
1
|
| 858
|
3749
|
| 860
|
1
|
| 861
|
2
|
| 863
|
|
| 864
|
1
|
| 866
|
2
|
| 867
|
2
|
| 869
|
2
|
| 870
|
3
|
| 872
|
12
|
| 873
|
5
|
| 875
|
1
|
| 876
|
414
|
| 878
|
1
|
| 879
|
11
|
| 881
|
47
|
| 882
|
5
|
| 884
|
5
|
| 885
|
2
|
| 887
|
5
|
| 888
|
1647
|
| 890
|
1
|
| 891
|
816
|
| 893
|
246
|
| 894
|
1
|
| 896
|
8
|
| 897
|
1
|
| 899
|
1
|
| 900
|
2
|
| 902
|
14
|
| 903
|
29
|
| 905
|
6
|
| 906
|
6
|
| 908
|
5
|
| 909
|
164
|
| 911
|
1
|
| 912
|
4917
|
| 914
|
12
|
| 915
|
1
|
| 917
|
2
|
| 918
|
1
|
| 920
|
1
|
| 921
|
137
|
| 923
|
11
|
| 924
|
12
|
| 926
|
6
|
| 927
|
1
|
| 929
|
3615
|
| 930
|
24
|
| 932
|
6
|
| 933
|
2
|
| 935
|
6
|
| 936
|
62
|
| 938
|
17
|
| 939
|
66
|
| 941
|
26
|
| 942
|
5
|
| 944
|
2
|
| 945
|
170
|
| 947
|
2693
|
| 948
|
33
|
| 950
|
1
|
| 951
|
12
|
| 953
|
2
|
| 954
|
2
|
| 956
|
2
|
| 957
|
2
|
| 959
|
1
|
| 960
|
1
|
| 962
|
|
| 963
|
357
|
| 965
|
17
|
| 966
|
6
|
| 968
|
5
|
| 969
|
1
|
| 971
|
2
|
| 972
|
26
|
| 974
|
1
|
| 975
|
2
|
| 977
|
24
|
| 978
|
2
|
| 980
|
17
|
| 981
|
1
|
| 983
|
1875
|
| 984
|
17
|
| 986
|
78
|
| 987
|
1
|
| 989
|
2
|
| 990
|
1
|
| 992
|
1
|
| 993
|
1
|
| 995
|
6
|
| 996
|
416
|
| 998
|
2
|
| 999
|
3761
|
| 1001
|
1
|
| 1002
|
1
|
| 1004
|
2
|
| 1005
|
8
|
| 1007
|
1
|
| 1008
|
2771
|
| 1010
|
3351
|
| 1011
|
1
|
| 1013
|
3
|
| 1014
|
3
|
| 1016
|
1
|
| 1017
|
|
| 1019
|
89
|
| 1020
|
1
|
| 1022
|
1
|
| 1023
|
6
|
