Carol primes for bases <= 1000

Near squares of the form (bn - 1)2 - 2.

Started: 2025-09-07
Last update: 2025-10-23

Compiled by Gary Barnes

Carol primes bases 1001-2000
Carol primes bases > 2000
Kynea primes bases <= 1000
Kynea primes bases 1001-2000
Kynea primes bases > 2000

Yellow = reserved by a person
Blue = base with no known primes
Mauve = not reserved and has prime > contiguous test limit (missing range); notated by (...)

Status date is date of reservation or last date that test limit was updated.

base Reserved by Status date Test limit # primes (bn - 1)2 - 2 is prime for the following n-values
2 768870 44 2, 3, 4, 6, 7, 10, 12, 15, 18, 19, 21, 25, 27, 55, 129, 132, 159, 171, 175, 315, 324, 358, 393, 435, 786, 1459, 1707, 2923, 6462, 14289, 39012, 51637, 100224, 108127, 110953, 175749, 185580, 226749, 248949, 253987, 520363, 653490, 688042, 695631
6 250K 23 1, 2, 6, 7, 20, 47, 255, 274, 279, 308, 1162, 2128, 3791, 9028, 9629, 10029, 13202, 38660, 46631, 48257, 117991, 157648, 163228
10 1M 13 1, 8, 21, 123, 4299, 6128, 11760, 18884, 40293, 334568, 393063, 657559, 859669
12 100K 9 3, 29, 51, 7824, 15456, 22614, 28312, 47014, 68835
14 100K 10 1, 6, 13, 45, 74, 240, 553, 12348, 13659, 50603
18 100K 13 2, 8, 30, 98, 110, 185, 912, 2514, 4074, 10208, 15123, 19395, 69354
20 100K 9 1, 2, 53, 183, 1281, 1300, 8041, 29936, 72820
22 100K 9 1, 8, 35, 88, 503, 8643, 8743, 14475, 92539
24 100K 7 2, 27, 92, 4950, 20047, 46309, 55716
26 100K 5 159, 879, 4744, 5602, 74387
28 100K 9 1, 22, 127, 165, 2520, 6492, 6577, 22960, 25528
30 100K 10 1, 6, 19, 30, 166, 495, 769, 826, 1648, 3993
34 100K 3 1, 4, 258
38 100K 5 1, 2, 13, 560, 28933
40 100K 7 4, 15, 39, 138, 2153, 4084, 5639
42 150K 14 3, 6, 14, 15, 29, 78, 195, 255, 272, 713, 2526, 4852, 10573, 40891
44 100K 8 1, 7, 30, 90, 1288, 1947, 12909, 25786
46 100K 5 12, 269, 1304, 5172, 59786
48 100K 15 1, 2, 4, 6, 12, 13, 3882, 6123, 15067, 15085, 33743, 42593, 54273, 60039, 93239
50 100K 15 1, 3, 4, 9, 31, 66, 115, 430, 1233, 2546, 2674, 6360, 53351, 69033, 69157
52 30K 5 2, 14, 24, 85, 23234
54 30K 6 9, 17, 65, 963, 5171, 8068
56 30K 7 1, 2, 3, 11, 177, 1698, 26698
58 30K 2 88, 1720
60 30K 5 2, 5, 155, 6665, 11549
62 30K 4 1, 454, 1573, 11080
66 30K 3 12, 475, 1902
68 30K 6 4, 59, 779, 2272, 2634, 16522
70 40K 12 1, 5, 9, 18, 24, 277, 337, 431, 516, 10744, 11260, 19370
72 40K 4 1, 9, 187, 37930
74 78K 5 183, 2300, 3855, 39227, 56039
76 40K 9 1, 2, 32, 37, 51, 220, 3081, 35617, 36090
78 40K 4 1, 2, 85, 6429
80 30K 2 320, 363
82 30K 4 24, 1074, 1212, 20148
84 30K 8 4, 66, 82, 140, 1253, 1922, 2613, 5582
86 30K 5 3, 39, 75, 1120, 2053
88 30K 5 2, 5, 9, 134, 594
90 30K 6 1, 5, 43, 1105, 2186, 6957
92 30K 9 3, 4, 6, 60, 78, 116, 638, 2831, 4281
94 30K 6 1, 2, 666, 13278, 16021, 20654
96 30K 5 5, 106, 448, 561, 609
98 30K 7 2, 21, 130, 378, 896, 2588, 5876
102 30K 9 2, 92, 165, 492, 2628, 2879, 4676, 5603, 13808
104 30K 5 1, 53, 59, 3867, 6328
106 30K 7 2, 3, 46, 47, 104, 2922, 17138
108 30K 4 1, 3807, 24374, 27756
110 30K 2 705, 1870
112 30K 5 2, 6, 542, 1656, 26024
114 30K 7 3, 72, 156, 406, 472, 3270, 6873
116 30K 4 29, 38, 10752, 12122
118 30K 7 1, 4, 55, 150, 223, 886, 3381
120 80K 9 1, 6, 7, 11, 12, 168, 2750, 12418, 42427
122 30K 7 1, 2, 489, 499, 2552, 2565, 27356
124 30K 1 4836
126 30K 3 20, 93, 5924
130 30K 1 135
132 30K 7 1, 2, 10, 57, 236, 665, 1876
134 30K 12 4, 16, 65, 81, 93, 161, 1932, 2677, 4681, 4695, 11556, 28877
136 30K 3 1, 6, 20581
138 30K 6 6, 10, 105, 4534, 9489, 18222
140 30K 11 1, 4, 5, 29, 155, 382, 485, 1375, 1528, 5757, 18327
142 30K 1 15
146 400K 5 1, 35, 37, 6965, 144882
148 10K 6 2, 60, 255, 422, 528, 1300
150 10K 4 8, 20, 30, 260
152 10K 4 3, 5, 1263, 1317
154 30K 3 24, 68, 1495
156 30K 3 1, 136, 1663
158 50K 2 14, 33873
160 30K 5 4, 11, 85, 127, 1104
162 10K 4 1, 82, 386, 3198
164 10K 2 2, 1358
166 10K 2 321, 9492
168 100K 4 11, 24, 380, 1140
170 10K 9 1, 18, 19, 135, 460, 1059, 1528, 1653, 9373
172 100K 9 174, 246, 302, 1191, 1302, 3680, 87690, 91277, 97119
174 10K 5 1, 15, 20, 96, 354
176 10K 4 6, 29, 2001, 7360
178 100K 6 1, 9, 174, 313, 609, 87525
180 30K 2 42, 251
182 10K 2 310, 1258
184 10K 4 1, 160, 2907, 3417
186 10K 4 2, 12, 206, 293
188 10K 8 27, 39, 55, 77, 1406, 2544, 6052, 6292
190 10K 5 2, 6, 18, 40, 431
192 10K 5 1, 2, 7, 26, 39
194 10K 3 29, 180, 5007
198 10K 2 103, 118
200 25K 2 20, 36
202 10K 1 63
204 30K 7 2, 5, 40, 11867, 14458, 17522, 18929
206 10K 4 1, 2, 103, 2607
208 10K 5 3, 10, 24, 660, 1468
210 10K 3 7, 17, 1197
212 10K 5 1, 6, 580, 1933, 4050
214 10K 3 5, 36, 1571
218 10K 4 1, 52, 397, 969
220 10K 4 30, 60, 63, 780
222 10K 4 3, 118, 186, 208
224 10K 8 1, 5, 6, 167, 460, 488, 1130, 1152
226 10K 3 22, 588, 2989
228 10K 1 2123
230 10K 7 3, 5, 59, 243, 256, 1382, 1659
232 10K 6 1, 5, 6, 50, 177, 390
234 10K 3 1, 2, 6447
236 10K 1 5
238 10K 7 1, 2, 7, 68, 2345, 4783, 5425
240 10K 2 1, 261
242 10K 2 5, 119
244 10K 2 25, 404
246 10K 9 4, 46, 57, 122, 266, 364, 565, 2302, 7589
248 10K 4 1, 6, 55, 1248
250 10K 3 4, 34, 132
252 10K 7 88, 337, 717, 1330, 1996, 3095, 6548
254 10K 4 1, 27, 45, 295
258 10K 7 1, 2, 9, 14, 39, 94, 5416
260 10K 6 1, 10, 231, 683, 2759, 4128
262 10K 3 2, 3, 18
264 10K 4 5, 304, 1797, 2584
266 10K 3 1, 3, 132
268 10K 4 1, 3, 3576, 5578
270 10K 4 30, 236, 711, 8133
272 10K 1 11
274 10K 6 1, 2, 11, 435, 1018, 7331
276 10K 5 3, 6, 96, 644, 8534
278 10K 1 826
280 10K 2 1, 4
282 10K 3 10, 112, 612
284 10K 2 11, 89
286 10K 8 1, 2, 7, 30, 78, 193, 1777, 2124
288 10K 4 43, 62, 319, 1263
290 175K 3 3, 3386, 124116
292 10K 8 24, 54, 65, 304, 700, 810, 993, 2586
294 10K 5 1, 8, 23, 1046, 1809
296 10K 1 45
298 10K 6 2, 12, 44, 254, 1227, 3074
300 10K 5 1, 70, 127, 1826, 5802
302 10K 5 1, 6, 414, 1774, 4521
304 10K 4 1, 2, 7, 31
306 10K 4 3, 11, 3963, 7797
308 10K 4 2, 14, 249, 4020
310 10K 3 1, 42, 94
312 10K 2 92, 3740
314 10K 5 1, 13, 22, 294, 4367
316 50K 7 1, 5, 27, 183, 5331, 14854, 17396
318 10K 2 6, 1117
320 10K 3 4, 81, 2014
322 10K 5 5, 15, 18, 789, 4420
326 10K 2 288, 290
328 10K 5 2, 38, 488, 1608, 3116
330 10K 3 6, 166, 384
332 10K 3 3, 259, 415
334 10K 5 3, 33, 690, 714, 4485
336 10K 6 1, 2, 3, 17, 76, 176
338 10K 1 1
340 10K 2 450, 7581
342 10K 3 1, 14, 26
344 10K 4 3, 1356, 2002, 4030
346 10K 3 7, 9, 15
348 10K 3 3, 51, 168
350 10K 7 3, 6, 10, 11, 13, 3240, 5512
352 10K 3 102, 208, 582
354 10K 4 2, 6, 1344, 1548
356 10K 4 1, 104, 568, 3027
358 10K 4 1, 11, 22, 31
360 10K 5 1, 3, 7, 31, 1080
362 140K 0
364 10K 1 1139
366 2K 4 15, 43, 61, 339
368 10K 1 1856
370 2K 5 2, 23, 24, 194, 244
372 2K 4 1, 2, 7, 51
374 2K 1 735
376 2K 2 10, 1545
378 2K 7 4, 10, 21, 48, 132, 763, 1277
380 2K 1 4
382 2K 2 5, 1491
384 2K 1 321
386 2K 7 2, 3, 8, 9, 12, 105, 399
388 2K 4 1, 9, 50, 63
390 2K 1 3
392 2K 4 1, 5, 15, 223
394 50K 1 49500
396 2K 1 3
398 2K 1 512
402 2K 3 6, 21, 135
404 2K 1 460
406 2K 5 1, 21, 49, 495, 1531
408 2K 4 72, 168, 1581, 1660
410 2K 2 3, 5
412 2K 8 2, 3, 15, 33, 280, 503, 544, 663
414 2K 2 2, 220
416 2K 3 1, 2, 12
418 2K 4 3, 4, 5, 6
420 2K 2 8, 345
422 2K 4 1, 6, 31, 42
424 2K 1 9
426 10K 6 1, 41, 680, 2042, 2233, 9475
428 2K 2 20, 200
430 2K 5 1, 2, 3, 18, 56
432 10K 1 8742
434 2K 3 2, 15, 141
436 2K 3 1, 6, 162
438 2K 5 2, 8, 201, 1731, 1826
440 2K 2 2, 231
442 2K 4 1, 97, 236, 397
444 2K 5 1, 2, 3, 8, 109
446 2K 3 5, 172, 300
448 20K 7 1, 13, 29, 57, 103, 212, 3666
450 2K 2 1, 78
452 2K 1 78
454 2K 5 2, 11, 16, 22, 31
456 2K 2 7, 34
458 2K 3 9, 33, 114
460 2K 6 3, 5, 11, 1133, 1253, 1636
462 2K 7 5, 44, 113, 135, 421, 703, 1254
464 2K 2 133, 630
466 2K 2 11, 68
468 2K 6 1, 6, 8, 400, 603, 998
470 2K 6 1, 2, 3, 15, 128, 451
472 50K 1 16077
474 2K 2 33, 231
476 2K 3 2, 8, 48
478 2K 3 3, 45, 900
480 2K 3 2, 50, 239
482 6K 2 1, 5900
486 2K 3 45, 138, 170
488 2K 2 12, 111
490 2K 6 1, 4, 13, 84, 210, 1885
492 2K 3 1, 370, 1518
494 2K 1 323
496 2K 3 1, 440, 690
498 2K 6 1, 5, 24, 92, 99, 1123
500 10K 1 981
502 2K 1 3
504 2K 4 2, 10, 117, 821
506 2K 4 1, 6, 136, 445
508 2K 3 2, 102, 816
510 2K 4 4, 9, 254, 305
514 2K 3 1, 30, 117
516 2K 1 100
518 2K 3 3, 19, 177
520 2K 2 3, 6
522 2K 2 2, 1059
524 2K 7 1, 8, 109, 156, 166, 244, 471
526 2K 2 1, 39
528 2K 2 3, 1059
530 2K 3 5, 84, 1049
532 2K 5 1, 17, 128, 716, 1982
534 2K 2 13, 510
536 2K 4 3, 357, 653, 1472
538 2K 1 319
540 2K 6 6, 55, 547, 752, 827, 1877
542 25K 7 1, 2, 3, 8, 954, 4669, 7267
544 2K 3 24, 84, 94
546 2K 6 1, 3, 51, 196, 426, 1196
548 2K 2 24, 1218
550 2K 4 30, 81, 168, 330
552 10K 1 6
554 2K 3 3, 72, 645
556 2K 2 3, 595
558 2K 1 162
560 2K 4 2, 4, 8, 706
562 2K 4 1, 4, 567, 1053
564 2K 3 110, 1016, 1050
566 2K 2 1, 77
568 2K 7 11, 15, 72, 212, 515, 1075, 1208
570 3K 3 1, 2, 2749
572 2K 3 15, 18, 293
574 2K 4 1, 3, 166, 651
578 2K 2 9, 539
580 2K 8 2, 3, 14, 53, 131, 167, 365, 559
582 2K 1 46
584 10K 1 1
586 2K 2 21, 465
588 2K 3 1, 5, 789
590 2K 2 235, 937
592 2K 2 393, 582
594 2K 1 3
596 2K 7 1, 2, 18, 25, 66, 185, 414
598 2K 2 2, 20
600 10K 2 4606, 6509
602 2K 4 5, 79, 221, 454
604 2K 3 13, 15, 48
606 2K 5 2, 23, 32, 60, 288
608 2K 5 1, 3, 13, 26, 326
610 2K 6 1, 9, 10, 78, 1165, 1252
612 2K 3 2, 6, 42
614 2K 1 838
616 2K 3 1, 19, 1208
618 2K 4 4, 16, 24, 618
620 2K 3 11, 21, 23
622 2K 5 1, 2, 4, 16, 323
624 2K 7 2, 56, 83, 102, 282, 285, 286
626 2K 3 8, 54, 146
628 2K 1 293
630 2K 5 2, 5, 19, 63, 117
632 10K 1 6915
634 30K 3 2, 1319, 26480
636 2K 2 52, 202
638 2K 3 1, 4, 1483
640 100K 0
642 2K 4 3, 4, 60, 1787
644 2K 2 9, 393
646 2K 3 1, 4, 1884
648 2K 4 3, 225, 759, 840
650 2K 5 2, 6, 7, 1042, 1603
652 2K 3 40, 107, 140
654 10K 4 1, 25, 38, 6577
656 2K 5 5, 6, 81, 136, 228
658 2K 3 60, 442, 1272
660 2K 2 43, 972
662 2K 5 2, 3, 137, 147, 438
664 2K 6 1, 2, 4, 50, 1010, 1600
666 40K 3 120, 3064, 9068
668 2K 2 1, 3
670 2K 2 54, 1524
672 2K 5 1, 46, 92, 133, 941
674 2K 2 3, 52
678 2K 6 1, 21, 37, 39, 50, 280
680 2K 4 9, 12, 15, 574
682 2K 1 30
684 2K 3 10, 15, 63
686 2K 6 2, 29, 44, 172, 1170, 1260
688 100K 0
690 2K 1 413
692 2K 3 57, 586, 1787
694 2K 4 2, 6, 62, 256
696 2K 3 3, 87, 1675
698 30K 5 4, 12, 15, 48, 65
700 2K 5 3, 16, 60, 70, 306
702 100K 1 86004
704 2K 4 2, 3, 5, 380
706 2K 4 2, 3, 6, 1955
708 2K 3 10, 14, 21
710 30K 7 6, 12, 18, 80, 5742, 10819, 26761
712 2K 2 9, 24
714 2K 3 1, 4, 84
716 2K 2 1, 210
718 2K 3 2, 48, 440
720 10K 5 1, 2, 91, 1703, 7583
722 2K 3 6, 86, 222
724 2K 3 7, 216, 595
726 2K 2 4, 669
728 2K 5 1, 4, 88, 364, 907
730 2K 6 3, 15, 69, 91, 97, 160
732 2K 3 5, 288, 464
734 2K 7 1, 4, 52, 151, 304, 620, 676
736 2K 2 2, 52
738 25K 1 15864
740 2K 3 18, 47, 503
742 2K 3 3, 6, 979
744 2K 2 1, 49
746 2K 3 2, 3, 516
748 2K 5 1, 124, 135, 179, 320
750 2K 2 3, 149
752 2K 3 1, 14, 804
754 2K 1 6
756 2K 2 2, 57
758 2K 2 1, 538
760 2K 4 2, 5, 38, 89
762 2K 3 1, 12, 1341
764 2K 2 1, 146
766 2K 3 93, 414, 420
768 2K 3 42, 154, 305
770 2K 5 3, 14, 77, 240, 513
772 30K 4 4, 46, 190, 1206
774 2K 1 26
776 2K 6 1, 32, 236, 610, 808, 1537
778 2K 2 8, 17
780 2K 5 1, 6, 288, 936, 1200
782 2K 3 3, 40, 760
786 10K 1 1
788 2K 1 447
790 2K 4 1, 2, 40, 602
792 2K 5 3, 10, 12, 112, 698
794 2K 4 3, 126, 290, 1232
796 2K 1 207
798 2K 3 1, 3, 1048
800 2K 2 13, 30
802 10K 1 2
804 2K 3 6, 257, 550
806 2K 8 2, 4, 10, 45, 51, 171, 1477, 1978
808 2K 5 1, 3, 6, 20, 314
810 2K 3 5, 9, 321
812 2K 5 1, 11, 276, 310, 376
814 2K 3 45, 69, 130
816 2K 2 6, 1910
818 10K 5 1, 47, 69, 108, 146
820 2K 3 5, 255, 901
822 2K 1 30
824 2K 1 1215
826 2K 7 1, 11, 14, 32, 190, 483, 852
828 2K 1 3
830 2K 1 375
832 52K 1 51686
834 2K 1 21
836 30K 6 6, 31, 87, 1471, 10712, 19370
838 2K 2 33, 78
840 2K 3 11, 54, 1595
842 2K 4 1, 19, 75, 1402
844 2K 1 21
846 2K 3 5, 27, 224
848 2K 1 38
850 2K 4 2, 12, 60, 78
852 2K 4 3, 4, 15, 54
854 2K 3 5, 211, 522
856 2K 3 10, 70, 306
858 2K 1 5
860 2K 3 10, 64, 1052
862 2K 2 42, 95
864 2K 4 1, 2, 104, 993
866 10K 1 8319
868 2K 3 7, 357, 1166
870 2K 1 385
872 2K 5 2, 5, 8, 17, 1415
874 2K 2 2, 123
876 2K 4 1, 21, 60, 105
878 2K 2 2, 7
880 2K 2 723, 971
882 2K 2 1, 493
884 2K 6 3, 4, 61, 75, 252, 1213
886 2K 4 5, 27, 33, 147
888 2K 2 11, 1505
890 2K 2 2, 24
892 2K 1 200
894 10K 3 35, 450, 7067
896 2K 1 11
898 2K 2 1, 4
902 10K 1 1
904 2K 2 3, 7
906 2K 2 3, 6
908 30K 4 3, 521, 1512, 23172
910 2K 8 2, 10, 24, 49, 51, 54, 90, 200
912 2K 3 60, 208, 1638
914 2K 1 278
916 2K 3 9, 27, 57
918 2K 4 3, 21, 26, 808
920 2K 2 14, 780
922 2K 2 190, 315
924 2K 4 2, 4, 16, 288
926 30K 4 699, 1932, 3132, 24279
928 10K 1 5831
930 2K 2 9, 843
932 2K 4 1, 10, 16, 98
934 2K 4 3, 20, 501, 1585
936 2K 2 58, 365
938 22K 1 21852
940 2K 3 10, 55, 1788
942 100K 1 49211
944 2K 6 1, 4, 9, 12, 14, 1302
946 2K 6 1, 6, 7, 64, 146, 1022
948 2K 5 6, 9, 13, 21, 1923
950 100K 0
952 2K 3 1, 245, 784
954 2K 5 10, 120, 247, 579, 1719
956 2K 2 5, 630
958 2K 2 15, 800
960 2K 4 1, 3, 5, 252
962 2K 3 51, 282, 732
964 10K 1 4995
966 30K 3 7, 47, 370
968 80K 1 79512
970 10K 3 1008, 1190, 3899
972 2K 1 46
974 2K 4 1, 10, 294, 1175
976 2K 1 3
978 2K 3 42, 53, 202
980 2K 7 1, 2, 21, 31, 175, 634, 1354
982 30K 1 1053
984 2K 3 5, 14, 527
986 7K 2 2, 6589
988 2K 3 1, 6, 61
990 2K 1 457
992 100K 0
994 2K 3 1, 9, 358
996 30K 3 1, 22, 1282
998 30K 7 2, 8, 12, 21, 44, 924, 10251

Original information obtained from:
Prime Wiki
Carol / Kynea Search