Kynea 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

Kynea primes bases 1001-2000
Kynea primes bases > 2000
Carol primes bases <= 1000
Carol primes bases 1001-2000
Carol 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 51 1, 2, 3, 5, 8, 9, 12, 15, 17, 18, 21, 23, 27, 32, 51, 65, 87, 180, 242, 467, 491, 501, 507, 555, 591, 680, 800, 1070, 1650, 2813, 3281, 4217, 5153, 6287, 6365, 10088, 10367, 37035, 45873, 69312, 102435, 106380, 108888, 110615, 281621, 369581, 376050, 442052, 621443, 661478, (...) 852770
6 250K 24 1, 2, 3, 4, 9, 12, 30, 49, 56, 115, 118, 376, 432, 1045, 1310, 6529, 7768, 8430, 21942, 26930, 33568, 50800, 209523, 235326
10 1M 5 22, 351, 1061, 410997, (...) 2332974
12 100K 9 1, 2, 8, 60, 513, 1047, 7021, 7506, 78858
14 100K 15 1, 5, 60, 72, 118, 181, 245, 310, 498, 820, 962, 2212, 3928, 5844, 5937
18 100K 8 1, 10, 21, 25, 31, 1083, 40485, 82516
20 100K 13 1, 15, 44, 77, 141, 208, 304, 1169, 3359, 5050, 22431, 34935, 92990
22 100K 11 3, 166, 814, 1851, 2197, 3172, 3865, 19791, 42356, 52147, 82020
24 100K 4 24, 321, 971, 984
26 100K 10 1, 2, 8, 78, 79, 111, 5276, 8226, 19545, 75993
28 100K 9 1, 2, 11, 15, 586, 993, 5048, 24990, 80543
30 200K 9 2, 3, 57, 129, 171, 9837, 30359, 157950, 177081
34 100K 9 1, 2, 14, 29, 61, 146, 2901, 6501, 8093
38 100K 4 6, 279, 3490, 90713
40 100K 10 2, 49, 144, 825, 2856, 2996, 5166, 7824, 9392, 40778
42 200K 15 1, 3, 4, 81, 119, 2046, 2466, 4020, 7907, 8424, 25002, 33475, 106238, 157323, 159530
44 100K 7 3, 195, 1482, 8210, 20502, 60212, 95940
46 100K 4 1, 54, 2040, 3063
48 100K 8 1, 207, 329, 1153, 4687, 13274, 25978, 43473
50 100K 7 4, 38, 93, 120, 4396, 11459, 25887
52 30K 5 3, 5, 166, 456, 14410
54 30K 5 1, 1910, 2575, 7639, 21415
56 30K 8 8, 14, 73, 122, 136, 706, 5411, 7771
58 30K 9 2, 21, 35, 213, 296, 1734, 2354, 23046, 29505
60 30K 7 1, 9, 21, 49, 1717, 3882, 11307
62 30K 9 1, 2, 212, 761, 2183, 3818, 8800, 13352, 17625
66 30K 6 172, 375, 945, 1751, 9832, 28522
68 30K 6 1, 3, 6, 32, 2960, 3014
70 40K 3 1, 7, 11
72 40K 3 354, 1920, 6831
74 78K 3 1, 3, 694
76 40K 9 1, 2, 3, 22, 29, 126, 173, 284, 2306
78 40K 5 3, 5, 13, 79, 6853
80 30K 8 29, 34, 45, 81, 148, 562, 1445, 22631
82 30K 4 3, 9, 595, 1866
84 30K 3 423, 4162, 14493
86 30K 5 8, 18, 36, 260, 11270
88 30K 6 1, 40, 324, 1072, 5100, 28032
90 30K 5 11, 504, 520, 676, 3120
92 30K 4 1, 2, 900, 1795
94 30K 3 5, 3305, 11045
96 30K 4 2, 13, 15, 54
98 30K 5 4, 12, 35, 459, 28725
102 30K 8 1, 3, 27, 33, 264, 292, 1630, 1993
104 30K 7 6, 85, 87, 638, 832, 2798, 6365
106 30K 8 1, 6, 25, 27, 219, 539, 1641, 2046
108 30K 6 3, 5, 24, 1078, 2104, 8292
110 30K 5 57, 1245, 2852, 6403, 17365
112 30K 4 24, 527, 1813, 12953
114 30K 4 368, 12141, 13896, 14021
116 30K 5 1, 12, 1272, 1852, 12655
118 30K 3 1, 17, 40
120 80K 11 1, 12, 16, 236, 1501, 2249, 3421, 7112, 8260, 10856, 22918
122 30K 5 11, 45, 244, 1474, 20196
124 30K 4 19, 36, 728, 23101
126 30K 13 1, 2, 37, 58, 84, 126, 276, 2318, 2877, 4514, 6212, 19560, 20563
130 30K 3 1, 178, 672
132 30K 2 13, 28285
134 30K 5 1, 11, 42, 204, 1171
136 30K 4 12, 47, 15340, 21467
138 30K 7 1, 2, 69, 1716, 5407, 6300, 16573
140 30K 8 41, 395, 4267, 4456, 5120, 5396, 24595, 28075
142 30K 3 3, 48, 4869
146 400K 7 3, 20, 403, 2475, 61827, 180482, 276995
148 10K 5 4, 20, 30, 43, 112
150 10K 2 4, 34
152 10K 4 2, 51, 156, 444
154 30K 6 1, 49, 75, 82, 371, 612
156 30K 4 152, 461, 24434, 27423
158 50K 1 1893
160 30K 7 1, 5, 24, 30, 104, 135, 148
162 10K 3 12, 447, 8342
164 10K 3 6, 15, 4967
166 10K 3 2, 3, 78
168 100K 6 1, 16, 44, 230, 6988, 13059
170 10K 5 11, 53, 692, 2921, 5141
172 100K 9 1, 3, 24, 126, 492, 745, 778, 13293, 19633
174 10K 5 2, 10, 396, 1100, 3894
176 10K 5 1, 7, 3385, 7566, 8866
178 10K 4 3, 4, 6, 839
180 30K 4 14, 189, 218, 360
182 10K 5 1, 5, 6, 227, 1348
184 10K 4 2, 12, 51, 671
186 10K 4 6, 459, 811, 1968
188 10K 6 2, 5, 926, 2225, 3863, 5495
190 10K 5 1, 4, 71, 262, 2841
192 10K 2 1017, 7989
194 10K 1 3
198 10K 2 6, 12
200 25K 3 3, 33, 37
202 10K 10 3, 5, 17, 68, 580, 858, 1100, 2323, 3893, 4942
204 30K 5 1, 7, 40, 3645, 23750
206 10K 4 6, 684, 2529, 2550
208 10K 2 2, 2244
210 10K 6 1, 5, 7, 34, 254, 6961
212 10K 6 2, 14, 33, 503, 1601, 4230
214 10K 3 52, 132, 2614
218 10K 5 17, 32, 78, 312, 1216
220 10K 2 3, 1728
222 10K 2 1, 93
224 10K 2 129, 1137
226 10K 2 788, 3775
228 10K 3 3, 48, 150
230 10K 4 1, 2, 27, 6534
232 10K 8 1, 26, 30, 216, 934, 1268, 1384, 2671
234 10K 5 3, 18, 27, 645, 1854
236 10K 2 1, 80
238 10K 8 1, 5, 114, 137, 213, 270, 5796, 6798
240 10K 4 3, 201, 779, 1211
242 10K 8 4, 13, 34, 93, 396, 514, 2056, 7765
244 10K 10 3, 17, 19, 21, 65, 70, 200, 1128, 6742, 7510
246 10K 8 1, 9, 236, 561, 735, 741, 816, 6940
248 10K 3 45, 100, 3588
250 10K 2 7, 90
252 10K 3 1, 177, 1468
254 10K 5 3, 56, 144, 2730, 5864
258 10K 8 1, 9, 14, 75, 105, 125, 159, 2703
260 10K 3 2, 1960, 2138
262 10K 2 3, 22
264 10K 4 1, 2, 33, 3458
266 10K 4 1, 7, 9, 1438
268 10K 5 5, 18, 108, 768, 977
270 10K 4 15, 112, 1338, 3454
272 10K 8 1, 6, 9, 11, 41, 105, 887, 1528
274 10K 10 4, 5, 6, 8, 11, 21, 87, 510, 813, 5207
276 10K 4 5, 10, 724, 4341
278 10K 5 1, 3, 7, 174, 2025
280 10K 5 35, 153, 2624, 2635, 3553
282 10K 4 3, 6, 26, 41
284 10K 8 1, 12, 34, 87, 373, 820, 1476, 3970
286 10K 7 2, 3, 1474, 4358, 4418, 4553, 5820
288 10K 2 5, 466
290 175K 0
292 10K 4 1, 13, 27, 1591
294 10K 6 47, 61, 330, 1824, 4386, 9708
296 10K 2 17, 846
298 10K 4 1, 10, 369, 1002
300 10K 5 1, 38, 135, 3055, 4672
302 10K 8 1, 4, 8, 22, 340, 1061, 2991, 4736
304 10K 4 3, 90, 1311, 2098
306 10K 5 7, 8, 20, 66, 5485
308 10K 6 1, 3, 4, 10, 85, 7430
310 10K 4 5, 50, 110, 6825
312 10K 4 1, 3, 132, 1290
314 10K 6 1, 2, 18, 38, 2072, 3862
316 50K 5 9, 41, 360, 521, 6421
318 10K 2 4, 5
320 10K 2 55, 9336
322 10K 7 1, 16, 44, 107, 4968, 7090, 9928
326 10K 1 8941
328 10K 6 9, 48, 288, 390, 672, 2315
330 10K 2 14, 340
332 10K 7 5, 34, 94, 201, 246, 1920, 4305
334 10K 2 1, 320
336 10K 6 1, 7, 127, 170, 403, 7070
338 10K 2 2, 462
340 10K 3 1, 18, 25
342 10K 2 81, 286
344 10K 3 10, 269, 9438
346 10K 3 12, 28, 2428
348 10K 3 2, 9, 19
350 10K 4 10, 52, 63, 475
352 10K 2 2, 8811
354 10K 2 1, 25
356 10K 5 1, 55, 1233, 5470, 7365
358 10K 9 1, 17, 26, 231, 267, 381, 417, 3053, 5600
360 10K 6 4, 15, 16, 63, 108, 2290
362 140K 7 156, 264, 630, 794, 14360, 46308, 133647
364 10K 3 4, 14, 16
366 2K 4 32, 149, 828, 947
368 10K 1 969
370 2K 7 1, 3, 86, 164, 590, 791, 1613
372 2K 7 6, 7, 31, 73, 103, 409, 1408
374 2K 2 22, 48
376 2K 3 2, 3, 90
378 2K 6 3, 4, 7, 18, 173, 427
380 2K 9 2, 3, 6, 44, 707, 1220, 1278, 1347, 1962
382 2K 3 75, 588, 696
384 2K 1 13
386 2K 3 1, 13, 254
388 2K 1 282
390 2K 6 1, 13, 79, 200, 441, 1645
392 2K 3 2, 32, 203
394 50K 1 198
396 2K 5 3, 13, 69, 130, 147
398 2K 4 1, 2, 4, 749
402 2K 2 6, 136
404 2K 4 1, 44, 74, 230
406 2K 4 5, 6, 9, 79
408 2K 2 3, 275
410 2K 3 3, 58, 655
412 2K 1 32
414 2K 3 1, 121, 297
416 2K 3 4, 5, 287
418 2K 1 270
420 2K 3 1, 645, 775
422 2K 1 647
424 2K 6 1, 4, 48, 220, 700, 828
426 10K 1 9708
428 2K 6 1, 2, 7, 8, 292, 1466
430 2K 2 4, 30
432 10K 2 6, 1227
434 10K 1 1
436 2K 4 2, 6, 8, 1944
438 2K 2 85, 106
440 2K 7 1, 2, 28, 35, 50, 98, 233
442 2K 4 1, 3, 28, 232
444 2K 4 21, 82, 657, 1630
446 2K 6 1, 2, 14, 44, 642, 769
448 20K 14 1, 3, 7, 106, 182, 216, 927, 1093, 1346, 1359, 5758, 13375, 15113, 18369
450 2K 3 45, 120, 783
452 2K 3 72, 88, 124
454 2K 2 264, 1547
456 2K 1 3
458 2K 2 12, 77
460 2K 3 85, 288, 1687
462 2K 2 15, 911
464 2K 3 2, 665, 1646
466 2K 4 1, 3, 6, 135
468 2K 7 1, 2, 5, 56, 61, 62, 1774
470 2K 5 2, 106, 162, 288, 586
472 50K 5 10, 459, 7307, 14542, 17019
474 2K 2 3, 57
476 2K 4 8, 12, 1030, 1692
478 2K 3 18, 140, 1611
480 2K 8 1, 3, 10, 13, 64, 153, 315, 535
482 2K 4 2, 42, 129, 132
486 2K 4 4, 15, 203, 1432
488 2K 3 1, 13, 85
490 2K 7 1, 2, 7, 183, 545, 1359, 1895
492 2K 3 8, 555, 774
494 2K 3 1, 16, 303
496 2K 7 1, 4, 6, 26, 116, 134, 751
498 2K 5 4, 9, 11, 216, 347
500 10K 4 4, 5, 11, 2195
502 2K 1 6
504 2K 5 1, 7, 34, 220, 490
506 2K 2 140, 404
508 2K 1 30
510 2K 3 216, 231, 1546
514 2K 1 3
516 10K 1 2
518 2K 5 10, 23, 55, 723, 819
520 2K 2 134, 1371
522 2K 3 1, 3, 517
524 2K 2 1, 3
526 2K 4 2, 3, 5, 154
528 2K 4 3, 4, 9, 1985
530 2K 2 1, 93
532 10K 1 2
534 2K 4 2, 12, 170, 1476
536 2K 3 7, 10, 70
538 2K 5 2, 6, 120, 868, 1374
540 2K 3 1, 2, 212
542 25K 1 13476
544 2K 4 1, 38, 90, 230
546 2K 2 11, 21
548 2K 8 6, 9, 33, 138, 162, 200, 444, 1496
550 2K 3 4, 181, 319
552 10K 2 2139, 2883
554 2K 3 6, 138, 1887
556 2K 1 405
558 2K 2 2, 314
560 2K 7 1, 2, 7, 20, 33, 68, 135
562 2K 1 330
564 2K 3 1, 76, 756
566 2K 3 56, 636, 643
568 2K 4 1, 11, 12, 844
570 2K 2 36, 1061
572 2K 2 1, 535
574 2K 8 1, 12, 144, 212, 298, 1190, 1353, 1951
578 2K 1 19
580 2K 3 2, 19, 68
582 2K 3 1, 152, 301
584 2K 3 9, 406, 591
586 2K 4 1, 2, 3, 12
588 2K 3 11, 13, 28
590 2K 3 23, 155, 762
592 2K 2 12, 1855
594 2K 7 1, 55, 107, 237, 280, 924, 1585
596 2K 3 79, 95, 1434
598 2K 3 57, 129, 845
600 10K 1 61
602 2K 1 640
604 2K 3 38, 159, 1356
606 2K 3 1, 100, 1129
608 2K 6 1, 2, 3, 8, 315, 513
610 2K 2 19, 456
612 2K 3 66, 288, 359
614 2K 6 1, 3, 31, 135, 252, 276
616 2K 3 3, 78, 89
618 2K 1 3
620 2K 3 1, 3, 766
622 2K 3 118, 312, 348
624 2K 4 13, 24, 32, 1589
626 2K 4 69, 120, 154, 534
628 2K 3 2, 120, 288
630 2K 2 234, 807
632 10K 5 2, 6, 15, 54, 444
634 100K 0
636 2K 2 1, 483
638 2K 2 3, 1288
640 44940 1 44940
642 2K 3 13, 20, 440
644 2K 6 1, 2, 5, 54, 146, 399
646 2K 1 201
648 2K 1 709
650 2K 3 29, 100, 287
652 2K 3 1, 3, 46
654 10K 1 7234
656 2K 4 2, 6, 8, 30
658 2K 3 8, 20, 1015
660 2K 1 1476
662 2K 2 1, 3
664 2K 9 23, 29, 44, 45, 169, 434, 483, 712, 839
666 40K 6 1, 2, 17, 25, 142, 742
668 2K 3 16, 125, 226
670 2K 5 1, 2, 19, 117, 660
672 2K 2 37, 64
674 2K 3 2, 722, 1182
678 2K 2 143, 193
680 2K 6 2, 4, 7, 44, 521, 569
682 2K 3 5, 9, 21
684 10K 1 2
686 2K 4 2, 3, 800, 1866
688 100K 3 10160, 70718, 85121
690 2K 4 30, 36, 681, 1162
692 2K 1 91
694 2K 3 2, 318, 591
696 2K 2 3, 897
698 100K 0
700 2K 5 29, 64, 151, 1047, 1410
702 50K 2 2, 14
704 2K 3 6, 7, 49
706 2K 6 3, 4, 5, 10, 49, 53
708 2K 8 2, 7, 162, 215, 282, 428, 538, 742
710 100K 0
712 2K 7 1, 7, 15, 37, 42, 375, 591
714 2K 4 1, 19, 81, 155
716 2K 5 2, 18, 39, 81, 1475
718 2K 6 1, 3, 6, 13, 408, 1708
720 10K 2 2, 590
722 2K 1 4
724 2K 3 275, 393, 948
726 2K 5 1, 2, 13, 494, 1005
728 2K 3 2, 1054, 1751
730 2K 2 27, 105
732 2K 7 1, 4, 15, 27, 61, 91, 273
734 2K 1 8
736 2K 2 2, 671
738 25K 3 3, 18, 5892
740 2K 3 3, 50, 291
742 2K 8 1, 4, 96, 585, 596, 618, 680, 1210
744 2K 3 3, 6, 14
746 2K 2 1, 535
748 2K 3 2, 14, 126
750 2K 5 1, 2, 6, 71, 381
752 2K 2 60, 328
754 2K 3 127, 372, 817
756 2K 3 1, 7, 1808
758 2K 3 2, 75, 548
760 2K 5 1, 3, 40, 61, 354
762 2K 5 1, 5, 39, 243, 1569
764 2K 1 115
766 2K 1 95
768 2K 3 2, 27, 43
770 2K 5 2, 31, 131, 771, 1680
772 100K 0
774 2K 4 1, 28, 45, 81
776 2K 8 2, 9, 11, 20, 71, 449, 973, 1432
778 2K 3 1, 2, 20
780 2K 2 15, 22
782 2K 3 48, 171, 645
786 2K 4 3, 8, 191, 677
788 2K 4 1, 3, 700, 759
790 2K 2 4, 213
792 2K 4 6, 51, 162, 696
794 2K 1 4
796 3K 2 1, 2871
798 2K 3 2, 689, 944
800 2K 2 5, 1506
802 2K 2 27, 48
804 2K 3 2, 4, 1660
806 2K 5 1, 8, 657, 774, 909
808 2K 4 4, 5, 52, 214
810 10K 1 1
812 2K 7 3, 20, 43, 56, 79, 107, 760
814 2K 1 530
816 2K 3 1, 345, 1149
818 10K 2 2198, 3216
820 2K 1 174
822 2K 3 3, 22, 454
824 2K 2 1, 195
826 2K 2 10, 18
828 2K 1 465
830 2K 1 487
832 52K 7 26, 51, 62, 5882, 7795, 8375, 18830
834 2K 7 45, 57, 110, 233, 730, 1294, 1626
836 100K 2 67648, 71232
838 2K 1 925
840 2K 2 1, 117
842 2K 4 21, 33, 72, 201
844 2K 1 33
846 2K 6 3, 5, 10, 41, 116, 181
848 2K 1 11
850 2K 2 6, 1815
852 2K 2 2, 462
854 2K 4 2, 12, 152, 613
856 2K 1 44
858 2K 1 88
860 2K 4 3, 31, 72, 269
862 2K 2 1, 454
864 2K 3 15, 42, 1049
866 10K 2 93, 2244
868 2K 3 105, 449, 517
870 2K 2 20, 795
872 2K 3 3, 4, 564
874 2K 3 1, 5, 200
876 2K 2 4, 5
878 2K 2 180, 244
880 2K 6 1, 3, 9, 80, 121, 386
882 2K 1 842
884 2K 1 198
886 2K 2 10, 84
888 2K 5 5, 29, 124, 1063, 1568
890 2K 1 25
892 2K 2 11, 112
894 10K 2 3134, 4905
896 2K 6 1, 2, 3, 12, 376, 978
898 2K 2 6, 18
902 2K 5 2, 449, 625, 1313, 1313
904 2K 3 14, 42, 78
906 2K 1 558
908 30K 1 16142
910 2K 2 110, 179
912 2K 3 12, 50, 1467
914 2K 2 46, 69
916 2K 2 2, 3
918 2K 2 8, 18
920 2K 2 221, 250
922 2K 2 3, 8
924 2K 4 3, 9, 18, 422
926 30K 1 24668
928 10K 4 40, 132, 379, 664
930 2K 4 1, 293, 712, 942
932 2K 5 46, 55, 79, 250, 260
934 2K 2 65, 77
936 2K 4 3, 26, 33, 103
938 22K 6 54, 56, 654, 749, 3916, 11463
940 2K 1 1692
942 30K 5 1, 4, 199, 475, 571
944 2K 5 1, 3, 112, 685, 1433
946 2K 6 10, 15, 49, 126, 140, 385
948 2K 3 5, 168, 1036
950 30K 5 1, 12, 31, 920, 1345
952 2K 5 3, 17, 83, 160, 855
954 2K 2 84, 147
956 2K 2 6, 529
958 2K 6 1, 2, 5, 14, 21, 110
960 2K 2 4, 706
962 2K 1 1901
964 10K 2 39, 48
966 100K 0
968 80K 2 165, 3650
970 10K 1 1452
972 2K 5 1, 6, 9, 151, 225
974 2K 2 2, 90
976 2K 1 40
978 2K 2 1, 1063
980 2K 2 129, 589
982 100K 0
984 2K 3 3, 10, 31
986 2K 5 1, 2, 216, 310, 565
988 2K 3 29, 275, 930
990 2K 3 5, 6, 47
992 100K 1 1
994 2K 5 1, 2, 19, 35, 100
996 100K 0
998 100K 0

Original information obtained from:
Prime Wiki
Carol / Kynea Search