Carol primes for bases > 2000

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

Started: 2025-09-07
Last update: 2025-12-14

Compiled by Gary Barnes

Carol primes bases <= 1000
Carol primes bases 1001-2000
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
2002 2K 10 1, 2, 4, 62, 223, 295, 341, 648, 882, 886
2004 2K 1 3
2006 2K 4 5, 6, 773, 1521
2008 2K 5 8, 11, 22, 1003, 1174
2010 50K 3 3, 35, 1967
2012 2K 2 6, 956
2014 2K 1 5
2016 2K 4 18, 78, 253, 1670
2018 27K 2 1800, 3720
2020 2K 2 6, 9
2022 2K 4 1, 6, 22, 771
2024 2K 3 85, 635, 1470
2026 20K 0
2028 2K 3 78, 99, 279
2030 2K 1 30
2032 2K 1 1
2034 20K 0
2036 2K 2 1, 62
2038 2K 3 1, 78, 120
2040 20K 0
2042 2K 3 4, 15, 501
2044 2K 4 1, 5, 12, 119
2046 2K 1 282
2050 2K 2 216, 1511
2052 2K 3 265, 1119, 1144
2054 2K 7 1, 9, 12, 24, 674, 1659, 1982
2056 2K 2 5, 813
2058 2K 4 1, 6, 105, 416
2060 2K 3 1, 16, 21
2062 2K 3 2, 5, 18
2064 20K 7 4, 20, 85, 148, 436, 2698, 18948
2066 2K 4 2, 12, 192, 203
2068 2K 1 105
2070 2K 2 310, 472
2072 2K 3 10, 17, 109
2074 2K 2 1, 144
2076 10K 1 6182
2078 2K 7 1, 5, 8, 31, 38, 114, 360
2080 2K 2 40, 310
2082 2K 1 1
2084 2K 1 3
2086 2K 3 141, 572, 1326
2088 2K 1 1
2090 2K 3 45, 93, 258
2092 2K 2 1, 2
2094 2K 7 1, 14, 16, 110, 277, 314, 1400
2096 2K 2 1, 132
2098 2K 4 3, 16, 34, 1881
2100 2K 5 33, 35, 92, 181, 190
2102 2K 8 1, 9, 19, 34, 79, 84, 162, 1678
2104 10K 1 2741
2106 2K 5 1, 119, 148, 700, 1620
2108 2K 3 1, 40, 115
2110 2K 5 1, 2, 6, 162, 302
2112 2K 2 17, 33
2114 2K 3 1, 2, 280
2118 2K 3 17, 65, 122
2120 2K 1 85
2122 2K 1 55
2124 2K 2 44, 87
2126 20K 0
2128 20K 0
2130 2K 2 1, 19
2132 20K 0
2134 2K 2 1, 1189
2136 2K 1 26
2138 2K 6 1, 2, 13, 92, 390, 578
2140 10K 1 3857
2142 2K 1 24
2144 2K 2 82, 189
2146 20K 3 2, 9, 7710
2148 2K 1 1323
2150 2K 3 40, 137, 510
2152 2K 2 1, 2
2154 2K 1 411
2156 2K 2 137, 491
2158 2K 1 193
2160 2K 4 3, 9, 212, 266
2162 2K 4 16, 80, 560, 689
2164 2K 2 1, 172
2166 2K 1 368
2168 20K 1 11445
2170 2K 2 9, 119
2172 2K 2 1, 40
2174 2K 1 5
2176 2K 2 15, 125
2178 2K 4 1, 3, 4, 25
2180 2K 5 1, 8, 15, 78, 1014
2182 20K 0
2184 2K 5 1, 8, 64, 715, 722
2186 2K 3 561, 1035, 1350
2188 2K 1 6
2190 2K 3 110, 114, 440
2192 2K 1 201
2194 2K 1 25
2196 2K 3 57, 100, 612
2198 2K 3 417, 552, 562
2200 2K 3 4, 6, 37
2202 2K 4 33, 200, 330, 627
2204 20K 0
2206 2K 1 8
2208 2K 2 37, 795
2210 2K 3 4, 347, 437
2212 2K 5 1, 2, 6, 15, 62
2214 2K 4 3, 16, 394, 1768
2216 2K 2 17, 50
2218 2K 1 233
2220 2K 4 5, 78, 122, 699
2222 2K 3 2, 13, 242
2224 2K 1 286
2226 2K 1 1
2228 2K 5 1, 6, 10, 13, 378
2230 2K 2 3, 228
2232 2K 3 8, 59, 1874
2234 2K 3 9, 12, 48
2236 2K 1 511
2238 2K 1 273
2240 2K 4 1, 2, 3, 1646
2242 2K 3 1, 3, 312
2244 2K 2 5, 885
2246 2K 5 2, 3, 4, 1134, 1919
2248 2K 5 1, 2, 8, 50, 94
2250 20K 1 294
2252 2K 1 1293
2254 2K 1 14
2256 2K 1 555
2258 2K 1 1215
2260 2K 2 4, 454
2262 2K 6 1, 2, 78, 98, 235, 1745
2264 20K 0
2266 20K 0
2268 2K 1 2
2270 2K 3 1, 24, 388
2272 2K 3 6, 1175, 1736
2274 2K 3 1, 79, 826
2276 2K 4 33, 36, 69, 820
2278 2K 2 1, 108
2280 20K 7 35, 125, 130, 528, 783, 2590, 3443
2282 2K 7 2, 3, 5, 33, 70, 1309, 1327
2284 2K 1 1
2286 2K 1 20
2288 2K 2 1, 193
2290 20K 0
2292 2K 3 7, 32, 60
2294 2K 1 4
2296 2K 4 15, 25, 85, 535
2298 20K 2 1, 4
2300 20K 1 135
2302 2K 2 3, 107
2306 2K 2 69, 165
2308 20K 0
2310 2K 3 1, 2, 1308
2312 10K 2 4671, 4887
2314 2K 1 1257
2316 2K 3 1, 13, 73
2318 2K 4 38, 39, 299, 306
2320 2K 4 2, 63, 200, 252
2322 2K 7 3, 5, 6, 22, 90, 154, 1762
2324 2K 4 2, 5, 37, 813
2326 2K 1 120
2328 2K 1 51
2330 20K 3 21, 573, 13400
2332 2K 1 3
2334 20K 3 13, 33, 456
2336 2K 2 15, 333
2338 2K 2 1, 1286
2340 2K 5 4, 7, 10, 24, 106
2342 20K 3 20, 492, 4232
2344 2K 1 4
2346 2K 3 1, 14, 141
2348 2K 1 13
2350 2K 4 3, 106, 267, 453
2352 2K 5 2, 29, 57, 944, 1270
2354 2K 1 154
2356 2K 1 140
2358 2K 3 5, 207, 605
2360 2K 4 1, 2, 11, 108
2362 2K 1 939
2364 2K 3 3, 6, 405
2366 2K 1 24
2368 2K 2 156, 864
2370 2K 5 2, 3, 80, 959, 1475
2372 2K 2 7, 13
2374 2K 1 4
2376 2K 4 1, 9, 84, 378
2378 2K 2 3, 18
2380 2K 1 346
2382 10K 1 1
2384 10K 1 7398
2386 2K 5 20, 36, 40, 180, 196
2388 2K 1 110
2390 2K 3 1, 14, 18
2392 2K 1 21
2394 2K 3 1, 205, 905
2396 2K 2 18, 1233
2398 20K 0
2400 10K 1 3148
2402 2K 5 1, 10, 23, 24, 661
2404 10K 1 2828
2406 2K 2 9, 1212
2408 2K 1 21
2410 2K 4 156, 316, 493, 1582
2412 2K 1 56
2414 2K 2 1, 3
2416 2K 1 3
2418 2K 4 2, 247, 1279, 1975
2420 2K 2 4, 900
2422 2K 4 1, 3, 10, 332
2424 2K 2 1, 420
2426 2K 3 6, 51, 495
2428 2K 1 2
2430 2K 8 3, 5, 12, 27, 122, 147, 155, 404
2432 2K 3 1, 7, 510
2434 2K 1 4
2436 2K 4 4, 19, 30, 133
2438 20K 0
2440 2K 4 3, 15, 65, 101
2442 2K 2 64, 115
2444 2K 3 26, 70, 205
2446 2K 3 6, 61, 63
2448 2K 1 1240
2450 2K 4 1, 34, 96, 126
2452 2K 1 127
2454 2K 1 15
2456 2K 3 1, 5, 17
2458 2K 5 4, 17, 19, 86, 318
2460 2K 2 13, 78
2462 2K 2 70, 1360
2464 2K 3 3, 482, 1882
2466 2K 2 1, 7
2468 2K 2 2, 1250
2470 2K 6 1, 6, 11, 14, 49, 195
2472 2K 2 76, 1853
2474 20K 5 43, 189, 860, 8041, 13106
2476 2K 2 3, 435
2478 2K 2 3, 22
2480 20K 0
2482 20K 0
2484 2K 2 713, 953
2486 2K 5 1, 40, 79, 217, 290
2488 2K 3 9, 128, 1249
2490 2K 1 83
2492 2K 5 1, 2, 81, 978, 1429
2494 2K 2 670, 1212
2496 2K 3 38, 126, 495
2498 2K 2 2, 9
2502 2K 2 2, 3
2504 2K 2 16, 59
2506 2K 4 3, 10, 13, 1755
2508 2K 4 1, 106, 331, 721
2510 2K 4 9, 12, 1271, 1496
2512 2K 5 1, 2, 10, 276, 583
2514 2K 3 1, 14, 270
2516 2K 4 1, 54, 144, 339
2518 20K 3 5, 6, 69
2520 2K 4 3, 10, 82, 819
2522 2K 1 90
2524 10K 1 3272
2526 2K 3 8, 38, 1219
2528 2K 7 18, 29, 188, 204, 434, 554, 581
2530 20K 1 1
2532 2K 1 4
2534 20K 3 1, 23, 1017
2536 2K 2 9, 646
2538 2K 1 2
2540 2K 2 122, 306
2542 2K 6 1, 7, 11, 538, 670, 1012
2544 2K 5 1, 2, 8, 21, 368
2546 2K 1 52
2548 2K 1 2
2550 2K 1 1
2552 2K 1 9
2554 2K 6 3, 4, 15, 121, 205, 231
2556 2K 4 1, 6, 34, 90
2558 2K 1 332
2560 20K 0
2562 2K 1 61
2564 2K 4 1, 93, 100, 268
2566 2K 2 2, 11
2568 2K 3 105, 130, 859
2570 2K 2 1, 8
2572 2K 1 3
2574 10K 1 2280
2576 2K 6 108, 119, 305, 648, 834, 1669
2578 2K 1 1
2580 2K 3 101, 497, 1085
2582 2K 5 3, 27, 92, 305, 1278
2584 2K 4 29, 46, 67, 512
2586 20K 3 1, 7, 638
2588 20K 0
2590 2K 6 1, 12, 25, 32, 335, 347
2592 2K 4 1, 373, 481, 756
2594 2K 2 200, 476
2596 2K 4 13, 18, 75, 82
2598 2K 6 1, 24, 104, 367, 719, 798
2600 2K 5 1, 3, 9, 39, 57
2602 2K 3 77, 84, 317
2604 2K 6 1, 5, 9, 17, 79, 1220
2606 20K 3 7, 37, 132
2608 2K 3 2, 27, 32
2610 10K 2 5581, 7874
2612 2K 3 1, 102, 1042
2614 10K 1 486
2616 10K 1 8123
2618 2K 2 81, 854
2620 2K 2 1, 217
2622 10K 1 6882
2624 10K 4 1, 7, 77, 223
2626 10K 3 3, 5, 8
2628 2K 1 115
2630 2K 2 10, 837
2632 2K 3 7, 196, 342
2634 100K 0
2636 2K 4 2, 18, 81, 357
2638 2K 2 1, 18
2640 2K 1 2
2642 2K 1 2
2644 2K 3 41, 267, 1155
2646 20K 0
2648 2K 5 1, 3, 12, 34, 751
2650 20K 3 3, 72, 9393
2652 2K 4 25, 154, 173, 299
2654 2K 4 1, 2, 354, 1139
2656 2K 1 12
2658 10K 1 2548
2660 10K 5 5, 21, 47, 139, 285
2662 2K 1 3
2664 2K 1 3
2666 2K 5 1, 6, 12, 24, 264
2668 2K 4 1, 2, 4, 6
2670 2K 2 12, 63
2672 2K 2 51, 575
2674 2K 2 305, 435
2676 2K 1 280
2678 20K 0
2680 2K 1 1
2682 2K 5 1, 34, 84, 106, 118
2684 2K 2 2, 44
2686 2K 2 257, 888
2688 20K 1 28
2690 2K 1 165
2692 2K 2 143, 893
2694 2K 3 36, 578, 1739
2696 2K 1 1134
2698 2K 3 2, 73, 93
2700 2K 1 159
2702 2K 1 1
2706 2K 1 5
2708 2K 4 1, 13, 61, 722
2710 2K 4 21, 284, 424, 542
2712 2K 2 103, 111
2714 2K 4 21, 149, 179, 216
2716 2K 4 1, 13, 79, 99
2718 2K 7 1, 3, 4, 9, 57, 312, 828
2720 2K 4 24, 39, 305, 1560
2722 2K 6 1, 2, 13, 22, 65, 1032
2724 2K 1 1300
2726 2K 4 1, 30, 43, 752
2728 2K 2 10, 11
2730 2K 3 1, 120, 340
2732 2K 3 3, 4, 6
2734 2K 1 17
2736 2K 4 1, 2, 16, 256
2738 2K 2 1, 3
2740 2K 2 1, 374
2742 20K 3 3, 10, 1125
2746 2K 2 28, 252
2748 2K 3 8, 26, 42
2750 2K 5 1, 2, 10, 44, 218
2752 2K 5 6, 57, 157, 167, 247
2754 2K 3 2, 42, 73
2756 2K 2 3, 27
2758 2K 2 24, 798
2760 2K 1 1
2762 2K 2 3, 234
2764 2K 3 5, 34, 1261
2766 2K 3 3, 5, 278
2768 20K 0
2770 20K 2 114, 387
2772 2K 1 1130
2774 20K 3 1, 184, 273
2776 2K 1 141
2778 2K 1 747
2780 2K 2 1, 4
2782 20K 0
2784 2K 1 1386
2786 2K 1 1
2788 2K 6 3, 24, 402, 435, 718, 1416
2790 2K 1 5
2792 2K 2 42, 1821
2794 20K 0
2796 2K 3 1, 2, 147
2798 20K 0
2800 2K 2 22, 1240
2802 20K 0
2804 20K 0
2806 2K 2 33, 133
2808 2K 2 1, 28
2810 2K 3 1, 691, 866
2812 2K 1 9
2814 2K 3 6, 11, 16
2816 2K 1 453
2818 2K 1 74
2820 2K 3 21, 194, 1718
2822 2K 2 1, 8
2824 2K 2 3, 26
2826 2K 3 9, 400, 753
2828 2K 2 9, 113
2830 20K 3 75, 240, 297
2832 2K 4 18, 72, 227, 1518
2834 2K 5 11, 157, 223, 386, 463
2836 2K 1 4
2838 2K 4 1, 2, 12, 25
2840 2K 4 4, 5, 34, 658
2842 2K 3 22, 196, 609
2844 2K 1 42
2846 10K 1 8189
2848 2K 4 8, 30, 589, 650
2850 2K 1 1
2852 2K 4 2, 13, 63, 1040
2854 2K 1 5
2856 2K 2 1, 2
2858 2K 3 7, 49, 393
2860 2K 1 50
2862 2K 4 7, 16, 97, 145
2864 2K 4 34, 58, 85, 1315
2866 2K 1 192
2868 2K 2 46, 108
2870 2K 2 1, 765
2872 2K 5 1, 7, 24, 37, 58
2874 2K 2 11, 332
2876 2K 2 51, 135
2878 2K 3 4, 33, 256
2880 2K 2 14, 243
2882 2K 1 681
2884 2K 4 1, 680, 852, 1048
2886 20K 3 6, 12, 7330
2888 2K 3 5, 20, 749
2890 2K 3 1, 16, 1931
2892 2K 3 6, 802, 1788
2894 2K 2 57, 584
2896 2K 3 17, 45, 850
2898 2K 5 1, 11, 13, 21, 633
2900 2K 1 40
2902 2K 4 15, 29, 62, 1142
2904 20K 0
2906 2K 3 7, 243, 820
2908 2K 2 39, 475
2910 2K 3 4, 226, 1974
2912 2K 3 1, 34, 333
2914 2K 2 4, 34
2918 20K 4 26, 350, 965, 1750
2920 2K 4 17, 34, 59, 136
2922 20K 0
2924 20K 0
2926 2K 5 1, 2, 6, 362, 1232
2928 2K 2 7, 217
2930 2K 1 134
2932 2K 3 1, 79, 468
2934 2K 3 1, 2, 35
2936 2K 1 12
2938 2K 1 454
2940 2K 3 3, 16, 90
2942 2K 2 1, 45
2944 20K 3 5, 56, 5817
2946 2K 3 2, 22, 138
2948 2K 5 31, 69, 426, 1577, 1586
2950 2K 1 21
2952 2K 4 4, 12, 420, 455
2954 2K 1 20
2956 2K 2 1, 25
2958 2K 3 3, 18, 798
2960 2K 3 25, 444, 1793
2962 20K 3 15, 34, 741
2964 2K 4 2, 27, 49, 129
2966 2K 2 3, 52
2968 2K 1 1475
2970 10K 2 10, 12
2972 2K 3 2, 32, 153
2974 20K 5 1, 11, 12, 125, 440
2976 2K 3 61, 91, 157
2978 20K 2 1, 14
2980 2K 2 1066, 1420
2982 2K 1 2
2984 2K 3 16, 64, 421
2986 2K 2 3, 6
2988 2K 2 3, 121
2990 2K 3 23, 28, 212
2992 2K 3 3, 8, 1800
2994 20K 3 4, 401, 12016
2996 2K 1 237
2998 2K 5 1, 12, 111, 378, 733
3000 2K 2 312, 366
5040 10K 3 2, 1055, 8996
40320 10K 5 2, 3, 6, 6582, 9492

Original information obtained from:
Prime Wiki
Carol / Kynea Search