Kynea 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

Kynea primes bases <= 1000
Kynea primes bases 1001-2000
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
2002 2K 6 6, 26, 201, 299, 385, 687
2004 2K 2 15, 144
2006 2K 5 12, 19, 66, 1204, 1717
2008 2K 5 3, 18, 30, 41, 78
2010 50K 2 3, 30505
2012 2K 2 4, 689
2014 2K 1 19
2016 2K 2 29, 608
2018 27K 2 2, 3143
2020 2K 1 1
2022 2K 2 351, 697
2024 2K 4 5, 276, 411, 424
2026 20K 1 5526
2028 2K 1 27
2030 2K 6 1, 7, 108, 277, 309, 424
2032 2K 1 1160
2034 20K 1 1
2036 2K 1 1
2038 2K 5 5, 10, 12, 66, 604
2040 20K 1 442
2042 2K 1 1
2044 2K 3 15, 50, 296
2046 2K 3 21, 336, 1011
2050 2K 2 2, 20
2052 2K 8 1, 3, 10, 77, 113, 1048, 1608, 1710
2054 2K 1 40
2056 2K 2 1, 115
2058 2K 5 1, 3, 231, 989, 1977
2060 2K 1 162
2062 2K 1 1029
2064 20K 0
2066 2K 2 2, 132
2068 2K 1 1551
2070 2K 2 9, 253
2072 2K 5 1, 17, 25, 138, 531
2074 2K 4 2, 3, 275, 996
2076 10K 3 1, 184, 2217
2078 2K 4 25, 143, 317, 1891
2080 2K 6 1, 2, 6, 20, 23, 30
2082 2K 3 4, 29, 148
2084 2K 4 2, 63, 75, 110
2086 2K 4 1, 2, 8, 288
2088 2K 4 2, 5, 23, 62
2090 2K 3 1, 57, 1588
2092 2K 4 1, 16, 30, 83
2094 2K 4 1, 16, 31, 58
2096 2K 2 4, 5
2098 2K 1 6
2100 2K 3 1, 47, 1252
2102 2K 2 63, 111
2104 10K 2 1, 6
2106 2K 2 1, 109
2108 2K 3 1, 4, 50
2110 2K 4 3, 5, 234, 413
2112 2K 6 1, 8, 9, 15, 44, 1327
2114 2K 1 8
2118 2K 3 25, 31, 220
2120 2K 4 2, 317, 394, 458
2122 2K 1 81
2124 2K 1 660
2126 20K 3 2, 15, 1543
2128 20K 4 1, 170, 891, 1504
2130 2K 1 8
2132 20K 1 1
2134 2K 3 3, 10, 1090
2136 2K 4 1, 6, 7, 104
2138 2K 3 28, 39, 1121
2140 10K 2 20, 26
2142 2K 1 831
2144 2K 5 3, 77, 156, 482, 1182
2146 20K 0
2148 2K 2 17, 724
2150 2K 3 1, 3, 273
2152 2K 4 3, 9, 47, 525
2154 2K 4 2, 24, 33, 120
2156 2K 2 3, 345
2158 2K 4 2, 14, 222, 327
2160 2K 2 10, 58
2162 2K 2 1, 524
2164 2K 5 10, 74, 128, 132, 344
2166 2K 1 27
2168 20K 3 31, 10026, 12879
2170 2K 4 1, 2, 875, 1238
2172 2K 1 12
2174 2K 2 106, 744
2176 2K 3 1, 6, 73
2178 2K 4 1, 2, 3, 543
2180 2K 3 5, 6, 10
2182 20K 4 1, 7, 8, 50
2184 2K 2 45, 60
2186 2K 2 2, 1284
2188 2K 1 51
2190 2K 2 49, 1824
2192 2K 3 8, 36, 47
2194 2K 2 15, 1245
2196 2K 2 110, 198
2198 2K 4 3, 10, 91, 425
2200 2K 3 5, 6, 200
2202 2K 4 15, 49, 280, 1024
2204 20K 3 6, 11, 1146
2206 2K 3 519, 1181, 1701
2208 2K 2 3, 11
2210 2K 4 1, 18, 1110, 1326
2212 2K 3 9, 53, 108
2214 2K 2 35, 89
2216 2K 1 58
2218 2K 4 5, 114, 647, 828
2220 2K 4 2, 15, 169, 204
2222 2K 3 17, 135, 334
2224 2K 2 1, 97
2226 2K 5 1, 2, 3, 79, 107
2228 2K 2 2, 26
2230 2K 1 13
2232 2K 2 2, 316
2234 2K 2 7, 97
2236 2K 1 147
2238 2K 1 1
2240 2K 6 1, 8, 13, 61, 101, 383
2242 2K 4 45, 65, 113, 429
2244 2K 1 46
2246 2K 1 1
2248 2K 1 7
2250 20K 0
2252 2K 3 50, 122, 181
2254 2K 2 2, 5
2256 2K 1 3
2258 2K 1 4
2260 2K 5 1, 4, 8, 15, 119
2262 2K 5 3, 53, 110, 154, 271
2264 20K 1 10098
2266 20K 2 195, 5906
2268 2K 6 1, 30, 54, 141, 286, 376
2270 2K 3 795, 1274, 1500
2272 2K 3 1, 9, 415
2274 2K 3 5, 13, 69
2276 2K 4 1, 29, 113, 903
2278 2K 6 18, 46, 99, 129, 233, 345
2280 20K 0
2282 2K 2 1, 385
2284 2K 3 18, 275, 1478
2286 2K 5 1, 6, 433, 1416, 1590
2288 2K 1 9
2290 20K 6 3, 4, 13, 4114, 11510, 14208
2292 2K 2 6, 258
2294 2K 3 87, 350, 481
2296 2K 7 1, 2, 6, 10, 26, 140, 1485
2298 20K 0
2300 20K 0
2302 2K 6 1, 3, 84, 216, 292, 323
2306 2K 1 29
2308 20K 4 1, 7, 198, 648
2310 2K 3 3, 4, 1252
2312 10K 3 2, 164, 1284
2314 2K 2 1, 52
2316 2K 3 43, 148, 387
2318 2K 5 12, 88, 94, 325, 375
2320 2K 2 15, 78
2322 2K 2 2, 67
2324 2K 3 28, 39, 237
2326 2K 1 833
2328 2K 2 3, 6
2330 20K 0
2332 2K 3 109, 156, 1089
2334 20K 0
2336 2K 3 1, 7, 432
2338 2K 2 204, 759
2340 2K 2 14, 1665
2342 20K 1 13267
2344 2K 4 1, 10, 239, 635
2346 2K 3 9, 12, 1930
2348 2K 2 4, 149
2350 2K 1 3
2352 2K 3 4, 8, 12
2354 2K 1 20
2356 2K 2 45, 1948
2358 2K 4 1, 28, 98, 1735
2360 2K 4 7, 182, 286, 1113
2362 2K 2 53, 1422
2364 2K 2 151, 1646
2366 2K 4 7, 109, 370, 625
2368 2K 2 2, 29
2370 2K 1 12
2372 2K 2 4, 171
2374 2K 3 1, 200, 214
2376 2K 1 54
2378 2K 1 2
2380 2K 4 1, 435, 521, 1723
2382 10K 2 2498, 4175
2384 10K 3 4, 609, 3411
2386 2K 3 24, 112, 1034
2388 2K 3 1, 4, 6
2390 2K 3 36, 69, 402
2392 2K 3 1, 8, 384
2394 2K 5 3, 4, 9, 54, 140
2396 2K 2 11, 161
2398 20K 4 4, 1567, 5485, 16722
2400 10K 7 1, 2, 46, 265, 4589, 7021, 9993
2402 2K 2 156, 366
2404 10K 1 77
2406 2K 5 2, 3, 6, 26, 153
2408 2K 2 7, 40
2410 2K 3 2, 3, 113
2412 2K 3 1, 3, 517
2414 2K 5 3, 21, 41, 87, 647
2416 2K 1 625
2418 2K 2 51, 57
2420 2K 5 1, 2, 21, 66, 1916
2422 2K 2 1, 10
2424 2K 1 827
2426 2K 2 7, 193
2428 2K 1 68
2430 2K 3 1, 11, 104
2432 2K 3 3, 6, 30
2434 2K 4 8, 66, 73, 434
2436 2K 1 590
2438 20K 1 2
2440 2K 3 3, 7, 375
2442 2K 2 33, 455
2444 2K 3 34, 104, 287
2446 2K 2 4, 190
2448 2K 4 1, 3, 25, 98
2450 2K 5 2, 21, 225, 423, 1344
2452 2K 2 3, 770
2454 2K 1 1
2456 2K 3 21, 425, 561
2458 2K 1 77
2460 2K 2 3, 6
2462 2K 1 74
2464 2K 1 1
2466 2K 2 35, 908
2468 2K 5 1, 9, 76, 223, 1272
2470 2K 1 5
2472 2K 2 3, 332
2474 20K 1 10995
2476 2K 3 42, 169, 1524
2478 2K 3 2, 6, 275
2480 20K 3 9, 15, 13715
2482 20K 1 18735
2484 2K 4 1, 207, 344, 866
2486 2K 3 41, 298, 562
2488 2K 1 310
2490 2K 1 1
2492 2K 4 2, 3, 6, 1090
2494 2K 1 182
2496 2K 1 3
2498 2K 4 33, 39, 251, 535
2502 2K 1 1329
2504 2K 4 2, 20, 198, 717
2506 2K 2 1, 43
2508 2K 2 38, 107
2510 2K 3 1, 76, 489
2512 2K 7 1, 5, 97, 362, 759, 1193, 1289
2514 2K 5 1, 7, 10, 13, 933
2516 2K 2 4, 159
2518 20K 0
2520 2K 2 3, 8
2522 2K 5 2, 6, 101, 710, 819
2524 10K 2 28, 2208
2526 2K 2 2, 37
2528 2K 2 1, 142
2530 20K 0
2532 2K 3 1, 271, 381
2534 20K 0
2536 2K 3 56, 795, 1610
2538 2K 2 10, 1081
2540 2K 1 1
2542 2K 4 1, 19, 132, 1782
2544 2K 2 34, 42
2546 2K 1 18
2548 2K 5 1, 3, 7, 44, 199
2550 2K 3 38, 1346, 1644
2552 2K 3 4, 61, 1455
2554 2K 3 1, 2, 182
2556 2K 1 57
2558 2K 2 22, 285
2560 20K 1 900
2562 2K 6 1, 2, 5, 12, 200, 995
2564 2K 4 5, 17, 62, 1310
2566 2K 3 114, 175, 535
2568 2K 4 1, 2, 290, 1676
2570 2K 2 6, 486
2572 2K 2 3, 47
2574 10K 2 13, 98
2576 2K 7 1, 2, 35, 196, 717, 1144, 1514
2578 2K 1 168
2580 2K 1 55
2582 2K 4 3, 4, 6, 342
2584 2K 2 1, 405
2586 20K 0
2588 20K 1 1
2590 2K 5 1, 2, 33, 89, 383
2592 2K 4 2, 9, 287, 312
2594 2K 5 16, 28, 271, 310, 1380
2596 2K 2 1, 6
2598 2K 2 1, 4
2600 2K 3 3, 130, 420
2602 2K 6 1, 2, 7, 20, 87, 145
2604 2K 2 135, 191
2606 20K 0
2608 2K 1 12
2610 10K 2 1, 8
2612 2K 2 4, 8
2614 10K 1 3383
2616 10K 3 3, 795, 2457
2618 2K 4 1, 29, 207, 976
2620 2K 2 209, 261
2622 10K 5 1, 12, 30, 100, 450
2624 10K 1 2702
2626 10K 1 4436
2628 2K 2 558, 748
2630 2K 1 2
2632 2K 5 3, 10, 15, 351, 1065
2634 100K 2 73796, 88719
2636 2K 1 1
2638 2K 7 2, 14, 23, 46, 462, 1053, 1786
2640 2K 2 79, 1960
2642 2K 1 132
2644 2K 2 8, 282
2646 20K 4 1, 2, 33, 702
2648 2K 2 20, 1157
2650 20K 0
2652 2K 5 1, 2, 7, 10, 86
2654 2K 1 2
2656 2K 2 16, 293
2658 10K 2 2, 39
2660 10K 1 3979
2662 2K 3 2, 5, 56
2664 2K 4 1, 10, 118, 124
2666 2K 2 1, 124
2668 2K 2 20, 1772
2670 2K 2 42, 113
2672 2K 2 2, 20
2674 2K 1 8
2676 2K 2 11, 435
2678 20K 2 1, 225
2680 2K 6 1, 2, 10, 15, 50, 107
2682 2K 2 78, 1708
2684 2K 2 5, 366
2686 2K 3 12, 42, 1112
2688 20K 0
2690 2K 1 2
2692 2K 2 90, 1870
2694 2K 5 2, 242, 470, 944, 1118
2696 2K 5 2, 35, 59, 330, 372
2698 2K 1 51
2700 2K 3 1, 2, 50
2702 2K 1 1
2706 2K 2 1, 7
2708 2K 5 2, 3, 52, 77, 160
2710 2K 1 50
2712 2K 2 15, 102
2714 2K 3 1, 12, 25
2716 2K 4 1, 10, 50, 790
2718 2K 3 9, 14, 1235
2720 2K 3 1, 177, 1168
2722 2K 5 3, 4, 33, 343, 1102
2724 2K 3 1, 23, 25
2726 2K 3 35, 58, 324
2728 2K 4 1, 6, 14, 73
2730 2K 4 2, 42, 124, 200
2732 2K 2 6, 27
2734 2K 3 1, 3, 343
2736 2K 5 1, 18, 245, 610, 796
2738 2K 4 1, 6, 15, 1267
2740 2K 4 6, 39, 210, 522
2742 20K 0
2746 2K 4 2, 45, 452, 537
2748 2K 3 1, 33, 109
2750 2K 5 2, 53, 64, 414, 526
2752 2K 2 17, 27
2754 2K 3 11, 12, 82
2756 2K 3 2, 9, 27
2758 2K 3 1, 5, 35
2760 2K 1 98
2762 2K 3 22, 94, 1450
2764 2K 4 27, 91, 627, 644
2766 2K 1 3
2768 20K 1 5
2770 20K 0
2772 2K 2 1, 63
2774 20K 1 10247
2776 2K 2 27, 397
2778 2K 3 1, 2, 1349
2780 2K 1 69
2782 20K 3 23, 52, 894
2784 2K 7 1, 3, 51, 174, 339, 1071, 1574
2786 2K 4 125, 137, 702, 965
2788 2K 4 2, 3, 36, 935
2790 2K 1 127
2792 2K 3 37, 89, 494
2794 20K 4 1, 2, 10, 14728
2796 2K 4 9, 29, 370, 1895
2798 20K 5 15, 80, 345, 1776, 17901
2800 2K 1 20
2802 20K 3 498, 938, 1959
2804 20K 1 868
2806 2K 1 1
2808 2K 4 1, 12, 584, 1547
2810 2K 2 190, 1390
2812 2K 1 26
2814 2K 2 12, 1626
2816 2K 1 2
2818 2K 3 4, 15, 420
2820 2K 7 1, 5, 11, 63, 303, 710, 1180
2822 2K 2 3, 1682
2824 2K 1 117
2826 2K 2 7, 50
2828 2K 3 3, 490, 542
2830 20K 0
2832 2K 1 30
2834 2K 4 6, 40, 42, 1814
2836 2K 3 1, 3, 185
2838 2K 2 186, 316
2840 2K 3 2, 3, 111
2842 2K 5 8, 29, 79, 121, 311
2844 2K 2 24, 384
2846 10K 1 145
2848 2K 5 1, 9, 59, 636, 829
2850 2K 2 4, 372
2852 2K 1 108
2854 2K 3 1, 97, 98
2856 2K 1 20
2858 2K 3 2, 291, 576
2860 2K 1 12
2862 2K 4 9, 121, 180, 265
2864 2K 1 2
2866 2K 1 21
2868 2K 2 1, 3
2870 2K 4 1, 22, 118, 1221
2872 2K 2 5, 8
2874 2K 1 1776
2876 2K 2 12, 93
2878 2K 5 44, 59, 99, 325, 765
2880 2K 1 1594
2882 2K 4 1, 24, 57, 170
2884 2K 3 4, 14, 44
2886 20K 1 19782
2888 2K 1 1
2890 2K 2 7, 501
2892 2K 1 154
2894 2K 5 30, 53, 198, 1071, 1906
2896 2K 4 1, 3, 60, 206
2898 2K 1 13
2900 2K 3 5, 6, 9
2902 2K 2 10, 103
2904 20K 5 5, 8, 9, 38, 3400
2906 2K 4 13, 29, 33, 76
2908 2K 2 3, 9
2910 2K 2 1, 2
2912 2K 3 6, 8, 13
2914 2K 4 2, 113, 285, 411
2918 20K 0
2920 2K 3 2, 6, 688
2922 20K 2 11, 35
2924 20K 2 1, 9
2926 2K 3 5, 11, 20
2928 2K 4 17, 20, 299, 884
2930 2K 4 1, 49, 1152, 1881
2932 2K 3 1, 2, 41
2934 2K 1 2
2936 2K 2 48, 65
2938 2K 2 31, 36
2940 2K 3 1, 2, 48
2942 2K 2 3, 551
2944 20K 0
2946 2K 2 20, 118
2948 2K 2 66, 128
2950 2K 2 57, 130
2952 2K 3 2, 207, 1920
2954 2K 3 1, 129, 1487
2956 2K 5 5, 24, 41, 80, 839
2958 2K 1 4
2960 2K 2 25, 367
2962 20K 0
2964 2K 2 15, 196
2966 2K 1 54
2968 2K 2 3, 12
2970 10K 1 2993
2972 2K 2 1, 169
2974 20K 0
2976 2K 2 1, 1673
2978 20K 0
2980 2K 1 2
2982 2K 5 4, 78, 82, 156, 606
2984 2K 1 18
2986 2K 1 237
2988 2K 2 120, 990
2990 2K 2 2, 53
2992 2K 3 6, 84, 102
2994 20K 0
2996 2K 4 1, 4, 30, 70
2998 2K 1 84
3000 2K 1 180
5040 10K 4 18, 54, 246, 8459
40320 10K 5 1, 22, 28, 241, 260

Original information obtained from:
Prime Wiki
Carol / Kynea Search