Kynea primes for bases 1001 - 2000

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

Started: 2025-09-07
Last update: 2025-10-12

Compiled by Gary Barnes

Kynea primes bases <= 1000
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
1002 2K 2 1, 13
1004 2K 1 258
1006 2K 4 140, 152, 254, 1111
1008 2K 3 4, 74, 115
1010 30K 0
1012 2K 6 1, 4, 22, 697, 1821, 1954
1014 2K 2 15, 954
1016 2K 3 11, 32, 42
1018 2K 5 3, 35, 132, 760, 1481
1020 2K 4 1, 33, 205, 450
1022 2K 5 1, 3, 28, 37, 1393
1026 2K 3 7, 9, 102
1028 2K 6 1, 2, 18, 53, 75, 201
1030 2K 2 2, 288
1032 10K 6 11, 12, 33, 75, 690, 1770
1034 2K 5 1, 2, 6, 37, 1842
1036 2K 1 2
1038 30K 0
1040 2K 2 10, 45
1042 2K 4 13, 141, 303, 1872
1044 2K 3 1, 261, 1966
1046 2K 2 9, 1632
1048 2K 1 2
1050 2K 2 1, 57
1052 2K 4 62, 312, 359, 627
1054 2K 1 3
1056 2K 4 1, 369, 476, 556
1058 2K 3 5, 12, 140
1060 2K 2 70, 1362
1062 2K 1 1814
1064 2K 4 3, 11, 29, 52
1066 2K 4 2, 72, 128, 147
1068 10K 5 1, 10, 87, 316, 3358
1070 2K 1 1
1072 2K 4 1, 2, 122, 206
1074 2K 1 12
1076 2K 2 2, 12
1078 2K 2 2, 902
1080 2K 2 77, 302
1082 2K 2 144, 279
1084 2K 4 1, 11, 381, 923
1086 2K 4 13, 72, 203, 967
1088 2K 2 41, 1235
1090 2K 2 1, 21
1092 2K 3 2, 1150, 1316
1094 2K 2 21, 210
1096 2K 4 10, 106, 136, 171
1098 2K 3 82, 100, 105
1100 2K 7 1, 2, 3, 5, 24, 90, 182
1102 2K 1 5
1104 2K 4 3, 15, 25, 56
1106 2K 4 3, 50, 218, 604
1108 30K 1 14
1110 2K 4 4, 52, 64, 379
1112 2K 5 1, 3, 5, 6, 280
1114 2K 4 15, 21, 75, 81
1116 30K 2 17638, 21105
1118 2K 3 1, 57, 126
1120 2K 5 2, 3, 8, 525, 1112
1122 2K 2 3, 696
1124 2K 4 1, 216, 264, 324
1126 30K 2 19428, 21738
1128 2K 2 40, 108
1130 2K 1 15
1132 30K 2 2, 1052
1134 2K 3 42, 154, 694
1136 30K 0
1138 2K 3 10, 12, 426
1140 2K 2 1, 74
1142 2K 1 1
1144 2K 1 3
1146 2K 7 1, 3, 91, 229, 459, 795, 878
1148 2K 7 1, 4, 10, 21, 58, 88, 1667
1150 30K 0
1152 30K 5 1, 7, 87, 100, 438
1154 2K 3 2, 3, 348
1158 2K 2 5, 792
1160 2K 4 1, 25, 141, 1922
1162 2K 4 3, 115, 126, 1273
1164 2K 2 9, 17
1166 10K 1 3981
1168 2K 3 6, 108, 322
1170 2K 3 12, 37, 661
1172 2K 2 17, 34
1174 2K 1 1
1176 2K 5 1, 11, 12, 66, 180
1178 2K 2 2, 1131
1180 2K 4 16, 21, 70, 1827
1182 2K 7 2, 5, 14, 23, 27, 70, 731
1184 2K 10 2, 4, 6, 7, 16, 26, 31, 279, 286, 505
1186 2K 1 627
1188 10K 1 139
1190 2K 7 2, 6, 7, 15, 141, 256, 259
1192 2K 4 3, 5, 8, 1239
1194 2K 2 63, 70
1196 2K 3 1, 180, 901
1198 2K 4 4, 25, 307, 633
1200 2K 4 3, 11, 75, 136
1202 2K 6 2, 7, 18, 37, 50, 1266
1204 2K 1 442
1206 2K 4 3, 5, 561, 609
1208 2K 2 6, 13
1210 20K 4 1, 2, 13, 72
1212 2K 2 3, 98
1214 2K 2 12, 1408
1216 10K 3 8, 267, 2587
1218 10K 1 8623
1220 2K 5 2, 15, 249, 252, 722
1222 10K 5 1, 12, 81, 253, 712
1224 2K 3 2, 672, 684
1226 2K 3 3, 16, 416
1228 2K 2 3, 767
1230 2K 4 1, 7, 67, 355
1232 2K 4 1, 9, 125, 202
1234 2K 2 99, 1406
1236 16K 1 232
1238 2K 4 1, 464, 1796, 1900
1240 2K 4 1, 165, 176, 1010
1242 2K 2 4, 347
1244 2K 3 6, 9, 158
1246 2K 4 5, 93, 202, 1707
1248 2K 1 786
1250 2K 4 1, 352, 379, 579
1252 2K 3 1, 12, 1058
1254 2K 4 5, 14, 175, 1646
1256 2K 3 4, 5, 23
1258 2K 3 3, 14, 859
1260 2K 3 1, 5, 10
1262 2K 4 11, 26, 66, 113
1264 2K 2 1, 72
1266 2K 3 1, 2, 446
1268 2K 2 5, 37
1270 2K 1 1253
1272 2K 2 20, 1034
1274 2K 2 15, 26
1276 2K 2 6, 111
1278 2K 3 6, 7, 783
1280 2K 3 2, 5, 1546
1282 2K 1 3
1284 2K 2 201, 1895
1286 100K 4 1, 12, 169, 1094
1288 2K 7 1, 2, 6, 7, 14, 142, 1713
1290 30K 0
1292 2K 1 37
1294 2K 1 375
1298 2K 3 6, 15, 108
1300 2K 6 3, 7, 12, 36, 56, 183
1302 2K 3 2, 6, 12
1304 2K 3 14, 60, 132
1306 2K 4 1, 6, 19, 682
1308 2K 1 6
1310 2K 2 1, 98
1312 2K 3 100, 189, 810
1314 2K 3 2, 12, 108
1316 2K 3 131, 235, 871
1318 2K 1 1013
1320 2K 3 1, 60, 426
1322 2K 1 435
1324 2K 2 6, 17
1326 10K 1 2211
1328 2K 4 2, 3, 30, 49
1330 2K 6 1, 2, 5, 52, 128, 427
1332 2K 2 182, 1304
1334 30K 0
1336 2K 1 756
1338 2K 6 5, 138, 179, 334, 893, 1419
1340 2K 3 5, 192, 700
1342 2K 2 1, 2
1344 2K 6 12, 15, 354, 534, 780, 1033
1346 100K 3 116, 797, 3159
1348 2K 1 3
1350 2K 4 3, 46, 700, 1224
1352 2K 4 9, 53, 93, 163
1354 2K 2 4, 40
1356 11K 5 1, 2, 8, 626, 1874
1358 2K 7 1, 4, 14, 16, 204, 265, 614
1360 20K 1 11064
1362 2K 2 1, 1083
1364 2K 3 1, 25, 990
1366 2K 4 1, 3, 15, 127
1368 2K 1 279
1370 2K 1 24
1372 2K 2 1248, 1574
1374 2K 2 99, 1706
1376 2K 2 9, 58
1378 2K 1 1
1380 2K 2 15, 100
1382 2K 1 664
1384 30K 1 28710
1386 2K 3 5, 57, 103
1388 30K 0
1390 2K 3 1, 10, 25
1392 2K 1 1
1394 2K 5 7, 9, 408, 880, 1738
1396 2K 2 168, 522
1398 2K 5 6, 18, 25, 90, 1369
1400 2K 1 5
1402 2K 1 6
1404 10K 1 5656
1406 2K 2 17, 50
1408 2K 6 1, 2, 15, 32, 36, 72
1410 2K 1 29
1412 2K 1 1176
1414 2K 2 1, 8
1416 2K 1 6
1418 2K 2 7, 513
1420 2K 1 210
1422 2K 3 7, 47, 353
1424 2K 2 946, 1396
1426 2K 5 39, 117, 560, 1392, 1452
1428 2K 2 1, 495
1430 2K 2 2, 39
1432 30K 1 18847
1434 2K 4 1, 127, 207, 442
1436 2K 4 4, 64, 103, 294
1438 2K 1 18
1440 2K 3 13, 51, 102
1442 41K 4 1, 5, 66, 40757
1446 2K 2 1, 6
1448 2K 1 1195
1450 2K 2 15, 52
1452 30K 1 574
1454 2K 3 38, 555, 1435
1456 2K 2 4, 32
1458 2K 2 3, 5
1460 2K 6 1, 21, 37, 72, 184, 522
1462 2K 3 1, 26, 43
1464 2K 7 7, 9, 23, 120, 142, 150, 1314
1466 30K 0
1468 30K 1 4351
1470 2K 2 85, 732
1472 30K 2 9, 576
1474 2K 2 10, 439
1476 2K 5 17, 53, 410, 1098, 1370
1478 2K 1 17
1480 2K 5 5, 36, 45, 177, 375
1482 30K 6 8, 13, 14, 15, 168, 2071
1484 25K 3 1011, 9606, 12298
1486 2K 1 1046
1488 2K 1 90
1490 2K 2 1, 2
1492 2K 2 10, 50
1494 2K 4 5, 6, 156, 1402
1496 2K 1 1128
1498 2K 6 1, 27, 420, 682, 1700, 1792
1500 2K 2 2, 39
1502 2K 3 87, 100, 1566
1504 2K 3 3, 120, 1307
1506 2K 2 2, 3
1508 2K 5 3, 6, 65, 106, 903
1510 2K 3 26, 92, 540
1512 2K 2 28, 621
1514 2K 1 1176
1516 20K 2 1, 13449
1518 2K 7 3, 6, 36, 94, 198, 948, 1624
1520 2K 3 1, 130, 944
1522 2K 3 5, 10, 101
1524 20K 5 1, 61, 728, 1098, 15710
1526 2K 5 2, 15, 36, 227, 694
1528 2K 1 365
1530 2K 2 265, 657
1532 2K 3 5, 11, 14
1534 20K 5 5, 14, 26, 2147, 2665
1536 2K 1 12
1538 2K 4 42, 79, 183, 1128
1540 20K 0
1542 20K 5 93, 357, 564, 5825, 6888
1544 2K 3 1, 87, 433
1546 2K 4 14, 30, 234, 599
1548 2K 4 1, 14, 32, 101
1550 2K 3 11, 30, 125
1552 2K 2 32, 302
1554 2K 2 564, 904
1556 2K 3 240, 263, 330
1558 2K 2 9, 16
1560 2K 1 1
1562 2K 4 1, 34, 84, 331
1564 2K 3 3, 288, 777
1566 10K 1 1
1568 2K 2 5, 16
1570 20K 3 5, 1178, 2310
1572 2K 1 1083
1574 2K 4 4, 35, 40, 114
1576 2K 1 907
1578 2K 4 3, 4, 47, 1913
1580 2K 3 2, 25, 1278
1582 2K 3 7, 45, 1493
1584 2K 1 42
1586 20K 1 13684
1588 2K 3 7, 103, 124
1590 2K 3 10, 48, 86
1592 20K 1 15
1594 2K 1 1119
1596 2K 6 1, 2, 4, 6, 149, 1012
1598 2K 2 122, 1688
1602 2K 3 1, 6, 26
1604 2K 2 55, 88
1606 2K 4 11, 42, 168, 198
1608 2K 3 13, 60, 138
1610 2K 4 1, 315, 730, 1484
1612 2K 2 95, 854
1614 20K 1 2907
1616 2K 4 1, 5, 80, 815
1618 2K 5 1, 13, 89, 390, 1217
1620 2K 2 3, 693
1622 2K 3 6, 13, 1916
1624 2K 2 2, 32
1626 2K 4 114, 126, 140, 168
1628 2K 3 3, 522, 810
1630 2K 3 2, 26, 1222
1632 2K 3 37, 707, 1131
1634 2K 6 4, 6, 22, 147, 148, 1665
1636 2K 2 18, 96
1638 2K 2 1, 192
1640 2K 3 80, 108, 324
1642 2K 2 15, 94
1644 2K 3 21, 67, 949
1646 2K 5 2, 3, 20, 26, 288
1648 2K 2 5, 6
1650 20K 0
1652 2K 1 1
1654 2K 2 5, 36
1656 100K 0
1658 2K 6 3, 10, 18, 40, 737, 896
1660 2K 6 2, 6, 26, 120, 182, 400
1662 2K 2 6, 89
1664 20K 2 66, 72
1666 2K 5 20, 233, 243, 247, 1126
1668 20K 0
1670 2K 1 3
1672 2K 5 1, 2, 34, 67, 689
1674 2K 2 12, 29
1676 2K 2 6, 111
1678 2K 2 1, 2
1680 2K 1 1
1682 2K 4 17, 24, 44, 680
1684 10K 1 5605
1686 2K 3 1, 39, 494
1688 2K 3 2, 158, 432
1690 20K 1 4
1692 2K 5 1, 7, 25, 345, 366
1694 2K 2 1, 12
1696 2K 2 2, 165
1698 2K 2 4, 321
1700 2K 3 1, 13, 47
1702 2K 5 1, 7, 31, 183, 266
1704 2K 3 9, 10, 315
1706 10K 1 378
1708 2K 3 9, 531, 794
1710 2K 1 26
1712 2K 1 934
1714 2K 4 1, 6, 198, 850
1716 2K 2 1, 2
1718 2K 1 184
1720 2K 2 1, 888
1722 2K 1 2
1724 20K 2 42, 336
1726 20K 5 1, 6, 204, 4221, 13105
1730 2K 4 6, 84, 223, 1727
1732 2K 1 1067
1734 2K 1 105
1736 2K 3 1, 9, 17
1738 2K 2 9, 417
1740 2K 2 1, 16
1742 2K 5 2, 5, 17, 86, 1384
1744 2K 2 13, 128
1746 2K 3 4, 6, 30
1748 2K 2 1, 56
1750 2K 2 1, 5
1752 2K 1 3
1754 2K 3 64, 66, 150
1756 2K 1 47
1758 2K 2 2, 4
1760 10K 1 6210
1762 2K 3 2, 8, 207
1766 2K 4 5, 11, 24, 1613
1768 2K 2 15, 46
1770 2K 5 2, 5, 9, 31, 69
1772 2K 4 2, 14, 756, 795
1774 10K 2 4, 2249
1776 2K 3 8, 12, 27
1778 2K 5 2, 3, 134, 198, 1456
1780 2K 2 2, 36
1782 2K 1 1
1784 2K 4 1, 44, 119, 386
1786 2K 2 2, 5
1788 20K 0
1790 2K 3 2, 36, 170
1792 2K 2 5, 54
1794 2K 3 11, 14, 1824
1796 2K 2 1, 9
1798 2K 5 4, 9, 11, 20, 244
1800 2K 2 104, 180
1802 2K 2 22, 538
1804 2K 2 175, 1743
1806 10K 3 1, 2, 18
1808 2K 2 20, 68
1810 2K 6 7, 10, 15, 16, 499, 520
1812 2K 2 32, 96
1814 2K 2 6, 270
1816 2K 1 534
1818 2K 4 1, 2, 7, 8
1820 2K 2 5, 665
1822 2K 4 6, 408, 1143, 1868
1824 2K 1 1069
1826 2K 4 1, 5, 11, 1508
1828 2K 1 34
1830 2K 1 4
1832 2K 5 50, 60, 115, 187, 559
1834 2K 3 2, 271, 1006
1836 2K 4 14, 17, 125, 1205
1838 2K 2 1, 808
1840 2K 3 1, 4, 75
1842 2K 6 15, 64, 159, 208, 1612, 1992
1844 2K 2 141, 363
1846 2K 2 267, 276
1848 2K 3 1, 5, 6
1850 2K 2 26, 33
1852 20K 0
1854 2K 2 2, 1376
1856 2K 2 63, 1016
1858 2K 5 18, 89, 90, 124, 1157
1860 2K 4 1, 2, 3, 1873
1862 2K 6 5, 25, 43, 50, 126, 310
1864 2K 4 6, 12, 114, 506
1866 2K 2 1, 79
1868 2K 3 8, 9, 22
1870 2K 1 11
1872 2K 2 17, 946
1874 2K 2 1, 153
1876 2K 5 2, 41, 402, 659, 953
1878 2K 2 9, 78
1880 2K 1 12
1882 2K 3 6, 16, 1393
1884 2K 6 1, 3, 95, 150, 494, 598
1886 2K 6 4, 23, 58, 123, 478, 910
1888 2K 1 3
1890 2K 2 20, 388
1892 2K 2 27, 29
1894 2K 3 1, 12, 36
1896 2K 2 1, 7
1898 2K 1 4
1900 2K 2 11, 23
1902 2K 3 15, 20, 1298
1904 2K 3 2, 16, 1772
1906 2K 6 2, 3, 15, 23, 71, 158
1908 2K 4 1, 9, 226, 1702
1910 2K 4 1, 2, 104, 480
1912 2K 3 1, 20, 97
1914 2K 2 6, 47
1916 2K 1 164
1918 2K 5 2, 5, 549, 1488, 1619
1920 2K 1 2
1922 2K 3 1, 3, 88
1924 2K 5 1, 42, 654, 1537, 1597
1926 2K 1 14
1928 10K 1 4870
1930 2K 3 1, 126, 1218
1932 2K 1 171
1934 2K 1 107
1938 2K 4 2, 29, 302, 309
1940 2K 5 3, 6, 20, 57, 131
1942 2K 1 1827
1944 2K 1 24
1946 2K 7 1, 2, 5, 43, 64, 69, 95
1948 2K 1 2
1950 20K 1 8442
1952 2K 4 1, 3, 993, 1852
1954 2K 2 11, 1776
1956 2K 2 21, 911
1958 2K 2 96, 192
1960 2K 2 50, 133
1962 20K 0
1964 2K 4 1, 3, 31, 211
1966 2K 2 15, 753
1968 100K 4 1, 36, 29656, 58533
1970 2K 2 276, 436
1972 2K 4 211, 284, 1179, 1746
1974 2K 5 1, 5, 6, 8, 14
1976 2K 1 50
1978 2K 1 1
1980 2K 5 3, 5, 6, 286, 780
1982 2K 3 52, 74, 126
1984 2K 1 540
1986 20K 2 222, 3738
1988 2K 6 1, 11, 12, 243, 370, 1789
1990 2K 3 30, 131, 731
1992 2K 1 472
1994 2K 5 3, 5, 27, 114, 854
1996 2K 3 1, 3, 666
1998 2K 1 15
2000 2K 4 1, 2, 27, 284

Original information obtained from:
Prime Wiki
Carol / Kynea Search