Carol 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

Carol primes bases <= 1000
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
1002 2K 2 2, 3
1004 2K 2 1, 27
1006 2K 4 3, 16, 18, 786
1008 2K 5 4, 77, 110, 1248, 1667
1010 30K 2 6, 25
1012 2K 1 14
1014 2K 5 1, 4, 7, 19, 1014
1016 2K 4 12, 299, 1375, 1426
1018 2K 6 2, 3, 9, 15, 597, 1531
1020 2K 3 574, 624, 970
1022 2K 5 1, 17, 62, 429, 1553
1026 2K 2 18, 33
1028 2K 2 4, 166
1030 2K 3 1, 4, 6
1032 10K 1 2169
1034 2K 1 1440
1036 2K 7 1, 9, 12, 20, 240, 377, 1197
1038 30K 1 2107
1040 2K 1 20
1042 2K 3 10, 273, 1511
1044 2K 1 2
1046 2K 2 1, 14
1048 2K 1 108
1050 2K 2 25, 267
1052 2K 4 1, 6, 42, 520
1054 2K 1 135
1056 2K 3 18, 118, 578
1058 2K 5 1, 2, 27, 35, 195
1060 2K 3 63, 396, 1880
1062 2K 1 5
1064 2K 6 3, 5, 18, 66, 130, 1995
1066 2K 2 6, 22
1068 10K 1 2072
1070 2K 4 1, 15, 382, 685
1072 2K 1 1
1074 2K 3 1, 2, 44
1076 2K 1 21
1078 2K 3 2, 5, 261
1080 2K 5 19, 48, 537, 1008, 1609
1082 2K 2 65, 71
1084 2K 5 4, 32, 40, 57, 408
1086 2K 2 1, 1201
1088 2K 2 9, 813
1090 2K 1 3
1092 2K 3 1, 5, 821
1094 2K 1 13
1096 2K 2 5, 230
1098 2K 2 3, 37
1100 2K 3 2, 4, 229
1102 2K 4 1, 36, 114, 127
1104 2K 2 6, 15
1106 2K 5 2, 11, 39, 182, 672
1108 30K 0
1110 2K 2 36, 179
1112 2K 1 10
1114 2K 7 1, 3, 4, 319, 434, 826, 1341
1116 30K 7 9, 85, 104, 1554, 2868, 2910, 9481
1118 2K 3 5, 63, 88
1120 2K 4 1, 7, 21, 67
1122 2K 2 153, 1416
1124 2K 1 117
1126 30K 7 1, 2, 33, 51, 66, 228, 3037
1128 2K 3 27, 56, 279
1130 2K 2 2, 18
1132 30K 1 20865
1134 2K 4 2, 13, 14, 1838
1136 30K 3 54, 2472, 15298
1138 2K 1 14
1140 2K 1 16
1142 2K 3 1, 200, 318
1144 2K 2 1, 37
1146 2K 1 66
1148 2K 3 1, 8, 10
1150 30K 5 1, 12, 273, 1191, 4464
1152 30K 1 16769
1154 2K 2 1, 7
1158 2K 4 1, 8, 43, 66
1160 2K 2 3, 9
1162 2K 6 1, 70, 125, 126, 740, 1687
1164 2K 2 12, 15
1166 10K 3 2, 5445, 5712
1168 2K 1 36
1170 2K 4 75, 121, 381, 420
1172 2K 4 2, 3, 6, 14
1174 2K 2 120, 837
1176 2K 6 1, 2, 7, 112, 212, 1672
1178 2K 4 1, 4, 117, 426
1180 2K 3 62, 72, 597
1182 2K 1 7
1184 2K 6 4, 15, 55, 56, 149, 410
1186 2K 7 3, 21, 54, 104, 254, 1272, 1899
1188 10K 3 2145, 3784, 3975
1190 2K 2 352, 1196
1192 2K 1 34
1194 2K 3 117, 120, 711
1196 2K 3 4, 20, 27
1198 2K 3 1, 6, 59
1200 2K 1 3
1202 2K 1 832
1204 2K 1 17
1206 2K 3 3, 61, 274
1208 2K 3 3, 9, 548
1210 20K 1 15112
1212 2K 1 1
1214 2K 1 397
1216 10K 1 2302
1218 10K 5 2, 4, 5, 6, 19
1220 2K 2 30, 76
1222 10K 1 8745
1224 2K 10 1, 6, 13, 24, 25, 64, 188, 197, 270, 453
1226 2K 5 12, 94, 185, 251, 534
1228 2K 1 129
1230 2K 1 65
1232 2K 5 1, 2, 7, 8, 118
1234 2K 3 1, 94, 1683
1236 16K 1 10646
1238 2K 2 2, 876
1240 2K 4 1, 111, 175, 518
1242 2K 2 1, 896
1244 2K 2 12, 436
1246 2K 2 3, 28
1248 2K 2 3, 4
1250 2K 3 2, 57, 348
1252 2K 4 1, 9, 25, 32
1254 2K 3 1, 1218, 1686
1256 2K 4 2, 3, 21, 228
1258 2K 6 39, 155, 245, 749, 843, 1260
1260 2K 4 5, 20, 121, 165
1262 2K 2 1, 165
1264 2K 3 41, 56, 425
1266 2K 6 1, 3, 4, 54, 152, 813
1268 2K 4 1, 132, 651, 1530
1270 2K 2 444, 680
1272 2K 2 30, 45
1274 2K 1 342
1276 2K 3 63, 118, 1077
1278 2K 1 1145
1280 2K 6 2, 3, 43, 176, 272, 400
1282 2K 2 358, 404
1284 2K 2 3, 224
1286 100K 0
1288 2K 3 1, 2, 160
1290 30K 4 1, 495, 9598, 22045
1292 2K 2 11, 41
1294 2K 3 3, 53, 98
1298 2K 3 1, 120, 312
1300 2K 3 4, 10, 65
1302 2K 1 231
1304 2K 5 4, 75, 195, 297, 889
1306 2K 4 2, 9, 42, 236
1308 2K 2 1, 9
1310 2K 4 66, 78, 391, 459
1312 2K 4 1, 2, 295, 799
1314 2K 2 3, 29
1316 2K 1 110
1318 2K 1 1749
1320 2K 3 168, 255, 1548
1322 2K 4 1, 21, 621, 1150
1324 2K 3 2, 3, 4
1326 10K 4 12, 39, 48, 2424
1328 2K 1 46
1330 2K 4 12, 20, 27, 119
1332 2K 3 1, 16, 43
1334 30K 3 5, 74, 444
1336 2K 3 59, 387, 516
1338 2K 2 2, 547
1340 2K 2 13, 18
1342 2K 4 4, 143, 334, 654
1344 2K 1 1
1346 100K 0
1348 2K 1 741
1350 2K 4 2, 10, 422, 488
1352 2K 4 3, 4, 39, 549
1354 2K 3 39, 54, 57
1356 11K 1 2554
1358 2K 2 1, 405
1360 20K 5 1, 43, 7302, 12555, 15288
1362 2K 1 65
1364 2K 3 1, 109, 315
1366 2K 5 1, 8, 39, 1087, 1436
1368 2K 3 1, 69, 876
1370 2K 1 3
1372 2K 3 3, 4, 1740
1374 2K 3 160, 456, 618
1376 2K 4 2, 21, 147, 1098
1378 2K 4 19, 43, 227, 619
1380 2K 2 1, 1466
1382 2K 1 355
1384 30K 3 5, 196, 204
1386 2K 4 4, 64, 604, 725
1388 30K 1 7458
1390 2K 2 102, 272
1392 2K 4 1, 4, 6, 597
1394 2K 4 1, 43, 59, 67
1396 2K 1 840
1398 2K 3 5, 6, 52
1400 2K 1 7
1402 2K 5 10, 90, 519, 1105, 1915
1404 10K 5 3, 56, 71, 75, 1853
1406 2K 2 2, 3
1408 2K 6 2, 31, 93, 312, 338, 1166
1410 2K 5 1, 2, 235, 915, 1021
1412 2K 1 310
1414 2K 1 154
1416 2K 4 1, 3, 30, 139
1418 2K 2 9, 768
1420 2K 4 6, 30, 781, 1965
1422 2K 3 2, 21, 236
1424 2K 3 24, 60, 87
1426 2K 2 5, 10
1428 2K 2 22, 29
1430 2K 1 1
1432 30K 1 1578
1434 2K 9 4, 15, 56, 59, 184, 462, 748, 830, 1714
1436 2K 4 1, 10, 11, 705
1438 2K 1 1500
1440 2K 1 5
1442 41K 0
1446 2K 2 5, 20
1448 2K 5 1, 18, 25, 240, 1116
1450 2K 4 126, 154, 156, 646
1452 30K 0
1454 2K 1 6
1456 2K 1 19
1458 2K 1 541
1460 2K 1 65
1462 2K 4 1, 5, 27, 34
1464 2K 2 1, 2
1466 30K 1 4249
1468 30K 0
1470 2K 1 9
1472 30K 0
1474 2K 1 2
1476 2K 2 7, 363
1478 2K 2 2, 20
1480 2K 1 111
1482 30K 0
1484 25K 2 581, 10128
1486 2K 2 3, 150
1488 2K 2 14, 548
1490 2K 3 8, 168, 236
1492 2K 3 1, 146, 383
1494 2K 2 9, 20
1496 2K 4 15, 27, 382, 1097
1498 2K 1 4
1500 2K 2 1, 190
1502 2K 3 2, 14, 905
1504 2K 3 1303, 1308, 1743
1506 2K 2 4, 196
1508 2K 3 24, 38, 1332
1510 2K 4 4, 6, 34, 125
1512 2K 4 6, 29, 145, 493
1514 2K 6 3, 37, 520, 1363, 1623, 1980
1516 20K 0
1518 2K 5 1, 3, 34, 514, 1010
1520 2K 4 5, 19, 26, 52
1522 2K 1 1
1524 20K 0
1526 2K 6 1, 2, 6, 13, 106, 334
1528 2K 4 3, 4, 42, 51
1530 2K 2 36, 257
1532 2K 4 3, 119, 166, 781
1534 20K 0
1536 2K 1 1633
1538 2K 1 9
1540 20K 5 5, 114, 181, 374, 4484
1542 20K 0
1544 2K 2 2, 62
1546 2K 6 1, 2, 3, 5, 104, 116
1548 2K 2 31, 388
1550 2K 2 1, 216
1552 2K 2 6, 996
1554 2K 3 26, 52, 216
1556 2K 2 4, 31
1558 2K 2 51, 270
1560 2K 4 4, 27, 40, 53
1562 2K 2 1, 53
1564 2K 3 1, 8, 1527
1566 10K 1 8188
1568 2K 2 1, 4
1570 20K 0
1572 2K 2 11, 62
1574 2K 2 2, 26
1576 2K 2 3, 1100
1578 2K 2 18, 763
1580 2K 3 3, 34, 233
1582 2K 4 2, 4, 8, 555
1584 2K 3 9, 19, 72
1586 20K 3 2, 8, 386
1588 2K 2 13, 867
1590 2K 4 5, 155, 355, 369
1592 20K 0
1594 2K 1 46
1596 2K 1 305
1598 2K 3 1, 10, 16
1602 2K 4 1, 49, 354, 1038
1604 2K 7 1, 10, 17, 18, 32, 186, 1614
1606 2K 1 237
1608 2K 1 45
1610 2K 4 2, 15, 70, 383
1612 2K 1 1
1614 20K 1 13641
1616 2K 5 3, 44, 960, 1059, 1231
1618 2K 4 1, 618, 1273, 1843
1620 2K 3 1, 2, 74
1622 2K 1 540
1624 2K 1 3
1626 2K 3 81, 334, 1639
1628 2K 1 50
1630 2K 2 61, 139
1632 2K 3 23, 37, 1460
1634 2K 4 3, 21, 37, 606
1636 2K 1 491
1638 2K 7 2, 9, 25, 160, 317, 660, 1233
1640 2K 4 1, 186, 229, 1723
1642 2K 2 2, 32
1644 2K 2 5, 99
1646 2K 2 70, 432
1648 2K 2 2, 660
1650 20K 4 3, 5, 3219, 13876
1652 2K 5 14, 49, 442, 878, 1257
1654 2K 3 1, 294, 510
1656 100K 0
1658 2K 5 2, 25, 142, 982, 1053
1660 2K 3 12, 101, 167
1662 2K 2 7, 1257
1664 20K 1 13776
1666 2K 2 11, 26
1668 20K 2 339, 1305
1670 2K 2 2, 5
1672 2K 3 2, 11, 14
1674 2K 2 1, 15
1676 2K 2 13, 14
1678 2K 5 5, 52, 83, 516, 1380
1680 2K 3 1, 429, 864
1682 2K 4 1, 39, 102, 120
1684 10K 3 2, 8, 17
1686 2K 4 4, 561, 951, 1334
1688 2K 5 1, 2, 7, 12, 397
1690 20K 0
1692 2K 1 174
1694 2K 2 1, 2
1696 2K 1 1
1698 2K 2 2, 1170
1700 2K 3 2, 33, 566
1702 2K 4 1, 3, 60, 95
1704 2K 2 1, 2
1706 10K 1 8028
1708 2K 2 183, 720
1710 2K 2 4, 7
1712 2K 1 140
1714 2K 2 859, 1627
1716 2K 3 1, 3, 553
1718 2K 4 1, 2, 50, 1064
1720 2K 2 3, 366
1722 2K 1 1
1724 20K 0
1726 20K 0
1730 2K 2 1095, 1653
1732 2K 2 384, 519
1734 2K 4 3, 102, 1011, 1889
1736 2K 3 8, 29, 104
1738 2K 2 1, 3
1740 2K 2 2, 329
1742 2K 3 1, 16, 328
1744 2K 1 26
1746 2K 2 170, 806
1748 2K 2 28, 684
1750 2K 5 1, 2, 123, 175, 765
1752 2K 3 1, 1182, 1522
1754 2K 2 3, 596
1756 2K 1 176
1758 2K 3 12, 153, 1340
1760 10K 2 3, 38
1762 2K 1 360
1766 2K 3 4, 34, 1227
1768 2K 4 17, 36, 59, 231
1770 2K 4 42, 68, 390, 780
1772 2K 1 1445
1774 10K 1 2061
1776 2K 2 23, 393
1778 2K 3 2, 14, 36
1780 2K 1 6
1782 2K 3 8, 50, 698
1784 2K 3 1, 2, 1845
1786 2K 4 1, 15, 71, 72
1788 20K 2 7, 1365
1790 2K 2 420, 462
1792 2K 2 2, 318
1794 2K 3 9, 28, 87
1796 2K 3 2, 6, 195
1798 2K 3 1, 486, 1128
1800 2K 4 30, 32, 264, 1280
1802 2K 2 61, 264
1804 2K 2 3, 437
1806 10K 3 3666, 8128, 9942
1808 2K 7 1, 9, 15, 25, 61, 1044, 1803
1810 2K 8 6, 21, 26, 39, 45, 114, 194, 290
1812 2K 1 1317
1814 2K 6 4, 16, 60, 63, 236, 1341
1816 2K 2 2, 54
1818 2K 2 101, 156
1820 2K 3 1, 165, 1090
1822 2K 1 3
1824 2K 2 2, 1530
1826 2K 5 3, 22, 363, 968, 1816
1828 2K 2 1, 304
1830 2K 1 2
1832 2K 2 5, 100
1834 2K 4 2, 16, 234, 299
1836 2K 2 64, 493
1838 2K 1 305
1840 2K 3 1, 427, 540
1842 2K 6 1, 2, 6, 13, 61, 280
1844 2K 2 2, 200
1846 2K 1 10
1848 2K 4 9, 205, 1032, 1650
1850 2K 2 1, 16
1852 20K 2 6341, 8999
1854 2K 8 5, 18, 42, 45, 374, 449, 985, 1779
1856 2K 6 2, 18, 55, 118, 1500, 1800
1858 2K 1 374
1860 2K 1 76
1862 2K 7 1, 4, 9, 61, 337, 732, 978
1864 2K 1 997
1866 2K 2 3, 65
1868 2K 5 1, 2, 7, 74, 371
1870 2K 4 5, 175, 752, 1190
1872 2K 5 3, 30, 62, 115, 824
1874 2K 2 10, 264
1876 2K 3 1, 16, 18
1878 2K 2 3, 1228
1880 2K 2 6, 20
1882 2K 1 22
1884 2K 2 4, 8
1886 2K 2 1, 15
1888 2K 1 717
1890 2K 7 2, 3, 4, 6, 14, 79, 149
1892 2K 2 3, 22
1894 2K 1 63
1896 2K 1 1
1898 2K 3 1, 99, 100
1900 2K 2 2, 25
1902 2K 3 6, 22, 141
1904 2K 5 4, 70, 193, 404, 1550
1906 2K 3 10, 309, 496
1908 2K 2 2, 1409
1910 2K 3 1, 4, 24
1912 2K 7 1, 2, 3, 4, 7, 10, 36
1914 2K 6 1, 2, 8, 116, 188, 1664
1916 2K 4 4, 6, 120, 779
1918 2K 3 20, 44, 68
1920 2K 2 4, 12
1922 2K 4 20, 53, 87, 417
1924 2K 5 1, 4, 6, 117, 431
1926 2K 1 1
1928 10K 3 3, 56, 4650
1930 2K 1 1246
1932 2K 2 1, 4
1934 2K 2 3, 18
1938 2K 5 4, 14, 154, 536, 1026
1940 2K 1 1881
1942 2K 3 206, 506, 1087
1944 2K 1 6
1946 2K 3 21, 394, 888
1948 2K 3 1, 7, 739
1950 20K 0
1952 2K 2 7, 86
1954 2K 3 1, 3, 180
1956 2K 1 27
1958 2K 3 10, 15, 69
1960 2K 2 11, 423
1962 20K 3 15, 217, 304
1964 2K 6 2, 89, 96, 134, 300, 1089
1966 2K 2 1, 355
1968 100K 6 3, 9, 78, 335, 782, 2737
1970 2K 2 1, 7
1972 2K 2 11, 90
1974 2K 3 2, 25, 326
1976 2K 2 1, 951
1978 2K 2 11, 1986
1980 2K 6 1, 5, 7, 11, 378, 1775
1982 2K 3 2, 4, 1810
1984 2K 1 6
1986 20K 0
1988 2K 3 87, 667, 1754
1990 2K 6 1, 4, 61, 127, 669, 828
1992 2K 1 1398
1994 2K 2 2, 37
1996 2K 3 32, 57, 960
1998 2K 5 1, 2, 15, 55, 150
2000 2K 1 562

Original information obtained from:
Prime Wiki
Carol / Kynea Search