.LOG Generalized Hyper-Cullen primes form k^n*n^k+1, k>n all ns less than 2048 searched to 3000 listed as "n k(s) [limit]" extra thanks to Mark Rodenkirch for his Multisieve program n k 2 3, 4, 21, 30, 33, 57, 100, 142, 144, 150, 198, 225, 304, 513, 782, 858, 3638, 6076, 9297, 11037, 12135(Lifchitz, g2, 1997), 12876(Lifchitz, g2, 1997), 30180(Lifchitz, g2, 1997), 48470(Oakes, p42, 2000) [200000](Harvey) 3 20, 110, 152 [100000] (Blazek) 4 6, 10, 12, 190, 382, 1218, 2300, 6072, 25844 [32750] 49518(Kazuyoshi, p14, 2001) 5 154, 1818, 12948 [30000] 6 16, 20, 46, 94, 2440, 7600 [16384] 8 28, 104, 116, 476, 2012, 3420 [16384] 9 20, 1640 [20000] 10 16, 28, 576, 759, 2114, 2256, 4774(Hugo Platzer 10-27-6) [10000] 11 1218 12 20, 28, 196, 2860 14 15, 254, 926, 1276, 1950 16 22, 46, 50, 153 17 802 18 316, 1664, 2413 20 33, 36, 192 21 38 22 23, 30, 38, 322 24 250, 1814, 2275, 2338 26 36, 46, 230, 320, 666 28 30, 584, 928, 2372 29 1468 30 122, 2576 32 1568 33 1312 34 65, 550 38 162 39 746 40 84 41 516 42 124 43 798 44 104, 328 46 390, 524 48 91, 455 50 56 51 110, 898 52 68 54 134, 143, 224, 230, 523 56 81, 88, 687 58 1264 60 592 62 610 64 740 68 404, 440 70 92 71 220 72 104 75 1064 78 218 80 1108 82 790 84 194, 278 85 2772 88 568, 1264 91 1198 92 1336 93 242 97 220 98 144, 822, 1884 100 614, 1924 102 302 104 114, 272, 420 106 164 110 597, 756 112 268, 2148 114 944, 2723 116 192 120 121 123 596 124 1324 126 430 131 706 134 543 136 858 139 2188 142 760, 907, 2825 144 1352 145 504 146 1394, 2966 147 416 148 1052, 2050 152 272 154 2540 160 1198 161 2928 162 802 164 422, 1515 165 266 169 2560 170 1016, 2853 171 622, 1468 172 2880 173 220 186 491 187 1614 188 384 192 1456 202 236 204 740, 2464 207 1820 208 885 209 582 212 2776 219 2492 220 1414 232 564 234 265 236 2979 242 1340 244 1108 248 1305 250 2254 252 2647 254 340, 754, 1473 256 566, 784 260 2854 264 475 268 668 270 412 277 2008 278 764, 2049 284 630 286 1055 288 680, 1676 292 879 294 1304 296 356, 1202, 1898 310 446 315 1448, 2966 318 556 320 1132, 1232 322 453, 2215 324 686 325 954 326 516 328 719, 1940 332 724 335 684 343 1518 348 452 354 1930 358 1644, 2330 365 472 367 2982 368 1209 376 386, 1133 385 2074 388 1336 392 424 396 1270 399 716 400 1112 404 1384 415 1638 416 2130 420 544 422 1041 428 852 430 1972 431 1632 436 862 437 1638 440 1546 446 510 447 662 448 564 454 1180, 1446 464 476 470 1202 472 1580 486 1786 488 1210 490 1688 492 844 493 2122 500 2396 502 2040, 2456 508 1152 509 1908 510 1936 512 2439 514 663 516 1150 518 1522 521 2050 522 1900 524 1908 536 554 538 789 540 2122 544 785 546 2594 554 2104 555 988, 2678 556 2554 572 747, 2240 580 822, 1606 582 1844 584 1598 585 776 586 2714 588 661 600 1748 604 2332 610 2026 620 952, 2626 626 2456 628 859 632 1488 644 1128 650 748, 1414 657 1292 670 886 674 1320 680 1896 686 1126 688 1370 692 2120 704 916 710 2306 715 2322 718 2370 720 962 724 1988 728 2364 732 1280 740 2301 744 1015 746 2006 748 1729 752 984 758 939 764 2928 776 2562 778 917, 2462 787 2914 796 1490 801 1022 802 899 806 2396 816 2872 832 968 836 1874 853 868 855 1654 858 2536 862 1576 864 2945 890 1254, 1902 908 1800 914 2220 936 1670 961 1902 966 2090 974 1814 982 1476 984 1196 994 1256 1004 2420 1018 1556 1031 2326 1036 2201 1044 2650 1046 2979 1059 2498 1072 1729, 2364 1082 1761 1082 1761 1132 1624 1174 2136 1206 2464 1230 2012 1258 2376 1260 1766 1332 1729 1334 2316 1336 2970 1342 1677 1348 2079 1358 1647 1376 2360 1434 2420 1446 1750 1476 2513 1496 2020 1500 1771 1534 1673 1550 2686 1570 1616 1575 1894 1606 1836 1632 2852 1642 2343 1652 2216 1658 2079 1676 2434 1678 2260 1684 1942 1710 1834 1711 2512 1736 1910 1740 2854, 2912 1810 1816 1820 2668 1838 2097 1850 2511 1866 1984 1877 2058 1893 1994 1934 2146 1940 2066 1950 2306 1954 2746 1972 2120 2002 2690 2016 2990 4000 4414 (Ian Brown, p90, 11-19-2) 30479 digits [20000] 4007 4074 (Ian Brown, p90, 11-20-2) 29144 digits [20000] 4022 6195 (Ian Brown, p90, 9-30-2) 37582 digits [20000] 4032 5230 (Ian Brown, p90, 9-16-2) 33850 digits [20000] 4057 8380 (Ian Brown, p90, 10-10-2) 46154 digits [20000] 4062 10379 (Ian Brown, p90, 10-10-2) 53769 digits [20000] News: 1/28/8 Blazek reports bases 2 and 3 checked to 100000, no new primes found. 5/21/7 John Blazek notes that base 2, primes 3 and 4 had been omitted. He's doubled checked base 2 to 50000 and also, checked base 3 to 50000. 1/2/7 Brown reports that bases 4000 to 4100 were checked through 20000. 10/27/6 Platzer reports base 5 range 16384 to 30000 checked, no primes; finds 4774^10*10^4774+1 is prime, with base 10 completed to 10000, reserves base 9 to 20000. 10/30/6 Platzer reports base 9 checked from 14001 to 20000, no primes found. send comments, corrections, additons, etc. to harvey563@yahoo.com 3:35 PM 1/31/2008