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Carol-Kynea prime
Contents
Carol numbers and Kynea numbers are numbers of the form [math]\displaystyle{ (b^n-1)^2-2 }[/math] and [math]\displaystyle{ (b^n+1)^2-2 }[/math], respectively, while Carol primes and Kynea primes are primes of those respective forms. Named and originally studied by Cletus Emmanuel starting in 1995, the search for new Carol and Kynea primes is now coordinated in a MersenneForum thread, and the results are stored here on Prime-Wiki.
Definitions
In the context of the Carol/Kynea prime search, a Carol number is a number of the form [math]\displaystyle{ (b^n-1)^2-2 }[/math] and a Kynea number is a number of the form [math]\displaystyle{ (b^n+1)^2-2 }[/math]. A Carol/Kynea prime is a prime which has one of the above forms. A prime of these forms must satisfy the following criteria:
- b must be even, since if it is odd then [math]\displaystyle{ (b^n±1)^2-2 }[/math] is always even, and thus can’t be prime.
- n must be greater than or equal to 1. For any b, if n is 0 then [math]\displaystyle{ (b^n±1)^2 }[/math] is equal to 1, and thus yields -1 when 2 is subtracted from it. By definition -1 is not prime. If n is negative then [math]\displaystyle{ (b^n±1)^2 }[/math] is not necessarily an integer.
- b may be a perfect power of another integer. However these form a subset of another base’s primes (ex. Base 4 Carol/Kynea primes are Base 2 Carol/Kynea primes where [math]\displaystyle{ n \bmod 2 \equiv 0 }[/math]). So it is not necessary to search these bases separately.
Due to the form of these numbers, they are also classified as near-square numbers (numbers of the form [math]\displaystyle{ n^2-k }[/math]).
History
Carol and Kynea numbers were first studied by Cletus Emmanuel in 1995[1], who named them after personal acquaintances[2]. He searched these forms for primes up to the limit of 15000.
Starting in 2004, Steven Harvey maintained a search for this form. At this time Multisieve and cksieve were used to sieve these forms and PFGW was used to test for primality. The search went dormant in 2011 and was resurrected in 2015 by Mark Rodenkirch. Initially Multisieve was used, but then later on he wrote cksieve which would later become part of the Mtsieve framework.
On 2015-12-26 Mark opened a thread[3] for a coordinated search of Carol/Kynea numbers on MersenneForum, which continues to this day.
All data are now collected here using the information from the forum posts. Feel free to get an account and editing pages by yourself.
Top 5 Carol primes
Prime | Digits | Found by | Date |
---|---|---|---|
(290124116-1)2-2 | 611246 | Karsten Bonath | 2019-03-01 |
(96879512-1)2-2 | 474826 | Karsten Bonath | 2021-01-13 |
(2695631-1)2-2 | 418812 | Mark Rodenkirch | 2016-07-16 |
(2688042-1)2-2 | 414243 | Mark Rodenkirch | 2016-07-05 |
(17887525-1)2-2 | 393937 | Serge Batalov | 2016-05-21 |
Top 5 Kynea primes
Prime | Digits | Found by | Date |
---|---|---|---|
(362133647+1)2-2 | 683928 | Karsten Bonath | 2019-06-17 |
(2852770+1)2-2 | 513419 | Ryan Propper | 2019-07-14 |
(42157323+1)2-2 | 510749 | Tanel Liiv | 2021-10-01 |
(68885121+1)2-2 | 483077 | Karsten Bonath | 2021-09-05 |
(30157950+1)2-2 | 466623 | Serge Batalov | 2016-05-22 |
OEIS sequences
These are available OEIS sequences:
Base | Carol | Kynea |
---|---|---|
2 | A091515 | A091513 |
6 | A100901 | A100902 |
10 | A100903 | A100904 |
14 | A100905 | A100906 |
22 | A100907 | A100908 |
Data
All bases
All bases with their own page are listed here: There are 382 sequences.
Bases which are a power of
There are 22 sequences.
Bases without a Carol prime
There are 62 sequences.
Bases without a Kynea prime
There are 61 sequences.
Bases without a Carol and Kynea prime
There are 1 sequences.
Remaining data
All bases <= 3000 not listed yet on their own page are tested to n=2000 and listed in a file.
The data file can be found here.
Base | Carol primes | Kynea primes
|
---|---|---|
366 | 15, 43, 61, 339 | 32, 149, 828, 947 |
370 | 2, 23, 24, 194, 244 | 1, 3, 86, 164, 590, 791, 1613 |
372 | 1, 2, 7, 51 | 6, 7, 31, 73, 103, 409, 1408 |
374 | 735 | 22, 48 |
376 | 10, 1545 | 2, 3, 90 |
378 | 4, 10, 21, 48, 132, 763, 1277 | 3, 4, 7, 18, 173, 427 |
380 | 4 | 2, 3, 6, 44, 707, 1220, 1278, 1347, 1962 |
382 | 5, 1491 | 75, 588, 696 |
384 | 321 | 13 |
386 | 2, 3, 8, 9, 12, 105, 399 | 1, 13, 254 |
388 | 1, 9, 50, 63 | 282 |
390 | 3 | 1, 13, 79, 200, 441, 1645 |
392 | 1, 5, 15, 223 | 2, 32, 203 |
396 | 3 | 3, 13, 69, 130, 147 |
398 | 512 | 1, 2, 4, 749 |
402 | 6, 21, 135 | 6, 136 |
404 | 460 | 1, 44, 74, 230 |
406 | 1, 21, 49, 495, 1531 | 5, 6, 9, 79 |
408 | 72, 168, 1581, 1660 | 3, 275 |
410 | 3, 5 | 3, 58, 655 |
412 | 2, 3, 15, 33, 280, 503, 544, 663 | 32 |
414 | 2, 220 | 1, 121, 297 |
416 | 1, 2, 12 | 4, 5, 287 |
418 | 3, 4, 5, 6 | 270 |
420 | 8, 345 | 1, 645, 775 |
422 | 1, 6, 31, 42 | 647 |
424 | 9 | 1, 4, 48, 220, 700, 828 |
428 | 20, 200 | 1, 2, 7, 8, 292, 1466 |
430 | 1, 2, 3, 18, 56 | 4, 30 |
434 | 2, 15, 141 | 1 |
436 | 1, 6, 162 | 2, 6, 8, 1944 |
438 | 2, 8, 201, 1731, 1826 | 85, 106 |
440 | 2, 231 | 1, 2, 28, 35, 50, 98, 233 |
442 | 1, 97, 236, 397 | 1, 3, 28, 232 |
444 | 1, 2, 3, 8, 109 | 21, 82, 657, 1630 |
446 | 5, 172, 300 | 1, 2, 14, 44, 642, 769 |
450 | 1, 78 | 45, 120, 783 |
452 | 78 | 72, 88, 124 |
454 | 2, 11, 16, 22, 31 | 264, 1547 |
456 | 7, 34 | 3 |
458 | 9, 33, 114 | 12, 77 |
460 | 3, 5, 11, 1133, 1253, 1636 | 85, 288, 1687 |
462 | 5, 44, 113, 135, 421, 703, 1254 | 15, 911 |
464 | 133, 630 | 2, 665, 1646 |
466 | 11, 68 | 1, 3, 6, 135 |
468 | 1, 6, 8, 400, 603, 998 | 1, 2, 5, 56, 61, 62, 1774 |
470 | 1, 2, 3, 15, 128, 451 | 2, 106, 162, 288, 586 |
474 | 33, 231 | 3, 57 |
476 | 2, 8, 48 | 8, 12, 1030, 1692 |
478 | 3, 45, 900 | 18, 140, 1611 |
480 | 2, 50, 239 | 1, 3, 10, 13, 64, 153, 315, 535 |
482 | 1 | 2, 42, 129, 132 |
486 | 45, 138, 170 | 4, 15, 203, 1432 |
488 | 12, 111 | 1, 13, 85 |
490 | 1, 4, 13, 84, 210, 1885 | 1, 2, 7, 183, 545, 1359, 1895 |
492 | 1, 370, 1518 | 8, 555, 774 |
494 | 323 | 1, 16, 303 |
496 | 1, 440, 690 | 1, 4, 6, 26, 116, 134, 751 |
498 | 1, 5, 24, 92, 99, 1123 | 4, 9, 11, 216, 347 |
502 | 3 | 6 |
504 | 2, 10, 117, 821 | 1, 7, 34, 220, 490 |
506 | 1, 6, 136, 445 | 140, 404 |
508 | 2, 102, 816 | 30 |
510 | 4, 9, 254, 305 | 216, 231, 1546 |
514 | 1, 30, 117 | 3 |
516 | 100 | 2 |
518 | 3, 19, 177 | 10, 23, 55, 723, 819 |
520 | 3, 6 | 134, 1371 |
522 | 2, 1059 | 1, 3, 517 |
524 | 1, 8, 109, 156, 166, 244, 471 | 1, 3 |
526 | 1, 39 | 2, 3, 5, 154 |
528 | 3, 1059 | 3, 4, 9, 1985 |
530 | 5, 84, 1049 | 1, 93 |
532 | 1, 17, 128, 716, 1982 | 2 |
534 | 13, 510 | 2, 12, 170, 1476 |
536 | 3, 357, 653, 1472 | 7, 10, 70 |
538 | 319 | 2, 6, 120, 868, 1374 |
540 | 6, 55, 547, 752, 827, 1877 | 1, 2, 212 |
544 | 24, 84, 94 | 1, 38, 90, 230 |
546 | 1, 3, 51, 196, 426, 1196 | 11, 21 |
548 | 24, 1218 | 6, 9, 33, 138, 162, 200, 444, 1496 |
550 | 30, 81, 168, 330 | 4, 181, 319 |
554 | 3, 72, 645 | 6, 138, 1887 |
556 | 3, 595 | 405 |
558 | 162 | 2, 314 |
560 | 2, 4, 8, 706 | 1, 2, 7, 20, 33, 68, 135 |
562 | 1, 4, 567, 1053 | 330 |
564 | 110, 1016, 1050 | 1, 76, 756 |
566 | 1, 77 | 56, 636, 643 |
568 | 11, 15, 72, 212, 515, 1075, 1208 | 1, 11, 12, 844 |
570 | 1, 2 | 36, 1061 |
572 | 15, 18, 293 | 1, 535 |
574 | 1, 3, 166, 651 | 1, 12, 144, 212, 298, 1190, 1353, 1951 |
578 | 9, 539 | 19 |
580 | 2, 3, 14, 53, 131, 167, 365, 559 | 2, 19, 68 |
582 | 46 | 1, 152, 301 |
584 | 1 | 9, 406, 591 |
586 | 21, 465 | 1, 2, 3, 12 |
588 | 1, 5, 789 | 11, 13, 28 |
590 | 235, 937 | 23, 155, 762 |
592 | 393, 582 | 12, 1855 |
594 | 3 | 1, 55, 107, 237, 280, 924, 1585 |
596 | 1, 2, 18, 25, 66, 185, 414 | 79, 95, 1434 |
598 | 2, 20 | 57, 129, 845 |
602 | 5, 79, 221, 454 | 640 |
604 | 13, 15, 48 | 38, 159, 1356 |
606 | 2, 23, 32, 60, 288 | 1, 100, 1129 |
608 | 1, 3, 13, 26, 326 | 1, 2, 3, 8, 315, 513 |
610 | 1, 9, 10, 78, 1165, 1252 | 19, 456 |
612 | 2, 6, 42 | 66, 288, 359 |
614 | 838 | 1, 3, 31, 135, 252, 276 |
616 | 1, 19, 1208 | 3, 78, 89 |
618 | 4, 16, 24, 618 | 3 |
620 | 11, 21, 23 | 1, 3, 766 |
622 | 1, 2, 4, 16, 323 | 118, 312, 348 |
624 | 2, 56, 83, 102, 282, 285, 286 | 13, 24, 32, 1589 |
626 | 8, 54, 146 | 69, 120, 154, 534 |
628 | 293 | 2, 120, 288 |
630 | 2, 5, 19, 63, 117 | 234, 807 |
636 | 52, 202 | 1, 483 |
638 | 1, 4, 1483 | 3, 1288 |
642 | 3, 4, 60, 1787 | 13, 20, 440 |
644 | 9, 393 | 1, 2, 5, 54, 146, 399 |
646 | 1, 4, 1884 | 201 |
648 | 3, 225, 759, 840 | 709 |
650 | 2, 6, 7, 1042, 1603 | 29, 100, 287 |
652 | 40, 107, 140 | 1, 3, 46 |
656 | 5, 6, 81, 136, 228 | 2, 6, 8, 30 |
658 | 60, 442, 1272 | 8, 20, 1015 |
660 | 43, 972 | 1476 |
662 | 2, 3, 137, 147, 438 | 1, 3 |
664 | 1, 2, 4, 50, 1010, 1600 | 23, 29, 44, 45, 169, 434, 483, 712, 839 |
666 | 120 | 1, 2, 17, 25, 142, 742 |
668 | 1, 3 | 16, 125, 226 |
670 | 54, 1524 | 1, 2, 19, 117, 660 |
672 | 1, 46, 92, 133, 941 | 37, 64 |
674 | 3, 52 | 2, 722, 1182 |
678 | 1, 21, 37, 39, 50, 280 | 143, 193 |
680 | 9, 12, 15, 574 | 2, 4, 7, 44, 521, 569 |
682 | 30 | 5, 9, 21 |
684 | 10, 15, 63 | 2 |
686 | 2, 29, 44, 172, 1170, 1260 | 2, 3, 800, 1866 |
690 | 413 | 30, 36, 681, 1162 |
692 | 57, 586, 1787 | 91 |
694 | 2, 6, 62, 256 | 2, 318, 591 |
696 | 3, 87, 1675 | 3, 897 |
700 | 3, 16, 60, 70, 306 | 29, 64, 151, 1047, 1410 |
704 | 2, 3, 5, 380 | 6, 7, 49 |
706 | 2, 3, 6, 1955 | 3, 4, 5, 10, 49, 53 |
708 | 10, 14, 21 | 2, 7, 162, 215, 282, 428, 538, 742 |
712 | 9, 24 | 1, 7, 15, 37, 42, 375, 591 |
714 | 1, 4, 84 | 1, 19, 81, 155 |
716 | 1, 210 | 2, 18, 39, 81, 1475 |
718 | 2, 48, 440 | 1, 3, 6, 13, 408, 1708 |
722 | 6, 86, 222 | 4 |
724 | 7, 216, 595 | 275, 393, 948 |
726 | 4, 669 | 1, 2, 13, 494, 1005 |
728 | 1, 4, 88, 364, 907 | 2, 1054, 1751 |
730 | 3, 15, 69, 91, 97, 160 | 27, 105 |
732 | 5, 288, 464 | 1, 4, 15, 27, 61, 91, 273 |
734 | 1, 4, 52, 151, 304, 620, 676 | 8 |
736 | 2, 52 | 2, 671 |
740 | 18, 47, 503 | 3, 50, 291 |
742 | 3, 6, 979 | 1, 4, 96, 585, 596, 618, 680, 1210 |
744 | 1, 49 | 3, 6, 14 |
746 | 2, 3, 516 | 1, 535 |
748 | 1, 124, 135, 179, 320 | 2, 14, 126 |
750 | 3, 149 | 1, 2, 6, 71, 381 |
752 | 1, 14, 804 | 60, 328 |
754 | 6 | 127, 372, 817 |
756 | 2, 57 | 1, 7, 1808 |
758 | 1, 538 | 2, 75, 548 |
760 | 2, 5, 38, 89 | 1, 3, 40, 61, 354 |
762 | 1, 12, 1341 | 1, 5, 39, 243, 1569 |
764 | 1, 146 | 115 |
766 | 93, 414, 420 | 95 |
768 | 42, 154, 305 | 2, 27, 43 |
770 | 3, 14, 77, 240, 513 | 2, 31, 131, 771, 1680 |
774 | 26 | 1, 28, 45, 81 |
776 | 1, 32, 236, 610, 808, 1537 | 2, 9, 11, 20, 71, 449, 973, 1432 |
778 | 8, 17 | 1, 2, 20 |
780 | 1, 6, 288, 936, 1200 | 15, 22 |
782 | 3, 40, 760 | 48, 171, 645 |
786 | 1 | 3, 8, 191, 677 |
788 | 447 | 1, 3, 700, 759 |
790 | 1, 2, 40, 602 | 4, 213 |
792 | 3, 10, 12, 112, 698 | 6, 51, 162, 696 |
794 | 3, 126, 290, 1232 | 4 |
796 | 207 | 1 |
798 | 1, 3, 1048 | 2, 689, 944 |
800 | 13, 30 | 5, 1506 |
802 | 2 | 27, 48 |
804 | 6, 257, 550 | 2, 4, 1660 |
806 | 2, 4, 10, 45, 51, 171, 1477, 1978 | 1, 8, 657, 774, 909 |
808 | 1, 3, 6, 20, 314 | 4, 5, 52, 214 |
810 | 5, 9, 321 | 1 |
812 | 1, 11, 276, 310, 376 | 3, 20, 43, 56, 79, 107, 760 |
814 | 45, 69, 130 | 530 |
816 | 6, 1910 | 1, 345, 1149 |
820 | 5, 255, 901 | 174 |
822 | 30 | 3, 22, 454 |
824 | 1215 | 1, 195 |
826 | 1, 11, 14, 32, 190, 483, 852 | 10, 18 |
828 | 3 | 465 |
830 | 375 | 487 |
834 | 21 | 45, 57, 110, 233, 730, 1294, 1626 |
838 | 33, 78 | 925 |
840 | 11, 54, 1595 | 1, 117 |
842 | 1, 19, 75, 1402 | 21, 33, 72, 201 |
844 | 21 | 33 |
846 | 5, 27, 224 | 3, 5, 10, 41, 116, 181 |
848 | 38 | 11 |
850 | 2, 12, 60, 78 | 6, 1815 |
852 | 3, 4, 15, 54 | 2, 462 |
854 | 5, 211, 522 | 2, 12, 152, 613 |
856 | 10, 70, 306 | 44 |
858 | 5 | 88 |
860 | 10, 64, 1052 | 3, 31, 72, 269 |
862 | 42, 95 | 1, 454 |
864 | 1, 2, 104, 993 | 15, 42, 1049 |
868 | 7, 357, 1166 | 105, 449, 517 |
870 | 385 | 20, 795 |
872 | 2, 5, 8, 17, 1415 | 3, 4, 564 |
874 | 2, 123 | 1, 5, 200 |
876 | 1, 21, 60, 105 | 4, 5 |
878 | 2, 7 | 180, 244 |
880 | 723, 971 | 1, 3, 9, 80, 121, 386 |
882 | 1, 493 | 842 |
884 | 3, 4, 61, 75, 252, 1213 | 198 |
886 | 5, 27, 33, 147 | 10, 84 |
888 | 11, 1505 | 5, 29, 124, 1063, 1568 |
890 | 2, 24 | 25 |
892 | 200 | 11, 112 |
896 | 11 | 1, 2, 3, 12, 376, 978 |
898 | 1, 4 | 6, 18 |
902 | 1 | 2, 449, 625, 1313, 1313 |
904 | 3, 7 | 14, 42, 78 |
906 | 3, 6 | 558 |
910 | 2, 10, 24, 49, 51, 54, 90, 200 | 110, 179 |
912 | 60, 208, 1638 | 12, 50, 1467 |
914 | 278 | 46, 69 |
916 | 9, 27, 57 | 2, 3 |
918 | 3, 21, 26, 808 | 8, 18 |
920 | 14, 780 | 221, 250 |
922 | 190, 315 | 3, 8 |
924 | 2, 4, 16, 288 | 3, 9, 18, 422 |
930 | 9, 843 | 1, 293, 712, 942 |
932 | 1, 10, 16, 98 | 46, 55, 79, 250, 260 |
934 | 3, 20, 501, 1585 | 65, 77 |
936 | 58, 365 | 3, 26, 33, 103 |
940 | 10, 55, 1788 | 1692 |
944 | 1, 4, 9, 12, 14, 1302 | 1, 3, 112, 685, 1433 |
946 | 1, 6, 7, 64, 146, 1022 | 10, 15, 49, 126, 140, 385 |
948 | 6, 9, 13, 21, 1923 | 5, 168, 1036 |
952 | 1, 245, 784 | 3, 17, 83, 160, 855 |
954 | 10, 120, 247, 579, 1719 | 84, 147 |
956 | 5, 630 | 6, 529 |
958 | 15, 800 | 1, 2, 5, 14, 21, 110 |
960 | 1, 3, 5, 252 | 4, 706 |
962 | 51, 282, 732 | 1901 |
972 | 46 | 1, 6, 9, 151, 225 |
974 | 1, 10, 294, 1175 | 2, 90 |
976 | 3 | 40 |
978 | 42, 53, 202 | 1, 1063 |
980 | 1, 2, 21, 31, 175, 634, 1354 | 129, 589 |
984 | 5, 14, 527 | 3, 10, 31 |
986 | 2 | 1, 2, 216, 310, 565 |
988 | 1, 6, 61 | 29, 275, 930 |
990 | 457 | 5, 6, 47 |
994 | 1, 9, 358 | 1, 2, 19, 35, 100 |
1002 | 2, 3 | 1, 13 |
1004 | 1, 27 | 258 |
1006 | 3, 16, 18, 786 | 140, 152, 254, 1111 |
1008 | 4, 77, 110, 1248, 1667 | 4, 74, 115 |
1012 | 14 | 1, 4, 22, 697, 1821, 1954 |
1014 | 1, 4, 7, 19, 1014 | 15, 954 |
1016 | 12, 299, 1375, 1426 | 11, 32, 42 |
1018 | 2, 3, 9, 15, 597, 1531 | 3, 35, 132, 760, 1481 |
1020 | 574, 624, 970 | 1, 33, 205, 450 |
1022 | 1, 17, 62, 429, 1553 | 1, 3, 28, 37, 1393 |
1026 | 18, 33 | 7, 9, 102 |
1028 | 4, 166 | 1, 2, 18, 53, 75, 201 |
1030 | 1, 4, 6 | 2, 288 |
1034 | 1440 | 1, 2, 6, 37, 1842 |
1036 | 1, 9, 12, 20, 240, 377, 1197 | 2 |
1040 | 20 | 10, 45 |
1042 | 10, 273, 1511 | 13, 141, 303, 1872 |
1044 | 2 | 1, 261, 1966 |
1046 | 1, 14 | 9, 1632 |
1048 | 108 | 2 |
1050 | 25, 267 | 1, 57 |
1052 | 1, 6, 42, 520 | 62, 312, 359, 627 |
1054 | 135 | 3 |
1056 | 18, 118, 578 | 1, 369, 476, 556 |
1058 | 1, 2, 27, 35, 195 | 5, 12, 140 |
1060 | 63, 396, 1880 | 70, 1362 |
1062 | 5 | 1814 |
1064 | 3, 5, 18, 66, 130, 1995 | 3, 11, 29, 52 |
1066 | 6, 22 | 2, 72, 128, 147 |
1070 | 1, 15, 382, 685 | 1 |
1072 | 1 | 1, 2, 122, 206 |
1074 | 1, 2, 44 | 12 |
1076 | 21 | 2, 12 |
1078 | 2, 5, 261 | 2, 902 |
1080 | 19, 48, 537, 1008, 1609 | 77, 302 |
1082 | 65, 71 | 144, 279 |
1084 | 4, 32, 40, 57, 408 | 1, 11, 381, 923 |
1086 | 1, 1201 | 13, 72, 203, 967 |
1088 | 9, 813 | 41, 1235 |
1090 | 3 | 1, 21 |
1092 | 1, 5, 821 | 2, 1150, 1316 |
1094 | 13 | 21, 210 |
1096 | 5, 230 | 10, 106, 136, 171 |
1098 | 3, 37 | 82, 100, 105 |
1100 | 2, 4, 229 | 1, 2, 3, 5, 24, 90, 182 |
1102 | 1, 36, 114, 127 | 5 |
1104 | 6, 15 | 3, 15, 25, 56 |
1106 | 2, 11, 39, 182, 672 | 3, 50, 218, 604 |
1110 | 36, 179 | 4, 52, 64, 379 |
1112 | 10 | 1, 3, 5, 6, 280 |
1114 | 1, 3, 4, 319, 434, 826, 1341 | 15, 21, 75, 81 |
1118 | 5, 63, 88 | 1, 57, 126 |
1120 | 1, 7, 21, 67 | 2, 3, 8, 525, 1112 |
1122 | 153, 1416 | 3, 696 |
1124 | 117 | 1, 216, 264, 324 |
1128 | 27, 56, 279 | 40, 108 |
1130 | 2, 18 | 15 |
1134 | 2, 13, 14, 1838 | 42, 154, 694 |
1138 | 14 | 10, 12, 426 |
1140 | 16 | 1, 74 |
1142 | 1, 200, 318 | 1 |
1144 | 1, 37 | 3 |
1146 | 66 | 1, 3, 91, 229, 459, 795, 878 |
1148 | 1, 8, 10 | 1, 4, 10, 21, 58, 88, 1667 |
1154 | 1, 7 | 2, 3, 348 |
1156 | 2, 129 | 1, 7, 73 |
1158 | 1, 8, 43, 66 | 5, 792 |
1160 | 3, 9 | 1, 25, 141, 1922 |
1162 | 1, 70, 125, 126, 740, 1687 | 3, 115, 126, 1273 |
1164 | 12, 15 | 9, 17 |
1168 | 36 | 6, 108, 322 |
1170 | 75, 121, 381, 420 | 12, 37, 661 |
1172 | 2, 3, 6, 14 | 17, 34 |
1174 | 120, 837 | 1 |
1176 | 1, 2, 7, 112, 212, 1672 | 1, 11, 12, 66, 180 |
1178 | 1, 4, 117, 426 | 2, 1131 |
1180 | 62, 72, 597 | 16, 21, 70, 1827 |
1182 | 7 | 2, 5, 14, 23, 27, 70, 731 |
1184 | 4, 15, 55, 56, 149, 410 | 2, 4, 6, 7, 16, 26, 31, 279, 286, 505 |
1186 | 3, 21, 54, 104, 254, 1272, 1899 | 627 |
1190 | 352, 1196 | 2, 6, 7, 15, 141, 256, 259 |
1192 | 34 | 3, 5, 8, 1239 |
1194 | 117, 120, 711 | 63, 70 |
1196 | 4, 20, 27 | 1, 180, 901 |
1198 | 1, 6, 59 | 4, 25, 307, 633 |
1200 | 3 | 3, 11, 75, 136 |
1202 | 832 | 2, 7, 18, 37, 50, 1266 |
1204 | 17 | 442 |
1206 | 3, 61, 274 | 3, 5, 561, 609 |
1208 | 3, 9, 548 | 6, 13 |
1212 | 1 | 3, 98 |
1214 | 397 | 12, 1408 |
1220 | 30, 76 | 2, 15, 249, 252, 722 |
1224 | 1, 6, 13, 24, 25, 64, 188, 197, 270, 453 | 2, 672, 684 |
1226 | 12, 94, 185, 251, 534 | 3, 16, 416 |
1228 | 129 | 3, 767 |
1230 | 65 | 1, 7, 67, 355 |
1232 | 1, 2, 7, 8, 118 | 1, 9, 125, 202 |
1234 | 1, 94, 1683 | 99, 1406 |
1238 | 2, 876 | 1, 464, 1796, 1900 |
1240 | 1, 111, 175, 518 | 1, 165, 176, 1010 |
1242 | 1, 896 | 4, 347 |
1244 | 12, 436 | 6, 9, 158 |
1246 | 3, 28 | 5, 93, 202, 1707 |
1248 | 3, 4 | 786 |
1250 | 2, 57, 348 | 1, 352, 379, 579 |
1252 | 1, 9, 25, 32 | 1, 12, 1058 |
1254 | 1, 1218, 1686 | 5, 14, 175, 1646 |
1256 | 2, 3, 21, 228 | 4, 5, 23 |
1258 | 39, 155, 245, 749, 843, 1260 | 3, 14, 859 |
1260 | 5, 20, 121, 165 | 1, 5, 10 |
1262 | 1, 165 | 11, 26, 66, 113 |
1264 | 41, 56, 425 | 1, 72 |
1266 | 1, 3, 4, 54, 152, 813 | 1, 2, 446 |
1268 | 1, 132, 651, 1530 | 5, 37 |
1270 | 444, 680 | 1253 |
1272 | 30, 45 | 20, 1034 |
1274 | 342 | 15, 26 |
1276 | 63, 118, 1077 | 6, 111 |
1278 | 1145 | 6, 7, 783 |
1280 | 2, 3, 43, 176, 272, 400 | 2, 5, 1546 |
1282 | 358, 404 | 3 |
1284 | 3, 224 | 201, 1895 |
1288 | 1, 2, 160 | 1, 2, 6, 7, 14, 142, 1713 |
1292 | 11, 41 | 37 |
1294 | 3, 53, 98 | 375 |
1296 | 5, 77, 532, 2257, 9665 | 1, 3, 14, 94, 108, 1942, 8392, 12700 |
1298 | 1, 120, 312 | 6, 15, 108 |
1300 | 4, 10, 65 | 3, 7, 12, 36, 56, 183 |
1302 | 231 | 2, 6, 12 |
1304 | 4, 75, 195, 297, 889 | 14, 60, 132 |
1306 | 2, 9, 42, 236 | 1, 6, 19, 682 |
1308 | 1, 9 | 6 |
1310 | 66, 78, 391, 459 | 1, 98 |
1312 | 1, 2, 295, 799 | 100, 189, 810 |
1314 | 3, 29 | 2, 12, 108 |
1316 | 110 | 131, 235, 871 |
1320 | 168, 255, 1548 | 1, 60, 426 |
1322 | 1, 21, 621, 1150 | 435 |
1324 | 2, 3, 4 | 6, 17 |
1328 | 46 | 2, 3, 30, 49 |
1330 | 12, 20, 27, 119 | 1, 2, 5, 52, 128, 427 |
1332 | 1, 16, 43 | 182, 1304 |
1336 | 59, 387, 516 | 756 |
1338 | 2, 547 | 5, 138, 179, 334, 893, 1419 |
1340 | 13, 18 | 5, 192, 700 |
1342 | 4, 143, 334, 654 | 1, 2 |
1344 | 1 | 12, 15, 354, 534, 780, 1033 |
1348 | 741 | 3 |
1350 | 2, 10, 422, 488 | 3, 46, 700, 1224 |
1352 | 3, 4, 39, 549 | 9, 53, 93, 163 |
1354 | 39, 54, 57 | 4, 40 |
1358 | 1, 405 | 1, 4, 14, 16, 204, 265, 614 |
1362 | 65 | 1, 1083 |
1364 | 1, 109, 315 | 1, 25, 990 |
1366 | 1, 8, 39, 1087, 1436 | 1, 3, 15, 127 |
1368 | 1, 69, 876 | 279 |
1370 | 3 | 24 |
1372 | 3, 4, 1740 | 1248, 1574 |
1374 | 160, 456, 618 | 99, 1706 |
1376 | 2, 21, 147, 1098 | 9, 58 |
1378 | 19, 43, 227, 619 | 1 |
1380 | 1, 1466 | 15, 100 |
1382 | 355 | 664 |
1386 | 4, 64, 604, 725 | 5, 57, 103 |
1390 | 102, 272 | 1, 10, 25 |
1392 | 1, 4, 6, 597 | 1 |
1394 | 1, 43, 59, 67 | 7, 9, 408, 880, 1738 |
1396 | 840 | 168, 522 |
1398 | 5, 6, 52 | 6, 18, 25, 90, 1369 |
1400 | 7 | 5 |
1402 | 10, 90, 519, 1105, 1915 | 6 |
1406 | 2, 3 | 17, 50 |
1408 | 2, 31, 93, 312, 338, 1166 | 1, 2, 15, 32, 36, 72 |
1410 | 1, 2, 235, 915, 1021 | 29 |
1412 | 310 | 1176 |
1414 | 154 | 1, 8 |
1416 | 1, 3, 30, 139 | 6 |
1418 | 9, 768 | 7, 513 |
1420 | 6, 30, 781, 1965 | 210 |
1422 | 2, 21, 236 | 7, 47, 353 |
1424 | 24, 60, 87 | 946, 1396 |
1426 | 5, 10 | 39, 117, 560, 1392, 1452 |
1428 | 22, 29 | 1, 495 |
1430 | 1 | 2, 39 |
1434 | 4, 15, 56, 59, 184, 462, 748, 830, 1714 | 1, 127, 207, 442 |
1436 | 1, 10, 11, 705 | 4, 64, 103, 294 |
1438 | 1500 | 18 |
1440 | 5 | 13, 51, 102 |
1444 | 1, 280 | 3, 1745 |
1446 | 5, 20 | 1, 6 |
1448 | 1, 18, 25, 240, 1116 | 1195 |
1450 | 126, 154, 156, 646 | 15, 52 |
1454 | 6 | 38, 555, 1435 |
1456 | 19 | 4, 32 |
1458 | 541 | 3, 5 |
1460 | 65 | 1, 21, 37, 72, 184, 522 |
1462 | 1, 5, 27, 34 | 1, 26, 43 |
1464 | 1, 2 | 7, 9, 23, 120, 142, 150, 1314 |
1470 | 9 | 85, 732 |
1474 | 2 | 10, 439 |
1476 | 7, 363 | 17, 53, 410, 1098, 1370 |
1478 | 2, 20 | 17 |
1480 | 111 | 5, 36, 45, 177, 375 |
1486 | 3, 150 | 1046 |
1488 | 14, 548 | 90 |
1490 | 8, 168, 236 | 1, 2 |
1492 | 1, 146, 383 | 10, 50 |
1494 | 9, 20 | 5, 6, 156, 1402 |
1496 | 15, 27, 382, 1097 | 1128 |
1498 | 4 | 1, 27, 420, 682, 1700, 1792 |
1500 | 1, 190 | 2, 39 |
1502 | 2, 14, 905 | 87, 100, 1566 |
1504 | 1303, 1308, 1743 | 3, 120, 1307 |
1506 | 4, 196 | 2, 3 |
1508 | 24, 38, 1332 | 3, 6, 65, 106, 903 |
1510 | 4, 6, 34, 125 | 26, 92, 540 |
1512 | 6, 29, 145, 493 | 28, 621 |
1514 | 3, 37, 520, 1363, 1623, 1980 | 1176 |
1518 | 1, 3, 34, 514, 1010 | 3, 6, 36, 94, 198, 948, 1624 |
1520 | 5, 19, 26, 52 | 1, 130, 944 |
1522 | 1 | 5, 10, 101 |
1526 | 1, 2, 6, 13, 106, 334 | 2, 15, 36, 227, 694 |
1528 | 3, 4, 42, 51 | 365 |
1530 | 36, 257 | 265, 657 |
1532 | 3, 119, 166, 781 | 5, 11, 14 |
1536 | 1633 | 12 |
1538 | 9 | 42, 79, 183, 1128 |
1544 | 2, 62 | 1, 87, 433 |
1546 | 1, 2, 3, 5, 104, 116 | 14, 30, 234, 599 |
1548 | 31, 388 | 1, 14, 32, 101 |
1550 | 1, 216 | 11, 30, 125 |
1552 | 6, 996 | 32, 302 |
1554 | 26, 52, 216 | 564, 904 |
1556 | 4, 31 | 240, 263, 330 |
1558 | 51, 270 | 9, 16 |
1560 | 4, 27, 40, 53 | 1 |
1562 | 1, 53 | 1, 34, 84, 331 |
1564 | 1, 8, 1527 | 3, 288, 777 |
1568 | 1, 4 | 5, 16 |
1572 | 11, 62 | 1083 |
1574 | 2, 26 | 4, 35, 40, 114 |
1576 | 3, 1100 | 907 |
1578 | 18, 763 | 3, 4, 47, 1913 |
1580 | 3, 34, 233 | 2, 25, 1278 |
1582 | 2, 4, 8, 555 | 7, 45, 1493 |
1584 | 9, 19, 72 | 42 |
1588 | 13, 867 | 7, 103, 124 |
1590 | 5, 155, 355, 369 | 10, 48, 86 |
1594 | 46 | 1119 |
1596 | 305 | 1, 2, 4, 6, 149, 1012 |
1598 | 1, 10, 16 | 122, 1688 |
1600 | 2, 69, 2042 | 1, 72, 1428, 1498, 2583, 3912, 4696, 20389 |
1602 | 1, 49, 354, 1038 | 1, 6, 26 |
1604 | 1, 10, 17, 18, 32, 186, 1614 | 55, 88 |
1606 | 237 | 11, 42, 168, 198 |
1608 | 45 | 13, 60, 138 |
1610 | 2, 15, 70, 383 | 1, 315, 730, 1484 |
1612 | 1 | 95, 854 |
1616 | 3, 44, 960, 1059, 1231 | 1, 5, 80, 815 |
1618 | 1, 618, 1273, 1843 | 1, 13, 89, 390, 1217 |
1620 | 1, 2, 74 | 3, 693 |
1622 | 540 | 6, 13, 1916 |
1624 | 3 | 2, 32 |
1626 | 81, 334, 1639 | 114, 126, 140, 168 |
1628 | 50 | 3, 522, 810 |
1630 | 61, 139 | 2, 26, 1222 |
1632 | 23, 37, 1460 | 37, 707, 1131 |
1634 | 3, 21, 37, 606 | 4, 6, 22, 147, 148, 1665 |
1636 | 491 | 18, 96 |
1638 | 2, 9, 25, 160, 317, 660, 1233 | 1, 192 |
1640 | 1, 186, 229, 1723 | 80, 108, 324 |
1642 | 2, 32 | 15, 94 |
1644 | 5, 99 | 21, 67, 949 |
1646 | 70, 432 | 2, 3, 20, 26, 288 |
1648 | 2, 660 | 5, 6 |
1652 | 14, 49, 442, 878, 1257 | 1 |
1654 | 1, 294, 510 | 5, 36 |
1658 | 2, 25, 142, 982, 1053 | 3, 10, 18, 40, 737, 896 |
1660 | 12, 101, 167 | 2, 6, 26, 120, 182, 400 |
1662 | 7, 1257 | 6, 89 |
1666 | 11, 26 | 20, 233, 243, 247, 1126 |
1670 | 2, 5 | 3 |
1672 | 2, 11, 14 | 1, 2, 34, 67, 689 |
1674 | 1, 15 | 12, 29 |
1676 | 13, 14 | 6, 111 |
1678 | 5, 52, 83, 516, 1380 | 1, 2 |
1680 | 1, 429, 864 | 1 |
1682 | 1, 39, 102, 120 | 17, 24, 44, 680 |
1686 | 4, 561, 951, 1334 | 1, 39, 494 |
1688 | 1, 2, 7, 12, 397 | 2, 158, 432 |
1692 | 174 | 1, 7, 25, 345, 366 |
1694 | 1, 2 | 1, 12 |
1696 | 1 | 2, 165 |
1698 | 2, 1170 | 4, 321 |
1700 | 2, 33, 566 | 1, 13, 47 |
1702 | 1, 3, 60, 95 | 1, 7, 31, 183, 266 |
1704 | 1, 2 | 9, 10, 315 |
1708 | 183, 720 | 9, 531, 794 |
1710 | 4, 7 | 26 |
1712 | 140 | 934 |
1714 | 859, 1627 | 1, 6, 198, 850 |
1716 | 1, 3, 553 | 1, 2 |
1718 | 1, 2, 50, 1064 | 184 |
1720 | 3, 366 | 1, 888 |
1722 | 1 | 2 |
1728 | 1, 17, 2608, 5152, 7538, 22945 | 20, 171, 349, 2502, 26286 |
1730 | 1095, 1653 | 6, 84, 223, 1727 |
1732 | 384, 519 | 1067 |
1734 | 3, 102, 1011, 1889 | 105 |
1736 | 8, 29, 104 | 1, 9, 17 |
1738 | 1, 3 | 9, 417 |
1740 | 2, 329 | 1, 16 |
1742 | 1, 16, 328 | 2, 5, 17, 86, 1384 |
1744 | 26 | 13, 128 |
1746 | 170, 806 | 4, 6, 30 |
1748 | 28, 684 | 1, 56 |
1750 | 1, 2, 123, 175, 765 | 1, 5 |
1752 | 1, 1182, 1522 | 3 |
1754 | 3, 596 | 64, 66, 150 |
1756 | 176 | 47 |
1758 | 12, 153, 1340 | 2, 4 |
1762 | 360 | 2, 8, 207 |
1764 | 3, 7, 39, 136, 1263, 2426 | 2, 1023, 1233, 2010, 4212, 12501 |
1766 | 4, 34, 1227 | 5, 11, 24, 1613 |
1768 | 17, 36, 59, 231 | 15, 46 |
1770 | 42, 68, 390, 780 | 2, 5, 9, 31, 69 |
1772 | 1445 | 2, 14, 756, 795 |
1776 | 23, 393 | 8, 12, 27 |
1778 | 2, 14, 36 | 2, 3, 134, 198, 1456 |
1780 | 6 | 2, 36 |
1782 | 8, 50, 698 | 1 |
1784 | 1, 2, 1845 | 1, 44, 119, 386 |
1786 | 1, 15, 71, 72 | 2, 5 |
1790 | 420, 462 | 2, 36, 170 |
1792 | 2, 318 | 5, 54 |
1794 | 9, 28, 87 | 11, 14, 1824 |
1796 | 2, 6, 195 | 1, 9 |
1798 | 1, 486, 1128 | 4, 9, 11, 20, 244 |
1800 | 30, 32, 264, 1280 | 104, 180 |
1802 | 61, 264 | 22, 538 |
1804 | 3, 437 | 175, 1743 |
1808 | 1, 9, 15, 25, 61, 1044, 1803 | 20, 68 |
1810 | 6, 21, 26, 39, 45, 114, 194, 290 | 7, 10, 15, 16, 499, 520 |
1812 | 1317 | 32, 96 |
1814 | 4, 16, 60, 63, 236, 1341 | 6, 270 |
1816 | 2, 54 | 534 |
1818 | 101, 156 | 1, 2, 7, 8 |
1820 | 1, 165, 1090 | 5, 665 |
1822 | 3 | 6, 408, 1143, 1868 |
1824 | 2, 1530 | 1069 |
1826 | 3, 22, 363, 968, 1816 | 1, 5, 11, 1508 |
1828 | 1, 304 | 34 |
1830 | 2 | 4 |
1832 | 5, 100 | 50, 60, 115, 187, 559 |
1834 | 2, 16, 234, 299 | 2, 271, 1006 |
1836 | 64, 493 | 14, 17, 125, 1205 |
1838 | 305 | 1, 808 |
1840 | 1, 427, 540 | 1, 4, 75 |
1842 | 1, 2, 6, 13, 61, 280 | 15, 64, 159, 208, 1612, 1992 |
1844 | 2, 200 | 141, 363 |
1846 | 10 | 267, 276 |
1848 | 9, 205, 1032, 1650 | 1, 5, 6 |
1850 | 1, 16 | 26, 33 |
1854 | 5, 18, 42, 45, 374, 449, 985, 1779 | 2, 1376 |
1856 | 2, 18, 55, 118, 1500, 1800 | 63, 1016 |
1858 | 374 | 18, 89, 90, 124, 1157 |
1860 | 76 | 1, 2, 3, 1873 |
1862 | 1, 4, 9, 61, 337, 732, 978 | 5, 25, 43, 50, 126, 310 |
1864 | 997 | 6, 12, 114, 506 |
1866 | 3, 65 | 1, 79 |
1868 | 1, 2, 7, 74, 371 | 8, 9, 22 |
1870 | 5, 175, 752, 1190 | 11 |
1872 | 3, 30, 62, 115, 824 | 17, 946 |
1874 | 10, 264 | 1, 153 |
1876 | 1, 16, 18 | 2, 41, 402, 659, 953 |
1878 | 3, 1228 | 9, 78 |
1880 | 6, 20 | 12 |
1882 | 22 | 6, 16, 1393 |
1884 | 4, 8 | 1, 3, 95, 150, 494, 598 |
1886 | 1, 15 | 4, 23, 58, 123, 478, 910 |
1888 | 717 | 3 |
1890 | 2, 3, 4, 6, 14, 79, 149 | 20, 388 |
1892 | 3, 22 | 27, 29 |
1894 | 63 | 1, 12, 36 |
1896 | 1 | 1, 7 |
1898 | 1, 99, 100 | 4 |
1900 | 2, 25 | 11, 23 |
1902 | 6, 22, 141 | 15, 20, 1298 |
1904 | 4, 70, 193, 404, 1550 | 2, 16, 1772 |
1906 | 10, 309, 496 | 2, 3, 15, 23, 71, 158 |
1908 | 2, 1409 | 1, 9, 226, 1702 |
1910 | 1, 4, 24 | 1, 2, 104, 480 |
1912 | 1, 2, 3, 4, 7, 10, 36 | 1, 20, 97 |
1914 | 1, 2, 8, 116, 188, 1664 | 6, 47 |
1916 | 4, 6, 120, 779 | 164 |
1918 | 20, 44, 68 | 2, 5, 549, 1488, 1619 |
1920 | 4, 12 | 2 |
1922 | 20, 53, 87, 417 | 1, 3, 88 |
1924 | 1, 4, 6, 117, 431 | 1, 42, 654, 1537, 1597 |
1926 | 1 | 14 |
1930 | 1246 | 1, 126, 1218 |
1932 | 1, 4 | 171 |
1934 | 3, 18 | 107 |
1936 | 15, 45, 644, 12893 | 741, 4105, 10251, 30106, 47970 |
1938 | 4, 14, 154, 536, 1026 | 2, 29, 302, 309 |
1940 | 1881 | 3, 6, 20, 57, 131 |
1942 | 206, 506, 1087 | 1827 |
1944 | 6 | 24 |
1946 | 21, 394, 888 | 1, 2, 5, 43, 64, 69, 95 |
1948 | 1, 7, 739 | 2 |
1952 | 7, 86 | 1, 3, 993, 1852 |
1954 | 1, 3, 180 | 11, 1776 |
1956 | 27 | 21, 911 |
1958 | 10, 15, 69 | 96, 192 |
1960 | 11, 423 | 50, 133 |
1964 | 2, 89, 96, 134, 300, 1089 | 1, 3, 31, 211 |
1966 | 1, 355 | 15, 753 |
1970 | 1, 7 | 276, 436 |
1972 | 11, 90 | 211, 284, 1179, 1746 |
1974 | 2, 25, 326 | 1, 5, 6, 8, 14 |
1976 | 1, 951 | 50 |
1978 | 11, 1986 | 1 |
1980 | 1, 5, 7, 11, 378, 1775 | 3, 5, 6, 286, 780 |
1982 | 2, 4, 1810 | 52, 74, 126 |
1984 | 6 | 540 |
1988 | 87, 667, 1754 | 1, 11, 12, 243, 370, 1789 |
1990 | 1, 4, 61, 127, 669, 828 | 30, 131, 731 |
1994 | 2, 37 | 3, 5, 27, 114, 854 |
1996 | 32, 57, 960 | 1, 3, 666 |
1998 | 1, 2, 15, 55, 150 | 15 |
2000 | 562 | 1, 2, 27, 284 |
2002 | 1, 2, 4, 62, 223, 295, 341, 648, 882, 886 | 6, 26, 201, 299, 385, 687 |
2004 | 3 | 15, 144 |
2006 | 5, 6, 773, 1521 | 12, 19, 66, 1204, 1717 |
2008 | 8, 11, 22, 1003, 1174 | 3, 18, 30, 41, 78 |
2012 | 6, 956 | 4, 689 |
2014 | 5 | 19 |
2016 | 18, 78, 253, 1670 | 29, 608 |
2020 | 6, 9 | 1 |
2022 | 1, 6, 22, 771 | 351, 697 |
2024 | 85, 635, 1470 | 5, 276, 411, 424 |
2028 | 78, 99, 279 | 27 |
2030 | 30 | 1, 7, 108, 277, 309, 424 |
2032 | 1 | 1160 |
2036 | 1, 62 | 1 |
2038 | 1, 78, 120 | 5, 10, 12, 66, 604 |
2042 | 4, 15, 501 | 1 |
2044 | 1, 5, 12, 119 | 15, 50, 296 |
2046 | 282 | 21, 336, 1011 |
2048 | 5, 12, 1299 | 22, 150 |
2050 | 216, 1511 | 2, 20 |
2052 | 265, 1119, 1144 | 1, 3, 10, 77, 113, 1048, 1608, 1710 |
2054 | 1, 9, 12, 24, 674, 1659, 1982 | 40 |
2056 | 5, 813 | 1, 115 |
2058 | 1, 6, 105, 416 | 1, 3, 231, 989, 1977 |
2060 | 1, 16, 21 | 162 |
2062 | 2, 5, 18 | 1029 |
2066 | 2, 12, 192, 203 | 2, 132 |
2068 | 105 | 1551 |
2070 | 310, 472 | 9, 253 |
2072 | 10, 17, 109 | 1, 17, 25, 138, 531 |
2074 | 1, 144 | 2, 3, 275, 996 |
2078 | 1, 5, 8, 31, 38, 114, 360 | 25, 143, 317, 1891 |
2080 | 40, 310 | 1, 2, 6, 20, 23, 30 |
2082 | 1 | 4, 29, 148 |
2084 | 3 | 2, 63, 75, 110 |
2086 | 141, 572, 1326 | 1, 2, 8, 288 |
2088 | 1 | 2, 5, 23, 62 |
2090 | 45, 93, 258 | 1, 57, 1588 |
2092 | 1, 2 | 1, 16, 30, 83 |
2094 | 1, 14, 16, 110, 277, 314, 1400 | 1, 16, 31, 58 |
2096 | 1, 132 | 4, 5 |
2098 | 3, 16, 34, 1881 | 6 |
2100 | 33, 35, 92, 181, 190 | 1, 47, 1252 |
2102 | 1, 9, 19, 34, 79, 84, 162, 1678 | 63, 111 |
2106 | 1, 119, 148, 700, 1620 | 1, 109 |
2108 | 1, 40, 115 | 1, 4, 50 |
2110 | 1, 2, 6, 162, 302 | 3, 5, 234, 413 |
2112 | 17, 33 | 1, 8, 9, 15, 44, 1327 |
2114 | 1, 2, 280 | 8 |
2116 | 6, 652, 2586 | 27, 1020 |
2118 | 17, 65, 122 | 25, 31, 220 |
2120 | 85 | 2, 317, 394, 458 |
2122 | 55 | 81 |
2124 | 44, 87 | 660 |
2130 | 1, 19 | 8 |
2134 | 1, 1189 | 3, 10, 1090 |
2136 | 26 | 1, 6, 7, 104 |
2138 | 1, 2, 13, 92, 390, 578 | 28, 39, 1121 |
2142 | 24 | 831 |
2144 | 82, 189 | 3, 77, 156, 482, 1182 |
2148 | 1323 | 17, 724 |
2150 | 40, 137, 510 | 1, 3, 273 |
2152 | 1, 2 | 3, 9, 47, 525 |
2154 | 411 | 2, 24, 33, 120 |
2156 | 137, 491 | 3, 345 |
2158 | 193 | 2, 14, 222, 327 |
2160 | 3, 9, 212, 266 | 10, 58 |
2162 | 16, 80, 560, 689 | 1, 524 |
2164 | 1, 172 | 10, 74, 128, 132, 344 |
2166 | 368 | 27 |
2170 | 9, 119 | 1, 2, 875, 1238 |
2172 | 1, 40 | 12 |
2174 | 5 | 106, 744 |
2176 | 15, 125 | 1, 6, 73 |
2178 | 1, 3, 4, 25 | 1, 2, 3, 543 |
2180 | 1, 8, 15, 78, 1014 | 5, 6, 10 |
2184 | 1, 8, 64, 715, 722 | 45, 60 |
2186 | 561, 1035, 1350 | 2, 1284 |
2188 | 6 | 51 |
2190 | 110, 114, 440 | 49, 1824 |
2192 | 201 | 8, 36, 47 |
2194 | 25 | 15, 1245 |
2196 | 57, 100, 612 | 110, 198 |
2198 | 417, 552, 562 | 3, 10, 91, 425 |
2200 | 4, 6, 37 | 5, 6, 200 |
2202 | 33, 200, 330, 627 | 15, 49, 280, 1024 |
2206 | 8 | 519, 1181, 1701 |
2208 | 37, 795 | 3, 11 |
2210 | 4, 347, 437 | 1, 18, 1110, 1326 |
2212 | 1, 2, 6, 15, 62 | 9, 53, 108 |
2214 | 3, 16, 394, 1768 | 35, 89 |
2216 | 17, 50 | 58 |
2218 | 233 | 5, 114, 647, 828 |
2220 | 5, 78, 122, 699 | 2, 15, 169, 204 |
2222 | 2, 13, 242 | 17, 135, 334 |
2224 | 286 | 1, 97 |
2226 | 1 | 1, 2, 3, 79, 107 |
2228 | 1, 6, 10, 13, 378 | 2, 26 |
2230 | 3, 228 | 13 |
2232 | 8, 59, 1874 | 2, 316 |
2234 | 9, 12, 48 | 7, 97 |
2236 | 511 | 147 |
2238 | 273 | 1 |
2240 | 1, 2, 3, 1646 | 1, 8, 13, 61, 101, 383 |
2242 | 1, 3, 312 | 45, 65, 113, 429 |
2244 | 5, 885 | 46 |
2246 | 2, 3, 4, 1134, 1919 | 1 |
2248 | 1, 2, 8, 50, 94 | 7 |
2252 | 1293 | 50, 122, 181 |
2254 | 14 | 2, 5 |
2256 | 555 | 3 |
2258 | 1215 | 4 |
2260 | 4, 454 | 1, 4, 8, 15, 119 |
2262 | 1, 2, 78, 98, 235, 1745 | 3, 53, 110, 154, 271 |
2268 | 2 | 1, 30, 54, 141, 286, 376 |
2270 | 1, 24, 388 | 795, 1274, 1500 |
2272 | 6, 1175, 1736 | 1, 9, 415 |
2274 | 1, 79, 826 | 5, 13, 69 |
2276 | 33, 36, 69, 820 | 1, 29, 113, 903 |
2278 | 1, 108 | 18, 46, 99, 129, 233, 345 |
2282 | 2, 3, 5, 33, 70, 1309, 1327 | 1, 385 |
2284 | 1 | 18, 275, 1478 |
2286 | 20 | 1, 6, 433, 1416, 1590 |
2288 | 1, 193 | 9 |
2292 | 7, 32, 60 | 6, 258 |
2294 | 4 | 87, 350, 481 |
2296 | 15, 25, 85, 535 | 1, 2, 6, 10, 26, 140, 1485 |
2302 | 3, 107 | 1, 3, 84, 216, 292, 323 |
2304 | 1, 2, 3, 6, 1941 | 6637, 12989 |
2306 | 69, 165 | 29 |
2310 | 1, 2, 1308 | 3, 4, 1252 |
2314 | 1257 | 1, 52 |
2316 | 1, 13, 73 | 43, 148, 387 |
2318 | 38, 39, 299, 306 | 12, 88, 94, 325, 375 |
2320 | 2, 63, 200, 252 | 15, 78 |
2322 | 3, 5, 6, 22, 90, 154, 1762 | 2, 67 |
2324 | 2, 5, 37, 813 | 28, 39, 237 |
2326 | 120 | 833 |
2328 | 51 | 3, 6 |
2332 | 3 | 109, 156, 1089 |
2336 | 15, 333 | 1, 7, 432 |
2338 | 1, 1286 | 204, 759 |
2340 | 4, 7, 10, 24, 106 | 14, 1665 |
2344 | 4 | 1, 10, 239, 635 |
2346 | 1, 14, 141 | 9, 12, 1930 |
2348 | 13 | 4, 149 |
2350 | 3, 106, 267, 453 | 3 |
2352 | 2, 29, 57, 944, 1270 | 4, 8, 12 |
2354 | 154 | 20 |
2356 | 140 | 45, 1948 |
2358 | 5, 207, 605 | 1, 28, 98, 1735 |
2360 | 1, 2, 11, 108 | 7, 182, 286, 1113 |
2362 | 939 | 53, 1422 |
2364 | 3, 6, 405 | 151, 1646 |
2366 | 24 | 7, 109, 370, 625 |
2368 | 156, 864 | 2, 29 |
2370 | 2, 3, 80, 959, 1475 | 12 |
2372 | 7, 13 | 4, 171 |
2374 | 4 | 1, 200, 214 |
2376 | 1, 9, 84, 378 | 54 |
2378 | 3, 18 | 2 |
2380 | 346 | 1, 435, 521, 1723 |
2386 | 20, 36, 40, 180, 196 | 24, 112, 1034 |
2388 | 110 | 1, 4, 6 |
2390 | 1, 14, 18 | 36, 69, 402 |
2392 | 21 | 1, 8, 384 |
2394 | 1, 205, 905 | 3, 4, 9, 54, 140 |
2396 | 18, 1233 | 11, 161 |
2402 | 1, 10, 23, 24, 661 | 156, 366 |
2406 | 9, 1212 | 2, 3, 6, 26, 153 |
2408 | 21 | 7, 40 |
2410 | 156, 316, 493, 1582 | 2, 3, 113 |
2412 | 56 | 1, 3, 517 |
2414 | 1, 3 | 3, 21, 41, 87, 647 |
2416 | 3 | 625 |
2418 | 2, 247, 1279, 1975 | 51, 57 |
2420 | 4, 900 | 1, 2, 21, 66, 1916 |
2422 | 1, 3, 10, 332 | 1, 10 |
2424 | 1, 420 | 827 |
2426 | 6, 51, 495 | 7, 193 |
2428 | 2 | 68 |
2430 | 3, 5, 12, 27, 122, 147, 155, 404 | 1, 11, 104 |
2432 | 1, 7, 510 | 3, 6, 30 |
2434 | 4 | 8, 66, 73, 434 |
2436 | 4, 19, 30, 133 | 590 |
2440 | 3, 15, 65, 101 | 3, 7, 375 |
2442 | 64, 115 | 33, 455 |
2444 | 26, 70, 205 | 34, 104, 287 |
2446 | 6, 61, 63 | 4, 190 |
2448 | 1240 | 1, 3, 25, 98 |
2450 | 1, 34, 96, 126 | 2, 21, 225, 423, 1344 |
2452 | 127 | 3, 770 |
2454 | 15 | 1 |
2456 | 1, 5, 17 | 21, 425, 561 |
2458 | 4, 17, 19, 86, 318 | 77 |
2460 | 13, 78 | 3, 6 |
2462 | 70, 1360 | 74 |
2464 | 3, 482, 1882 | 1 |
2466 | 1, 7 | 35, 908 |
2468 | 2, 1250 | 1, 9, 76, 223, 1272 |
2470 | 1, 6, 11, 14, 49, 195 | 5 |
2472 | 76, 1853 | 3, 332 |
2476 | 3, 435 | 42, 169, 1524 |
2478 | 3, 22 | 2, 6, 275 |
2484 | 713, 953 | 1, 207, 344, 866 |
2486 | 1, 40, 79, 217, 290 | 41, 298, 562 |
2488 | 9, 128, 1249 | 310 |
2490 | 83 | 1 |
2492 | 1, 2, 81, 978, 1429 | 2, 3, 6, 1090 |
2494 | 670, 1212 | 182 |
2496 | 38, 126, 495 | 3 |
2498 | 2, 9 | 33, 39, 251, 535 |
2500 | 2, 33, 215, 1273, 1337, 3180 | 2, 19, 60, 2198 |
2502 | 2, 3 | 1329 |
2504 | 16, 59 | 2, 20, 198, 717 |
2506 | 3, 10, 13, 1755 | 1, 43 |
2508 | 1, 106, 331, 721 | 38, 107 |
2510 | 9, 12, 1271, 1496 | 1, 76, 489 |
2512 | 1, 2, 10, 276, 583 | 1, 5, 97, 362, 759, 1193, 1289 |
2514 | 1, 14, 270 | 1, 7, 10, 13, 933 |
2516 | 1, 54, 144, 339 | 4, 159 |
2520 | 3, 10, 82, 819 | 3, 8 |
2522 | 90 | 2, 6, 101, 710, 819 |
2526 | 8, 38, 1219 | 2, 37 |
2528 | 18, 29, 188, 204, 434, 554, 581 | 1, 142 |
2532 | 4 | 1, 271, 381 |
2536 | 9, 646 | 56, 795, 1610 |
2538 | 2 | 10, 1081 |
2540 | 122, 306 | 1 |
2542 | 1, 7, 11, 538, 670, 1012 | 1, 19, 132, 1782 |
2544 | 1, 2, 8, 21, 368 | 34, 42 |
2546 | 52 | 18 |
2548 | 2 | 1, 3, 7, 44, 199 |
2550 | 1 | 38, 1346, 1644 |
2552 | 9 | 4, 61, 1455 |
2554 | 3, 4, 15, 121, 205, 231 | 1, 2, 182 |
2556 | 1, 6, 34, 90 | 57 |
2558 | 332 | 22, 285 |
2562 | 61 | 1, 2, 5, 12, 200, 995 |
2564 | 1, 93, 100, 268 | 5, 17, 62, 1310 |
2566 | 2, 11 | 114, 175, 535 |
2568 | 105, 130, 859 | 1, 2, 290, 1676 |
2570 | 1, 8 | 6, 486 |
2572 | 3 | 3, 47 |
2576 | 108, 119, 305, 648, 834, 1669 | 1, 2, 35, 196, 717, 1144, 1514 |
2578 | 1 | 168 |
2580 | 101, 497, 1085 | 55 |
2582 | 3, 27, 92, 305, 1278 | 3, 4, 6, 342 |
2584 | 29, 46, 67, 512 | 1, 405 |
2590 | 1, 12, 25, 32, 335, 347 | 1, 2, 33, 89, 383 |
2592 | 1, 373, 481, 756 | 2, 9, 287, 312 |
2594 | 200, 476 | 16, 28, 271, 310, 1380 |
2596 | 13, 18, 75, 82 | 1, 6 |
2598 | 1, 24, 104, 367, 719, 798 | 1, 4 |
2600 | 1, 3, 9, 39, 57 | 3, 130, 420 |
2602 | 77, 84, 317 | 1, 2, 7, 20, 87, 145 |
2604 | 1, 5, 9, 17, 79, 1220 | 135, 191 |
2608 | 2, 27, 32 | 12 |
2612 | 1, 102, 1042 | 4, 8 |
2618 | 81, 854 | 1, 29, 207, 976 |
2620 | 1, 217 | 209, 261 |
2628 | 115 | 558, 748 |
2630 | 10, 837 | 2 |
2632 | 7, 196, 342 | 3, 10, 15, 351, 1065 |
2636 | 2, 18, 81, 357 | 1 |
2638 | 1, 18 | 2, 14, 23, 46, 462, 1053, 1786 |
2640 | 2 | 79, 1960 |
2642 | 2 | 132 |
2644 | 41, 267, 1155 | 8, 282 |
2648 | 1, 3, 12, 34, 751 | 20, 1157 |
2652 | 25, 154, 173, 299 | 1, 2, 7, 10, 86 |
2654 | 1, 2, 354, 1139 | 2 |
2656 | 12 | 16, 293 |
2662 | 3 | 2, 5, 56 |
2664 | 3 | 1, 10, 118, 124 |
2666 | 1, 6, 12, 24, 264 | 1, 124 |
2668 | 1, 2, 4, 6 | 20, 1772 |
2670 | 12, 63 | 42, 113 |
2672 | 51, 575 | 2, 20 |
2674 | 305, 435 | 8 |
2676 | 280 | 11, 435 |
2680 | 1 | 1, 2, 10, 15, 50, 107 |
2682 | 1, 34, 84, 106, 118 | 78, 1708 |
2684 | 2, 44 | 5, 366 |
2686 | 257, 888 | 12, 42, 1112 |
2690 | 165 | 2 |
2692 | 143, 893 | 90, 1870 |
2694 | 36, 578, 1739 | 2, 242, 470, 944, 1118 |
2696 | 1134 | 2, 35, 59, 330, 372 |
2698 | 2, 73, 93 | 51 |
2700 | 159 | 1, 2, 50 |
2702 | 1 | 1 |
2704 | 1, 7, 12, 11617 | 83, 228, 7205 |
2706 | 5 | 1, 7 |
2708 | 1, 13, 61, 722 | 2, 3, 52, 77, 160 |
2710 | 21, 284, 424, 542 | 50 |
2712 | 103, 111 | 15, 102 |
2714 | 21, 149, 179, 216 | 1, 12, 25 |
2716 | 1, 13, 79, 99 | 1, 10, 50, 790 |
2718 | 1, 3, 4, 9, 57, 312, 828 | 9, 14, 1235 |
2720 | 24, 39, 305, 1560 | 1, 177, 1168 |
2722 | 1, 2, 13, 22, 65, 1032 | 3, 4, 33, 343, 1102 |
2724 | 1300 | 1, 23, 25 |
2726 | 1, 30, 43, 752 | 35, 58, 324 |
2728 | 10, 11 | 1, 6, 14, 73 |
2730 | 1, 120, 340 | 2, 42, 124, 200 |
2732 | 3, 4, 6 | 6, 27 |
2734 | 17 | 1, 3, 343 |
2736 | 1, 2, 16, 256 | 1, 18, 245, 610, 796 |
2738 | 1, 3 | 1, 6, 15, 1267 |
2740 | 1, 374 | 6, 39, 210, 522 |
2744 | 2, 15, 80, 4116, 4553 | 20, 24, 166, 1948, 1979 |
2746 | 28, 252 | 2, 45, 452, 537 |
2748 | 8, 26, 42 | 1, 33, 109 |
2750 | 1, 2, 10, 44, 218 | 2, 53, 64, 414, 526 |
2752 | 6, 57, 157, 167, 247 | 17, 27 |
2754 | 2, 42, 73 | 11, 12, 82 |
2756 | 3, 27 | 2, 9, 27 |
2758 | 24, 798 | 1, 5, 35 |
2760 | 1 | 98 |
2762 | 3, 234 | 22, 94, 1450 |
2764 | 5, 34, 1261 | 27, 91, 627, 644 |
2766 | 3, 5, 278 | 3 |
2772 | 1130 | 1, 63 |
2776 | 141 | 27, 397 |
2778 | 747 | 1, 2, 1349 |
2780 | 1, 4 | 69 |
2784 | 1386 | 1, 3, 51, 174, 339, 1071, 1574 |
2786 | 1 | 125, 137, 702, 965 |
2788 | 3, 24, 402, 435, 718, 1416 | 2, 3, 36, 935 |
2790 | 5 | 127 |
2792 | 42, 1821 | 37, 89, 494 |
2796 | 1, 2, 147 | 9, 29, 370, 1895 |
2800 | 22, 1240 | 20 |
2806 | 33, 133 | 1 |
2808 | 1, 28 | 1, 12, 584, 1547 |
2810 | 1, 691, 866 | 190, 1390 |
2812 | 9 | 26 |
2814 | 6, 11, 16 | 12, 1626 |
2816 | 453 | 2 |
2818 | 74 | 4, 15, 420 |
2820 | 21, 194, 1718 | 1, 5, 11, 63, 303, 710, 1180 |
2822 | 1, 8 | 3, 1682 |
2824 | 3, 26 | 117 |
2826 | 9, 400, 753 | 7, 50 |
2828 | 9, 113 | 3, 490, 542 |
2832 | 18, 72, 227, 1518 | 30 |
2834 | 11, 157, 223, 386, 463 | 6, 40, 42, 1814 |
2836 | 4 | 1, 3, 185 |
2838 | 1, 2, 12, 25 | 186, 316 |
2840 | 4, 5, 34, 658 | 2, 3, 111 |
2842 | 22, 196, 609 | 8, 29, 79, 121, 311 |
2844 | 42 | 24, 384 |
2848 | 8, 30, 589, 650 | 1, 9, 59, 636, 829 |
2850 | 1 | 4, 372 |
2852 | 2, 13, 63, 1040 | 108 |
2854 | 5 | 1, 97, 98 |
2856 | 1, 2 | 20 |
2858 | 7, 49, 393 | 2, 291, 576 |
2860 | 50 | 12 |
2862 | 7, 16, 97, 145 | 9, 121, 180, 265 |
2864 | 34, 58, 85, 1315 | 2 |
2866 | 192 | 21 |
2868 | 46, 108 | 1, 3 |
2870 | 1, 765 | 1, 22, 118, 1221 |
2872 | 1, 7, 24, 37, 58 | 5, 8 |
2874 | 11, 332 | 1776 |
2876 | 51, 135 | 12, 93 |
2878 | 4, 33, 256 | 44, 59, 99, 325, 765 |
2880 | 14, 243 | 1594 |
2882 | 681 | 1, 24, 57, 170 |
2884 | 1, 680, 852, 1048 | 4, 14, 44 |
2888 | 5, 20, 749 | 1 |
2890 | 1, 16, 1931 | 7, 501 |
2892 | 6, 802, 1788 | 154 |
2894 | 57, 584 | 30, 53, 198, 1071, 1906 |
2896 | 17, 45, 850 | 1, 3, 60, 206 |
2898 | 1, 11, 13, 21, 633 | 13 |
2900 | 40 | 5, 6, 9 |
2902 | 15, 29, 62, 1142 | 10, 103 |
2906 | 7, 243, 820 | 13, 29, 33, 76 |
2908 | 39, 475 | 3, 9 |
2910 | 4, 226, 1974 | 1, 2 |
2912 | 1, 34, 333 | 6, 8, 13 |
2914 | 4, 34 | 2, 113, 285, 411 |
2916 | 4034 | 955 |
2920 | 17, 34, 59, 136 | 2, 6, 688 |
2926 | 1, 2, 6, 362, 1232 | 5, 11, 20 |
2928 | 7, 217 | 17, 20, 299, 884 |
2930 | 134 | 1, 49, 1152, 1881 |
2932 | 1, 79, 468 | 1, 2, 41 |
2934 | 1, 2, 35 | 2 |
2936 | 12 | 48, 65 |
2938 | 454 | 31, 36 |
2940 | 3, 16, 90 | 1, 2, 48 |
2942 | 1, 45 | 3, 551 |
2946 | 2, 22, 138 | 20, 118 |
2948 | 31, 69, 426, 1577, 1586 | 66, 128 |
2950 | 21 | 57, 130 |
2952 | 4, 12, 420, 455 | 2, 207, 1920 |
2954 | 20 | 1, 129, 1487 |
2956 | 1, 25 | 5, 24, 41, 80, 839 |
2958 | 3, 18, 798 | 4 |
2960 | 25, 444, 1793 | 25, 367 |
2964 | 2, 27, 49, 129 | 15, 196 |
2966 | 3, 52 | 54 |
2968 | 1475 | 3, 12 |
2972 | 2, 32, 153 | 1, 169 |
2976 | 61, 91, 157 | 1, 1673 |
2980 | 1066, 1420 | 2 |
2982 | 2 | 4, 78, 82, 156, 606 |
2984 | 16, 64, 421 | 18 |
2986 | 3, 6 | 237 |
2988 | 3, 121 | 120, 990 |
2990 | 23, 28, 212 | 2, 53 |
2992 | 3, 8, 1800 | 6, 84, 102 |
2996 | 237 | 1, 4, 30, 70 |
2998 | 1, 12, 111, 378, 733 | 84 |
3000 | 312, 366 | 180 |
How to participate?
Reserving
- Reserve your base(s)/range(s) in this thread.
Sieving
- Use cksieve (from Mtsieve) and
- run a new sieve by calling
cksieve -b 12 -n 1 -N 10000 -P 1000000000
(for base=12, n-range=1-10000, max prime factor 109). The sieve file will be written to ck_12.pfgw. - rerun an old sieve by calling
cksieve -P 1e12 -i ck_12.pfgw -o ck_12.pfgw -f factors.txt
(for base=12, max prime factor 1012, input/output files given, storing factors to "factors.txt").
- run a new sieve by calling
PRP testing
- Use PFGW calling
pfgw64.exe -f0 ck_12.pfgw
(running candidates file for base 12, no further factoring).
Prime testing
After testing with PFGW higher probable primes will be written in "pfgw.log". These have to be checked prime by calling like pfgw64 -tp -q"(12^68835-1)^2-2"
.
Reporting
Once you have completed your range, report any primes found in this thread. Then report the completed range in the reservation thread and specify whether you will continue with the base or release it.
References
External links
Current
- "Carol / Kynea Coordinated Search - Reservations" at MersenneForum up to post #284 (2021-05-19)
- "Carol / Kynea Primes" at MersenneForum up to post #250 (2021-05-19 )
- 2021 project goals
Others
General numbers |
Special numbers |
|
Prime numbers |
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