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+ | '''Carol numbers''' and '''Kynea numbers''' are numbers of the form <math>(b^n-1)^2-2</math> and <math>(b^n+1)^2-2</math>, respectively, while '''Carol primes''' and '''Kynea primes''' are [[prime]]s 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== | ==Definitions== | ||
In the context of the Carol/Kynea prime search, a Carol number is a number of the form <math>(b^n-1)^2-2</math> and a Kynea number is a number of the form <math>(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: | In the context of the Carol/Kynea prime search, a Carol number is a number of the form <math>(b^n-1)^2-2</math> and a Kynea number is a number of the form <math>(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: | ||
− | * | + | *{{Vb}} must be even, since if it is odd then <math>(b^n±1)^2-2</math> is always even, and thus can’t be prime. |
− | * | + | *{{Vn}} must be greater than or equal to 1. For any {{Vb}}, if {{Vn}} is 0 then <math>(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 {{Vn}} is negative then <math>(b^n±1)^2</math> is not necessarily an integer. |
− | * | + | *{{Vb}} 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>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 | + | Due to the form of these numbers, they are also classified as near-square numbers (numbers of the form <math>n^2-k</math>). |
==History== | ==History== | ||
Line 11: | Line 14: | ||
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. | 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<ref>[https://www.mersenneforum.org/showthread.php?t=20784 Thread "Carol / Kynea search (Near-power primes)"]</ref> for a coordinated search of Carol/Kynea numbers on [[MersenneForum]], which continues to this day | + | On 2015-12-26 Mark opened a thread<ref>[https://www.mersenneforum.org/showthread.php?t=20784 Thread "Carol / Kynea search (Near-power primes)"]</ref> for a coordinated search of Carol/Kynea numbers on [[MersenneForum]], which continues to this day. |
+ | |||
+ | <b>All data are now collected here using the information from the forum posts.</b> Feel free to get an [[Help:Logging_in|account]] and editing pages by yourself. | ||
==Top 5 Carol primes== | ==Top 5 Carol primes== | ||
Line 17: | Line 22: | ||
! Prime !! Digits !! Found by !! Date | ! Prime !! Digits !! Found by !! Date | ||
|- | |- | ||
− | |{{T5000| | + | |{{T5000|133970|(10<sup>859669</sup>-1)<sup>2</sup>-2}}||1719339||[[Ryan Propper]]||2022-05-25 |
|- | |- | ||
− | |{{T5000| | + | |{{T5000|133946|(10<sup>657559</sup>-1)<sup>2</sup>-2}}||1315119||[[Ryan Propper]]||2022-05-18 |
|- | |- | ||
− | |{{T5000| | + | |{{T5000|133929|(10<sup>393063</sup>-1)<sup>2</sup>-2}}||786127||[[Ryan Propper]]||2022-05-14 |
|- | |- | ||
− | |{{T5000| | + | |{{T5000|133928|(10<sup>334568</sup>-1)<sup>2</sup>-2}}||669137||[[Ryan Propper]]||2022-05-14 |
|- | |- | ||
− | |{{T5000| | + | |{{T5000|133974|(146<sup>144882</sup>-1)<sup>2</sup>-2}}||627152||[[Ryan Propper]]||2022-06-05 |
|} | |} | ||
Line 32: | Line 37: | ||
! Prime !! Digits !! Found by !! Date | ! Prime !! Digits !! Found by !! Date | ||
|- | |- | ||
− | |{{T5000| | + | |{{T5000|133993|(146<sup>276995</sup>+1)<sup>2</sup>-2}}||1199030||[[Ryan Propper]]||2022-05-29 |
|- | |- | ||
− | |{{T5000| | + | |{{T5000|133930|(10<sup>410997</sup>+1)<sup>2</sup>-2}}||821995||[[Ryan Propper]]||2022-05-14 |
|- | |- | ||
− | |{{T5000| | + | |{{T5000|133980|(146<sup>180482</sup>+1)<sup>2</sup>-2}}||781254||[[Ryan Propper]]||2022-06-05 |
|- | |- | ||
− | |{{T5000| | + | |{{T5000|126558|(362<sup>133647</sup>+1)<sup>2</sup>-2}}||683928||[[Karsten Bonath]]||2019-06-17 |
|- | |- | ||
− | |( | + | |{{T5000|136056|(2634<sup>88719</sup>+1)<sup>2</sup>-2}}||606948||[[Mischa Rodermond]]||2023-05-18 |
|} | |} | ||
Line 48: | Line 53: | ||
!Base!!Carol!!Kynea | !Base!!Carol!!Kynea | ||
|- | |- | ||
− | |[[Carol- | + | |[[Carol-Kynea prime 2|2]]||{{OEIS|s|A091515}}||{{OEIS|s|A091513}} |
+ | |- | ||
+ | |[[Carol-Kynea prime 6|6]]||{{OEIS|s|A100901}}||{{OEIS|s|A100902}} | ||
+ | |- | ||
+ | |[[Carol-Kynea prime 10|10]]||{{OEIS|s|A100903}}||{{OEIS|s|A100904}} | ||
+ | |- | ||
+ | |[[Carol-Kynea prime 12|12]]||{{OEIS|s|A364076}}||{{OEIS|s|A364077}} | ||
|- | |- | ||
− | |[[Carol- | + | |[[Carol-Kynea prime 14|14]]||{{OEIS|s|A100905}}||{{OEIS|s|A100906}} |
|- | |- | ||
− | |[[Carol- | + | |[[Carol-Kynea prime 18|18]]||{{OEIS|s|A364078}}||{{OEIS|s|A364079}} |
|- | |- | ||
− | |[[Carol- | + | |[[Carol-Kynea prime 20|20]]||{{OEIS|s|A364080}}||{{OEIS|s|A364081}} |
|- | |- | ||
− | |[[Carol- | + | |[[Carol-Kynea prime 22|22]]||{{OEIS|s|A100907}}||{{OEIS|s|A100908}} |
|} | |} | ||
Line 128: | Line 139: | ||
==External links== | ==External links== | ||
===Current=== | ===Current=== | ||
− | |||
*[https://www.mersenneforum.org/showthread.php?t=21216 "Carol / Kynea Coordinated Search - Reservations"] at [[MersenneForum]] up to post #284 (2021-05-19) | *[https://www.mersenneforum.org/showthread.php?t=21216 "Carol / Kynea Coordinated Search - Reservations"] at [[MersenneForum]] up to post #284 (2021-05-19) | ||
*[https://www.mersenneforum.org/showthread.php?t=21251 "Carol / Kynea Primes"] at [[MersenneForum]] up to post #250 (2021-05-19 ) | *[https://www.mersenneforum.org/showthread.php?t=21251 "Carol / Kynea Primes"] at [[MersenneForum]] up to post #250 (2021-05-19 ) | ||
Line 135: | Line 145: | ||
===Others=== | ===Others=== | ||
*[http://mathworld.wolfram.com/Near-SquarePrime.html Near-Square primes] | *[http://mathworld.wolfram.com/Near-SquarePrime.html Near-Square primes] | ||
− | |||
− | |||
*[https://www.mersenneforum.org/showthread.php?t=20784 Old thread] | *[https://www.mersenneforum.org/showthread.php?t=20784 Old thread] | ||
*[http://harvey563.tripod.com/Carol_Kynea.txt Old project by S.Harvey] | *[http://harvey563.tripod.com/Carol_Kynea.txt Old project by S.Harvey] | ||
{{Navbox NumberClasses}} | {{Navbox NumberClasses}} | ||
[[Category:Carol-Kynea prime| ]] | [[Category:Carol-Kynea prime| ]] |
Latest revision as of 00:38, 6 July 2023
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 |
---|---|---|---|
(10859669-1)2-2 | 1719339 | Ryan Propper | 2022-05-25 |
(10657559-1)2-2 | 1315119 | Ryan Propper | 2022-05-18 |
(10393063-1)2-2 | 786127 | Ryan Propper | 2022-05-14 |
(10334568-1)2-2 | 669137 | Ryan Propper | 2022-05-14 |
(146144882-1)2-2 | 627152 | Ryan Propper | 2022-06-05 |
Top 5 Kynea primes
Prime | Digits | Found by | Date |
---|---|---|---|
(146276995+1)2-2 | 1199030 | Ryan Propper | 2022-05-29 |
(10410997+1)2-2 | 821995 | Ryan Propper | 2022-05-14 |
(146180482+1)2-2 | 781254 | Ryan Propper | 2022-06-05 |
(362133647+1)2-2 | 683928 | Karsten Bonath | 2019-06-17 |
(263488719+1)2-2 | 606948 | Mischa Rodermond | 2023-05-18 |
OEIS sequences
These are available OEIS sequences:
Base | Carol | Kynea |
---|---|---|
2 | A091515 | A091513 |
6 | A100901 | A100902 |
10 | A100903 | A100904 |
12 | A364076 | A364077 |
14 | A100905 | A100906 |
18 | A364078 | A364079 |
20 | A364080 | A364081 |
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 |
|