## PRP Records

### Probable Primes Top 10000

#### (293510 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 5501 2^365838-461267 110129 Enzo Doria 07/2015 5502 30152^4491+4491^30152 110126 Hans Havermann 11/2020 5503 10^110111+464019 110112 Patrick De Geest 05/2021 5504 10^110111-40001 110111 Robert Price 01/2021 5505 2^365763-6555 110106 Lelio R Paula 04/2017 5506 (2^365689+2^182845+1)/5 110083 11/2006 5507 2^365666-459161 110077 Enzo Doria 05/2015 5508 3*10^110076-7 110077 Robert Price 08/2015 5509 13^98785-72 110041 Lelio R Paula 03/2017 5510 (25^78707+1)/26 110027 Robert Price 06/2013 5511 (7*10^110027-277)/9 110027 Robert Price 02/2022 5512 (16*10^110014-73)/3 110015 Robert Price 07/2020 5513 (7*10^110006-151)/9 110006 Robert Price 02/2018 5514 6^141361-7 110001 Lelio R Paula 11/2014 5515 20^84536+81 109984 Lelio R Paula 03/2017 5516 5*2^365347-9 109982 Lelio R Paula 09/2014 5517 9*6^141303+7 109957 Lelio R Paula 11/2014 5518 27635^9522+9522^27635 109953 Hans Havermann 11/2020 5519 78^58099+77 109929 Norbert Schneider 02/2015 5520 2*10^109928-7 109929 Robert Price 10/2015 5521 30580^3933+3933^30580 109927 Hans Havermann 11/2020 5522 26380^14689+14689^26380 109926 Hans Havermann 11/2020 5523 (2^365161+1130)/2 109925 Stefano Morozzi 09/2020 5524 (27*2^365137-1)/2021 109916 Lelio R Paula 03/2014 5525 (4441*29^75152-24)/7 109905 Curtis Bright 05/2015 5526 (2^365087+7)/6015 109899 Lelio R Paula 01/2014 5527 (2^365069+3774)/2 109897 Stefano Morozzi 02/2021 5528 29652^5083+5083^29652 109894 Mark Rodenkirch 10/2020 5529 (2^365049+722)/2 109891 Stefano Morozzi 09/2020 5530 (35*10^109888-89)/9 109889 Robert Price 02/2022 5531 18^87533-11 109878 Lelio R Paula 04/2017 5532 2^364982-5 109871 Henri Lifchitz 04/2006 5533 3*10^109861+59 109862 Robert Price 08/2018 5534 5*10^109860-69 109861 Robert Price 02/2021 5535 2^364936-1867979 109857 Enzo Doria 04/2016 5536 27013^11652+11652^27013 109846 Hans Havermann 10/2020 5537 2^364867-112087 109836 Enzo Doria 06/2014 5538 4^182415-85061 109825 Mike Oakes 06/2011 5539 (2^364809+1034)/2 109819 Stefano Morozzi 09/2020 5540 (53*10^109809-287)/9 109810 Robert Price 02/2022 5541 (52*10^109807-133)/9 109808 Robert Price 09/2021 5542 25708^18675+18675^25708 109806 Hans Havermann 10/2020 5543 (17^89227+16^89227)/33 109788 Robert Price 08/2013 5544 2^364687-187 109782 Lelio R Paula 01/2012 5545 2^364644+67 109769 Lelio R Paula 01/2012 5546 (9787*2^364625-1)/24947 109763 Lelio R Paula 05/2015 5547 (2^364616+5)/9 109760 Lelio R Paula 01/2014 5548 (55*10^109759+89)/9 109760 Robert Price 03/2019 5549 (14*32^72921+4171)/31 109757 Eric Chen 04/2023 5550 12^101694+73 109747 Lelio R Paula 03/2017 5551 13^98518-66 109744 Lelio R Paula 03/2017 5552 (8*10^109721-269)/9 109721 Robert Price 09/2021 5553 2^364478-113261 109719 Enzo Doria 07/2014 5554 (2^364513+1)/(3*44290516579) 109719 Gord Palameta 08/2018 5555 (24737*2^364454+1)/3 109716 Lelio R Paula 07/2014 5556 27814^8777+8777^27814 109681 Hans Havermann 10/2020 5557 (62*10^109673+1)/9 109674 Serge Batalov 11/2010 5558 3^229824+340 109654 Lelio R Paula 03/2017 5559 (16623*33^72206-8095)/16 109649 Eric Chen 05/2023 5560 (2*10^109645-71)/3 109645 Robert Price 12/2017 5561 2^364169-112813 109626 Enzo Doria 06/2014 5562 28822^6359+6359^28822 109622 Hans Havermann 11/2020 5563 10^109615+21 109616 Lelio R Paula 03/2017 5564 10^109615-456267 109615 Patrick De Geest 03/2017 5565 2^364094-113 109604 Lelio R Paula 01/2012 5566 25251^21898+21898^25251 109600 Hans Havermann 11/2020 5567 (4^182026+11)/3 109591 Robert Price 02/2017 5568 2^364041-6883 109588 Lelio R Paula 09/2011 5569 12^101545+11 109586 Lelio R Paula 03/2017 5570 26536^13475+13475^26536 109582 Hans Havermann 11/2020 5571 2^363842-2787101 109528 Enzo Doria 03/2016 5572 (2^363812+3570)/2 109519 Stefano Morozzi 09/2020 5573 (22699*2^363782+1)/763 109511 Lelio R Paula 07/2014 5574 2^363769+5711 109506 Lelio R Paula 04/2017 5575 (31*2^363748+1)/49 109499 Lelio R Paula 03/2014 5576 (2^363670+100280245065) 109476 Paul Bourdelais 05/2022 5577 p(22245)#/2-8 109462 Robert Price 01/2017 5578 2^363556+55 109442 Lelio R Paula 01/2012 5579 (509*10^109414+31)/9 109416 Robert Price 08/2022 5580 (2^363437+1682)/2 109406 Stefano Morozzi 09/2020 5581 (55459*2^363411+1)/81 109401 Lelio R Paula 07/2014 5582 2^363406+1871569 109397 Enzo Doria 05/2016 5583 (2^363370+1338)/2 109385 Stefano Morozzi 02/2021 5584 (2^363349+7)/9 109378 Lelio R Paula 01/2014 5585 3^229236+100 109374 Lelio R Paula 03/2017 5586 (2^363315+3258)/2 109369 Stefano Morozzi 02/2021 5587 2^363268-58695 109355 Lelio R Paula 04/2017 5588 2^363191-112321 109332 Enzo Doria 06/2014 5589 26231^14718+14718^26231 109327 Hans Havermann 10/2020 5590 25461^19672+19672^25461 109326 Hans Havermann 10/2020 5591 4*10^109316-63 109317 Robert Price 10/2018 5592 2^363120+3 109311 Donovan Johnson 04/2006 5593 (10^109297-1)/9 109297 Paul Bourdelais, Harvey Dubner 04/2007 5594 2^363042-114641 109287 Enzo Doria 04/2015 5595 2^363020-112793 109280 Enzo Doria 06/2014 5596 (85*10^109253+203)/9 109254 Robert Price 09/2020 5597 24990^23431+23431^24990 109202 Hans Havermann 10/2020 5598 (2^362746+3738)/2 109198 Stefano Morozzi 09/2020 5599 (2^362716+1282)/2 109189 Stefano Morozzi 01/2021 5600 (67607*2^362695+1)/70499 109183 Lelio R Paula 07/2014 5601 25060^22737+22737^25060 109180 Hans Havermann 10/2020 5602 (9*2^362644+1)/5 109167 Lelio R Paula 03/2014 5603 5^156181+38 109166 Lelio R Paula 02/2017 5604 (2^362623+3618)/2 109161 Stefano Morozzi 09/2020 5605 25138^21993+21993^25138 109157 Hans Havermann 10/2020 5606 4*10^109142+91 109143 Robert Price 08/2018 5607 3^228750+68 109142 Lelio R Paula 03/2017 5608 (2^362561+786)/2 109142 Stefano Morozzi 09/2020 5609 (23*10^109113+61)/3 109114 Robert Price 01/2022 5610 2*10^109100-49 109101 Robert Price 09/2020 5611 (10223*2^362376+1)/9 109090 Lelio R Paula 07/2014 5612 65^60167-64^60167 109078 Robert Price 08/2013 5613 7*3^228589-2 109066 Lelio R Paula 09/2014 5614 24874^24243+24243^24874 109063 Hans Havermann 11/2020 5615 (17*10^109059-161)/9 109060 Robert Price 02/2021 5616 29158^5495+5495^29158 109050 Hans Havermann 11/2020 5617 (78557*2^362188+1)/189 109033 Lelio R Paula 07/2014 5618 2*7^129008+9 109025 Lelio R Paula 11/2014 5619 88*10^109022+7 109024 Robert Price 03/2020 5620 28194^7337+7337^28194 108985 Hans Havermann 10/2020 5621 (5*10^108960+91)/3 108961 Robert Price 04/2018 5622 2^361957+76367 108960 Enzo Doria 05/2016 5623 2^361873-1411 108935 Yves Minet 01/2013 5624 (24737*2^361857+1)/35 108933 Lelio R Paula 07/2014 5625 115^52842-114 108892 Norbert Schneider 07/2018 5626 13^97745-24 108883 Lelio R Paula 03/2017 5627 (2^361696+2562)/2 108882 Stefano Morozzi 09/2020 5628 17^88475+8 108864 Lelio R Paula 04/2017 5629 2^361567+51 108843 Lelio R Paula 01/2012 5630 2^361563-109501 108842 Enzo Doria 04/2014 5631 12^100852+83 108838 Lelio R Paula 03/2017 5632 2^361497+767 108822 Lelio R Paula 01/2012 5633 28019^7630+7630^28019 108785 Hans Havermann 10/2020 5634 24723^24758-24758^24723 108765 Norbert Schneider 11/2020 5635 2^361280-112349 108757 Enzo Doria 06/2014 5636 2^361271-5955 108754 Lelio R Paula 04/2017 5637 12^100757+19 108736 Lelio R Paula 03/2017 5638 25368^19333+19333^25368 108735 Hans Havermann 11/2020 5639 (2^361195+3618)/2 108731 Stefano Morozzi 09/2020 5640 2^361153-111546435 108718 Paul Bourdelais 10/2021 5641 14^94849-61 108710 Lelio R Paula 05/2017 5642 27267^9700+9700^27267 108708 Hans Havermann 11/2020 5643 (19^85009-5^85009)/14 108705 Robert Price 07/2013 5644 24832^23853+23853^24832 108704 Hans Havermann 11/2020 5645 27502^8963+8963^27502 108701 Hans Havermann 11/2020 5646 25807^16278+16278^25807 108689 Hans Havermann 11/2020 5647 (11*2^361027+1)/40463 108677 Lelio R Paula 03/2014 5648 2^360973+1299 108664 Lelio R Paula 04/2017 5649 2^360959-109101 108660 Enzo Doria 04/2014 5650 6*5^155454+7 108659 Lelio R Paula 11/2014 5651 10^108656+79 108657 Lelio R Paula 02/2017 5652 10^108656-50001 108656 Patrick De Geest 03/2017 5653 2^360918-35 108648 Lelio R Paula 01/2012 5654 4*10^108646-47 108647 Robert Price 10/2021 5655 (11*2^360886-1)/7 108638 Lelio R Paula 03/2014 5656 3*10^108624-49 108625 Robert Price 07/2018 5657 (2^360831+666)/2 108621 Stefano Morozzi 09/2020 5658 (134*10^108610+7)/3 108612 Robert Price 02/2020 5659 2*10^108609+29 108610 Robert Price 02/2021 5660 (10^108604+7)/71/191 108600 Alfred Reich 06/2021 5661 (2^360742+3222)/2 108594 Stefano Morozzi 09/2020 5662 2^360706-458903 108584 Enzo Doria 04/2015 5663 31112^3087+3087^31112 108567 Hans Havermann 11/2020 5664 2^360641-113185 108564 Enzo Doria 07/2014 5665 (29*10^108559-71)/3 108560 Robert Price 07/2021 5666 2^360618+75019 108557 Enzo Doria 04/2016 5667 2^360607-216367 108554 Harrison Mesh 06/2022 5668 (14*10^108545-221)/9 108546 Robert Price 04/2018 5669 (44*10^108544-233)/9 108545 Robert Price 01/2019 5670 3*5^155286+2 108541 Lelio R Paula 11/2014 5671 7^128422+4 108530 Lelio R Paula 11/2014 5672 7^128421-80 108529 Lelio R Paula 03/2017 5673 2^360497+53807 108521 Yves Minet 07/2010 5674 2^360468-4559 108512 Yves Minet 03/2019 5675 (2^360451+578)/2 108507 Stefano Morozzi 09/2020 5676 2^360366+1459 108481 Lelio R Paula 09/2011 5677 2^360364-1499 108481 Yves Minet 05/2013 5678 25662^16871+16871^25662 108477 Hans Havermann 10/2020 5679 25009^21748+21748^25009 108475 Hans Havermann 10/2020 5680 14^94642-23 108472 Lelio R Paula 05/2017 5681 (197*10^108446-11)/3 108448 Robert Price 03/2020 5682 (2^360229+1290)/2 108440 Stefano Morozzi 01/2021 5683 4*10^108412+9 108413 Robert Price 05/2015 5684 (259*10^108409-1)/3 108411 Robert Price 12/2020 5685 (2^360122+1194)/2 108408 Stefano Morozzi 09/2020 5686 133^51042-132 108406 Norbert Schneider 02/2019 5687 2^360093-351103 108399 Enzo Doria 06/2015 5688 2^360042+723 108384 Lelio R Paula 01/2012 5689 85^56164-2 108364 Lelio R Paula 10/2013 5690 2^359937-29323 108352 Enzo Doria 07/2015 5691 (2^359922+1762)/2 108348 Stefano Morozzi 09/2020 5692 (2^359903+758)/2 108342 Stefano Morozzi 09/2020 5693 2^359898-19997 108341 Enzo Doria 06/2013 5694 (2^359886+2122)/2 108337 Stefano Morozzi 09/2020 5695 2*5^154948-7 108305 Lelio R Paula 11/2014 5696 10^108303+13 108304 Lelio R Paula 02/2017 5697 10^108303-207959 108303 Patrick De Geest 03/2017 5698 7*10^108300+69 108301 Robert Price 07/2019 5699 2^359730+753 108290 Lelio R Paula 12/2011 5700 (8*10^108273+13)/3 108274 Robert Price 06/2018 5701 2^359650-19797 108266 Enzo Doria 06/2013 5702 (47*10^108261+259)/9 108262 Robert Price 03/2022 5703 91^55259-90^55259 108255 Robert Price 07/2015 5704 10^108251+85749 108252 Patrick De Geest 02/2021 5705 10^108251-50000000001 108251 Robert Price 12/2020 5706 10^108251-252081 108251 Patrick De Geest 02/2021 5707 4*10^108238-71 108239 Robert Price 12/2018 5708 3^226845+68 108233 Lelio R Paula 03/2017 5709 31836^2509+2509^31836 108227 Hans Havermann 10/2020 5710 5^154822-12866 108216 Enzo Doria 05/2014 5711 (9*2^359480+1)/5 108215 Lelio R Paula 03/2014 5712 2^359454-177 108207 Lelio R Paula 12/2011 5713 (19*10^108184+191)/3 108185 Robert Price 05/2019 5714 6^139022-59 108181 Lelio R Paula 02/2017 5715 (19*10^108176-43)/3 108177 Robert Price 05/2019 5716 2^359352-179 108176 Lelio R Paula 12/2011 5717 2^359338-1858781 108172 Enzo Doria 04/2016 5718 12^100230-97 108167 Lelio R Paula 03/2017 5719 27028^10043+10043^27028 108163 Hans Havermann 11/2020 5720 (25*2^359297-1)/137 108159 Lelio R Paula 03/2014 5721 (2^359262-509203)/9 108148 Lelio R Paula 12/2013 5722 26583^11702+11702^26583 108147 Hans Havermann 11/2020 5723 (3^226648-8)/352715633 108131 Lelio R Paula 12/2013 5724 6^138956-59 108129 Lelio R Paula 02/2017 5725 2^359184+30285 108126 Lelio R Paula 04/2017 5726 13^97059+10 108119 Lelio R Paula 03/2017 5727 2^359137-81 108112 Lelio R Paula 12/2011 5729 (15185*2^359105-1)/567 108103 Lelio R Paula 05/2015 5728 2^359110-11655 108103 Lelio R Paula 04/2017 5730 2^359069-933075 108091 Paul Bourdelais 06/2021 5731 26227^13222+13222^26227 108090 Hans Havermann 10/2020 5732 8*6^138875+5 108067 Lelio R Paula 11/2014 5733 2^358987-216919 108066 Enzo Doria 05/2014 5734 (2^358977+2714)/2 108063 Stefano Morozzi 09/2020 5735 39^67918-67918^39 108062 Norbert Schneider 02/2017 5736 24^78283-1*78283^24 108048 Dylan Delgado 12/2019 5737 25282^18767+18767^25282 108040 Hans Havermann 11/2020 5738 2^358785-16933 108006 Enzo Doria 05/2013 5739 (2^358783+5)/33383 108000 Lelio R Paula 12/2013 5740 6^138770-77 107985 Lelio R Paula 02/2017 5741 (2^358727-1017)/94178479 107980 Lelio R Paula 12/2013 5742 10^107976+19 107977 Lelio R Paula 02/2017 5743 10^107976-202103 107976 Patrick De Geest 03/2017 5744 2^358684+75781 107975 Enzo Doria 04/2016 5745 24928^21411+21411^24928 107955 Hans Havermann 10/2020 5746 99^54094+2 107952 Lelio R Paula 06/2013 5747 (2^358583-9)/391 107942 Lelio R Paula 12/2013 5748 (2^358562+838)/2 107938 Stefano Morozzi 02/2021 5749 2^358538+55 107931 Lelio R Paula 12/2011 5750 2^358517-109009 107925 Enzo Doria 03/2014

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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