## PRP Records

### Probable Primes Top 10000

#### (294113 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 ? 6501 32958^1441+1441^32958 104104 Hans Havermann 09/2020 6502 29127^3748+3748^29127 104095 Hans Havermann 09/2020 6503 322^41507+41507^322 104094 Norbert Schneider 12/2014 6504 6^133768-17423 104092 Enzo Doria 03/2013 6505 2^345786-19557 104092 Enzo Doria 05/2013 6506 171^46606-2 104072 Lelio R Paula 10/2017 6507 (29*10^104071+91)/3 104072 Robert Price 04/2020 6508 norm(Mod(x,x^3-x-1)^852167-1) 104070 Paul Vanderveen 09/2022 6509 2^345704-149 104068 Lelio R Paula 09/2011 6510 25821^10712+10712^25821 104056 Hans Havermann 09/2020 6511 (2^345662+2038)/2 104055 Stefano Morozzi 09/2020 6512 6^133704-17273 104042 Enzo Doria 02/2013 6513 (3*2^345590-1)/23 104033 Lelio R Paula 03/2014 6514 (19*2^345590+1)/33859 104030 Lelio R Paula 12/2013 6515 2^345547+11 104021 Lelio R Paula 09/2011 6516 (19*10^104014-49)/3 104015 Robert Price 05/2019 6517 (2^345519+1794)/2 104012 Stefano Morozzi 01/2021 6518 2^345504+723 104008 Lelio R Paula 09/2011 6519 2^345498-20037 104006 Enzo Doria 06/2013 6521 18^82854-37 104005 Lelio R Paula 01/2017 6520 (2^345497+2070)/2 104005 Stefano Morozzi 09/2020 6522 2^345486-109065 104002 Enzo Doria 04/2014 6523 2^345487-1851507 104002 Enzo Doria 08/2015 6524 2^345476+777 103999 Lelio R Paula 09/2011 6525 (2^345477+1554)/2 103999 Stefano Morozzi 09/2020 6526 4*10^103981-83 103982 Robert Price 10/2018 6527 (2^345327+3206)/2 103954 Stefano Morozzi 09/2020 6528 (5*2^345321-1)/3 103953 Lelio R Paula 03/2014 6529 (2^345267-9)/539049127 103927 Lelio R Paula 12/2013 6530 (19*10^103907+77)/3 103908 Robert Price 05/2019 6531 (78557*2^345163+1)/78589 103905 Lelio R Paula 07/2014 6532 2^345106-112181 103888 Enzo Doria 06/2014 6533 (2^345105+1326)/2 103887 Stefano Morozzi 02/2021 6534 2^345079+99 103880 Lelio R Paula 09/2011 6535 (2^345034+1198)/2 103866 Stefano Morozzi 09/2020 6536 11^99736-1500 103865 Enzo Doria 12/2012 6537 (569^37699-1)/568 103863 Serge Batalov 06/2022 6538 (2^345010+2082)/2 103859 Stefano Morozzi 09/2020 6539 23263^23784-23784^23263 103857 Norbert Schneider 01/2020 6540 3*10^103844+31 103845 Robert Price 06/2021 6541 444*33^68368+19 103821 Eric Chen 05/2023 6542 23927^21814+21814^23927 103813 Hans Havermann 09/2020 6543 2^344842-20157 103808 Enzo Doria 06/2013 6544 (47*2^344822+1)/1071 103801 Lelio R Paula 05/2015 6545 2^344802-20765 103796 Enzo Doria 06/2013 6546 2^344794-3821 103794 Yves Minet 05/2011 6547 2^344782-109103 103790 Enzo Doria 04/2014 6548 3^217521-112292 103784 Enzo Doria 06/2014 6549 2^344759-3505 103783 Lelio R Paula 11/2016 6550 2^344735-147 103776 Lelio R Paula 09/2011 6551 L(496533)-p(496533) 103770 Robert Price 02/2018 6552 2*10^103749-69 103750 Robert Price 03/2018 6553 (55459*2^344617+1)/3 103745 Lelio R Paula 07/2014 6554 2^344607-108891 103738 Enzo Doria 03/2014 6556 (2^344608+3798)/2 103738 Stefano Morozzi 02/2021 6555 (1097^34123-1)/1096 103738 Serge Batalov 06/2022 6557 2^344560+22411 103723 Enzo Doria 09/2023 6558 (148*10^103718-1)/3 103720 Robert Price 03/2020 6559 2^344541-19561 103718 Enzo Doria 05/2013 6560 (1017*2^344529-1)/569 103714 Lelio R Paula 05/2015 6561 (8896^26263-1)/8895 103714 Serge Batalov 06/2022 6562 (2^344503+1758)/2 103706 Stefano Morozzi 09/2020 6563 (4*10^103703-1)/3 103704 Serge Batalov 08/2009 6564 2^344444-455 103688 Yves Minet 03/2012 6565 (4*10^103678-43)/3 103679 Robert Price 01/2022 6566 (13*53^238539*617^9)/10^307661 103673 Hans Havermann 06/2017 6567 (2^344367+2738)/2 103665 Stefano Morozzi 01/2021 6569 2^344317-109933 103650 Enzo Doria 04/2014 6568 26055^9508+9508^26055 103650 Hans Havermann 09/2020 6570 2^344309-1852033 103648 Enzo Doria 08/2015 6571 25729^10672+10672^25729 103643 Hans Havermann 09/2020 6572 (2^344289+1166)/2 103642 Stefano Morozzi 09/2020 6573 3*10^103637+61 103638 Robert Price 09/2020 6574 (2^344246+1614)/2 103629 Stefano Morozzi 09/2020 6575 2^344213-21253 103619 Enzo Doria 06/2013 6576 2^344196-465 103614 Lelio R Paula 11/2016 6577 2^344187-20001 103611 Enzo Doria 06/2013 6578 (117191#+(355573#)/(117191#))/(200233679) 103602 Makoto Morimoto 10/2017 6579 (237^43627-1)/236 103601 Serge Batalov 06/2022 6580 20^79621-19^79621 103590 Jean-Louis Charton 03/2011 6581 Phi(155391,10)/1243129 103586 Maksym Voznyy 09/2015 6582 (9^108553-2^108553)/7 103586 Jon Grantham 07/2023 6583 2^344085-20365 103580 Enzo Doria 06/2013 6584 5^148169+54 103566 Lelio R Paula 11/2016 6585 2^344017-108795 103560 Enzo Doria 03/2014 6586 (2^343974+2670)/2 103547 Stefano Morozzi 09/2020 6587 2^343971-5077 103546 Lelio R Paula 09/2011 6588 (7*10^103531+71)/3 103532 Robert Price 05/2018 6589 2^343899+141 103524 Lelio R Paula 08/2011 6590 (2^343933+1)/(3*98294339989393) 103520 Gord Palameta 08/2018 6591 6^133029-67 103517 Lelio R Paula 11/2016 6592 (17*2^343877+1)/13625 103515 Lelio R Paula 12/2013 6593 66*10^103507+7 103509 Robert Price 07/2020 6594 26297^8614+8614^26297 103485 Hans Havermann 09/2020 6595 (2^343764+2658)/2 103483 Stefano Morozzi 09/2020 6596 26499^8036+8036^26499 103480 Hans Havermann 09/2020 6597 (136*10^103474-1)/9 103476 Serge Batalov 12/2014 6598 5^148014-24 103458 Lelio R Paula 11/2016 6599 28316^4503+4503^28316 103453 Hans Havermann 09/2020 6600 (22*10^103450+53)/3 103451 Robert Price 07/2019 6601 2^343604+9931 103436 Yves Minet 01/2011 6602 2^343601-21189 103435 Enzo Doria 06/2013 6603 (10^103423+173)/3 103423 Robert Price 05/2021 6604 2^343508-115229 103407 Enzo Doria 06/2015 6605 (8766^26227-1)/8765 103404 Serge Batalov 06/2022 6606 (509203*2^343491-1)/16147 103403 Lelio R Paula 05/2015 6607 3^216685-113056 103386 Enzo Doria 07/2014 6608 24829^14580+14580^24829 103382 Hans Havermann 08/2020 6609 91355!4+1024 103381 Robert Price 09/2019 6610 44^62903-43^62903 103379 Jean-Louis Charton 08/2012 6611 11^99262-20 103371 Lelio R Paula 12/2016 6612 (509203*2^343357-1)/5 103366 Lelio R Paula 05/2015 6613 (2^343363+3570)/2 103363 Stefano Morozzi 09/2020 6614 2^343356-2791889 103361 Enzo Doria 03/2016 6615 (25*10^103360-241)/9 103361 Robert Price 05/2018 6616 Phi(104989,10)/2939693 103350 Maksym Voznyy 09/2015 6617 (371*33^68040-19)/32 103321 Eric Chen 05/2023 6618 24826^14511+14511^24826 103319 Hans Havermann 09/2020 6619 2^343182-171 103309 Lelio R Paula 08/2011 6620 (23619^23619+23620^23620)/7187 103294 David Broadhurst 09/2009 6621 (16487^24649-1)/(16487^157-1) 103287 Ryan Propper 11/2023 6622 (10680^25639-1)/10679 103285 Serge Batalov 06/2022 6623 (7427^26683-1)/7426 103282 Serge Batalov 06/2022 6624 2^343079-1835611 103278 Enzo Doria 05/2015 6625 2^343063-1147 103273 Yves Minet 06/2013 6626 24741^14930+14930^24741 103271 Hans Havermann 09/2020 6627 (16*10^103255-73)/3 103256 Robert Price 07/2020 6628 (219^44119-1)/218 103256 Serge Batalov 06/2022 6629 9*6^132689+7 103254 Lelio R Paula 11/2014 6630 2^342979-18085 103247 Enzo Doria 05/2013 6631 (16*10^103244-31)/3 103245 Robert Price 03/2019 6632 2^342966-16995 103244 Lelio R Paula 11/2016 6633 23797^21774+21774^23797 103230 Hans Havermann 09/2020 6634 25388^11637+11637^25388 103224 Hans Havermann 09/2020 6635 (2^342876+2086)/2 103216 Stefano Morozzi 09/2020 6636 (16*10^103214-31)/3 103215 Robert Price 03/2019 6638 (37*10^103211+611)/9 103212 Robert Price 11/2018 6637 (238*10^103210-1)/3 103212 Robert Price 04/2020 6639 5^147650+16 103203 Lelio R Paula 11/2016 6640 gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809) 103201 Serge Batalov 04/2015 6641 2^342817+2707067 103199 Enzo Doria 03/2016 6642 43^63177-42 103198 Theodore Burton 02/2007 6643 2^342805-21025 103195 Enzo Doria 06/2013 6644 24129^18890+18890^24129 103182 Hans Havermann 09/2020 6645 (622*10^103171-1)/9 103173 Robert Price 11/2021 6646 2^342714+12285 103168 Lelio R Paula 11/2016 6647 (2*10^103161-17)/3 103161 Serge Batalov 11/2022 6648 18^82178-4481 103156 Enzo Doria 03/2013 6649 2^342665-17349 103153 Enzo Doria 05/2013 6650 30408^2467+2467^30408 103150 Hans Havermann 09/2020 6651 (5^147571-3^147571)/2 103148 Kellen Shenton 05/2022 6652 (2^342615+3090)/2 103138 Stefano Morozzi 09/2020 6653 2^342612+175 103137 Lelio R Paula 08/2011 6654 5*2^342585-3 103130 Lelio R Paula 09/2014 6655 (16*10^103127+77)/3 103128 Robert Price 03/2019 6656 (2^342527+3774)/2 103111 Stefano Morozzi 02/2021 6657 2^342503-19209 103104 Enzo Doria 05/2013 6658 (2^342484+2586)/2 103098 Stefano Morozzi 09/2020 6659 2^342476+51 103096 Lelio R Paula 08/2011 6660 2^342460-18885 103091 Enzo Doria 05/2013 6661 (2^342442+862)/2 103086 Stefano Morozzi 02/2021 6662 (194*10^103074-17)/3 103076 Robert Price 09/2020 6663 7^121968+82 103075 Lelio R Paula 10/2016 6664 2^342392-108863 103071 Enzo Doria 03/2014 6665 (2^342389+806)/2 103070 Stefano Morozzi 01/2021 6666 3^216014+28 103065 Lelio R Paula 11/2016 6667 2^342353-108879 103059 Enzo Doria 03/2014 6668 10^103055+276081 103056 Patrick De Geest 12/2016 6669 10^103055-53 103055 Lelio R Paula 11/2016 6670 (58*10^103046+419)/9 103047 Robert Price 05/2019 6671 7^121933+4 103046 Lelio R Paula 11/2014 6672 (71*10^103028-143)/9 103029 Robert Price 10/2021 6673 (2^342235+3618)/2 103023 Stefano Morozzi 09/2020 6674 19^80560-68 103017 Lelio R Paula 10/2016 6675 2^342209+76607 103016 Enzo Doria 05/2016 6677 328^40945+40945^328 103013 Norbert Schneider 12/2014 6676 12^95454-91 103013 Lelio R Paula 10/2016 6678 25833^9716+9716^25833 103009 Hans Havermann 01/2019 6679 (893*10^103004+7)/9 103006 Robert Price 06/2021 6680 (1475^32503-1)/1474 102993 Serge Batalov 06/2022 6681 65^56809-64^56809 102990 Robert Price 08/2013 6682 5^147338-6 102985 Lelio R Paula 11/2014 6683 2^342084-112739 102978 Enzo Doria 06/2014 6684 9*6^132330+7 102974 Lelio R Paula 11/2014 6685 2^342034-16737 102963 Enzo Doria 05/2013 6686 (9787*2^342011-1)/25 102959 Lelio R Paula 05/2015 6687 (3^215802-5)/124343756 102956 Lelio R Paula 12/2013 6688 2^341991-17421 102950 Enzo Doria 05/2013 6689 2^341969-112225 102943 Enzo Doria 06/2014 6690 (9787*2^341864-1)/3 102915 Lelio R Paula 05/2015 6691 2^341859+1869413 102910 Enzo Doria 05/2016 6692 10^102909+61 102910 Lelio R Paula 11/2016 6693 10^102909-67049 102909 Patrick De Geest 12/2016 6694 23814^20935+20935^23814 102898 Hans Havermann 02/2019 6695 28345^4264+4264^28345 102888 Hans Havermann 02/2019 6696 25665^10204+10204^25665 102886 Hans Havermann 02/2019 6697 26288^8181+8181^26288 102860 Hans Havermann 02/2019 6698 2^341659+1836773 102850 Enzo Doria 03/2016 6699 2^341608-110639 102835 Enzo Doria 05/2014 6700 10^102824+49 102825 Lelio R Paula 11/2016 6701 10^102824-168011 102824 Patrick De Geest 12/2016 6702 11^98708-8 102794 Lelio R Paula 10/2016 6703 2^341466+4429 102792 Lelio R Paula 09/2011 6704 2^341460-107 102790 Lelio R Paula 08/2011 6705 (2^341388+47)/21014943 102761 Lelio R Paula 12/2013 6706 2^341355+21 102759 Lelio R Paula 08/2011 6707 (6496^26947-1)/6495 102736 Serge Batalov 06/2022 6708 2^341246+40755 102726 Lelio R Paula 11/2016 6709 (2^341256-5)/991699 102723 Lelio R Paula 12/2013 6710 7^121547+78 102720 Lelio R Paula 10/2016 6711 2^341223-461197 102719 Enzo Doria 06/2015 6712 27838^4893+4893^27838 102711 Hans Havermann 03/2019 6714 2^341190-20577 102709 Enzo Doria 06/2013 6713 (27*2^341212+1)/84674449 102709 Lelio R Paula 12/2013 6715 (25*10^102698+77)/3 102699 Robert Price 09/2022 6716 6^131976-65 102698 Lelio R Paula 10/2016 6717 2^341134+2533 102692 Henri Lifchitz 09/2005 6718 13^92184-54 102688 Lelio R Paula 10/2016 6719 2^341116-20873 102687 Enzo Doria 06/2013 6720 2^341094-19953 102680 Enzo Doria 06/2013 6721 23761^20950+20950^23761 102676 Hans Havermann 03/2019 6723 2^341053+129 102668 Lelio R Paula 08/2011 6722 (4724^27943-1)/4723 102668 Serge Batalov 06/2022 6725 (31*2^341006-1)/3 102655 Lelio R Paula 03/2014 6724 7^121471+94 102655 Lelio R Paula 10/2016 6727 2^341004-173 102653 Lelio R Paula 08/2011 6726 20^78901+3 102653 Lelio R Paula 10/2016 6728 (2^341001+1674)/2 102652 Stefano Morozzi 09/2020 6729 5^146853-52 102646 Lelio R Paula 10/2016 6730 2^340969-216931 102642 Enzo Doria 05/2014 6731 122^49196+121 102641 Norbert Schneider 10/2018 6732 2^340952+1870021 102637 Enzo Doria 05/2016 6733 5*2^340940-3 102634 Lelio R Paula 08/2014 6734 (6^131891+1)/7 102631 Paul Bourdelais 01/2010 6735 (11*10^102629-23)/3 102630 Robert Price 09/2021 6736 3^215094+5*2^215094 102626 Jon Grantham 08/2023 6737 25876^9239+9239^25876 102615 Hans Havermann 02/2019 6738 (4*10^102612+83)/3 102613 Robert Price 02/2018 6739 75^54717+74 102598 Norbert Schneider 01/2015 6740 (17*10^102597+13)/3 102598 Robert Price 01/2019 6741 2^340806-20393 102593 Enzo Doria 06/2013 6742 (2^340790+5)/138267 102583 Lelio R Paula 12/2013 6743 6^131821+77 102577 Lelio R Paula 10/2016 6744 (203*10^102561-11)/3 102563 Robert Price 12/2020 6745 2^340688-29 102558 Henri Lifchitz 05/2005 6746 2^340685-109101 102557 Enzo Doria 04/2014 6747 65^56567-64 102552 Norbert Schneider 11/2014 6748 26230^8121+8121^26230 102550 Hans Havermann 03/2019 6749 (64*10^102547+161)/9 102548 Robert Price 08/2022 6750 (8*10^102541+49)/3 102542 Robert Price 05/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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