## PRP Records

### Probable Primes Top 10000

#### (292102 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 ? 8502 3^206977-112756 98754 Enzo Doria 07/2014 8501 10^98754-40000000001 98754 Robert Price 09/2020 8503 7^116846-50 98747 Lelio R Paula 08/2016 8504 (19152^23059-1)/19151 98740 Serge Batalov 06/2022 8505 23267^17512+17512^23267 98730 Hans Havermann 04/2020 8506 2^327967-28635 98728 Lelio R Paula 08/2016 8507 707^34642+34642^707 98710 Norbert Schneider 12/2017 8508 (10771^24481-1)/10770 98710 Serge Batalov 06/2022 8509 6^126850-47 98709 Lelio R Paula 08/2016 8510 (2^327886+2170)/2 98704 Stefano Morozzi 09/2020 8511 (22*10^98697+47)/3 98698 Robert Price 06/2021 8512 8*6^126830-7 98694 Lelio R Paula 11/2014 8513 11^94770-270 98693 Enzo Doria 08/2012 8514 (2^327846+3250)/2 98692 Stefano Morozzi 01/2021 8515 2^327832+43 98688 Lelio R Paula 12/2012 8516 2^327795+761 98677 Lelio R Paula 02/2013 8517 (2^327796+1522)/2 98677 Stefano Morozzi 09/2020 8518 10^98669+147411 98670 Patrick De Geest 11/2016 8520 10^98669-9^(98669-1) 98669 Robert Price 05/2016 8519 10^98669-105249 98669 Patrick De Geest 11/2016 8521 (7911^25309-1)/7910 98657 Serge Batalov 06/2022 8522 2^327671-109801 98639 Enzo Doria 04/2014 8523 24398^11037+11037^24398 98638 Hans Havermann 10/2019 8524 5^141090-14 98618 Lelio R Paula 08/2016 8525 20^75799+47 98617 Lelio R Paula 08/2016 8526 (5452^26393-1)/5451 98616 Serge Batalov 06/2022 8527 28101^3226+3226^28101 98597 Hans Havermann 07/2020 8528 2^327515-1017 98592 Lelio R Paula 08/2016 8529 6^126692+97681 98586 Mike Oakes 04/2011 8530 2^327467-741 98578 Lelio R Paula 08/2016 8531 (2947^28411-1)/2946 98566 Serge Batalov 06/2022 8532 22713^21800+21800^22713 98540 Hans Havermann 05/2020 8533 (2^327329+9)/19 98535 Lelio R Paula 10/2013 8534 7^116577-66 98519 Lelio R Paula 08/2016 8535 (3*2^327250+1)/7 98512 Lelio R Paula 11/2013 8536 23220^17479+17479^23220 98512 Hans Havermann 03/2020 8537 (2^327240+3798)/2 98509 Stefano Morozzi 02/2021 8538 (28514^22111-1)/28513 98502 Serge Batalov 06/2022 8539 (19*2^327192+1)/275 98494 Lelio R Paula 11/2013 8540 2^327162-66945 98486 Lelio R Paula 08/2016 8541 30139^1852+1852^30139 98484 Hans Havermann 02/2020 8542 23182^17703+17703^23182 98479 Hans Havermann 01/2020 8543 4*10^98472-3 98473 Erik Branger 11/2013 8544 26167^5794+5794^26167 98466 Hans Havermann 01/2020 8545 (6883*2^327047-1)/77 98453 Lelio R Paula 05/2015 8546 (71*10^98446+1)/9 98447 Serge Batalov 11/2010 8547 (2009^29803-1)/2008 98436 Serge Batalov 06/2022 8548 13^88363+94 98432 Lelio R Paula 08/2016 8549 48^58543-47^58543 98425 Jean-Louis Charton 11/2005 8550 6^126481+41 98422 Lelio R Paula 08/2016 8551 78*10^98413-7 98415 Robert Price 05/2017 8552 22634^22263+22263^22634 98404 Hans Havermann 07/2020 8553 (47*10^98386+241)/9 98387 Robert Price 06/2022 8554 7^116416+46 98383 Lelio R Paula 08/2016 8555 7^116407-24 98376 Lelio R Paula 07/2016 8556 439^37228+37228^439 98374 Norbert Schneider 08/2018 8557 2^326782-1860671 98372 Enzo Doria 03/2016 8558 17^79948+58 98372 Lelio R Paula 08/2016 8559 22499^22602-22602^22499 98368 Norbert Schneider 08/2020 8560 3^206143-98 98356 Lelio R Paula 08/2016 8561 8*5^140705+7 98350 Lelio R Paula 11/2014 8562 (2^326632+1662)/2 98326 Stefano Morozzi 09/2020 8563 (638^35053-1)/637 98315 Serge Batalov 06/2022 8564 2^326585+11 98312 Lelio R Paula 12/2012 8565 2^326582-459161 98311 Enzo Doria 05/2015 8566 (1266^31687-1)/1265 98304 Serge Batalov 06/2022 8568 (2^326548+9)/5 98301 Lelio R Paula 10/2013 8567 (2^326549+18)/10 98301 Stefano Morozzi 03/2020 8569 2^326538+71659 98298 Enzo Doria 04/2016 8570 (2^326520+2082)/2 98293 Stefano Morozzi 09/2020 8571 (2^326521+1002)/2 98293 Stefano Morozzi 09/2020 8572 15^83575-58 98292 Lelio R Paula 08/2016 8573 10^98288+3 98289 Robert Price 03/2011 8574 10^98288-117017 98288 Patrick De Geest 11/2011 8575 (44*10^98284-719)/9 98285 Robert Price 12/2017 8576 (5985^26021-1)/5984 98280 Serge Batalov 06/2022 8577 23466^15419+15419^23466 98277 Hans Havermann 02/2020 8578 2^326421-2797573 98263 Enzo Doria 04/2016 8579 2^326401+16095 98257 Lelio R Paula 07/2016 8580 (6494^25771-1)/6493 98249 Serge Batalov 06/2022 8581 7^116240-116240^7 98235 Norbert Schneider 05/2017 8582 17^79826-78 98222 Lelio R Paula 08/2016 8583 2^326268-809 98217 Yves Minet 04/2011 8584 22659^21590+21590^22659 98210 Hans Havermann 10/2019 8585 22268^22587-22587^22268 98202 Norbert Schneider 08/2020 8586 (418*10^98199+23)/9 98201 Robert Price 08/2017 8587 12*10^98198-7 98200 Robert Price 11/2017 8588 15^83496-76 98199 Lelio R Paula 08/2016 8589 (10223*2^326179+1)/6125 98190 Lelio R Paula 07/2014 8590 9*5^140471-4 98186 Lelio R Paula 11/2014 8591 (35103^21601-1)/35102 98180 Serge Batalov 06/2022 8593 22774^20455+20455^22774 98175 Hans Havermann 07/2020 8592 (4516^26863-1)/4515 98175 Serge Batalov 06/2022 8594 2^326069-2383 98157 Yves Minet 10/2013 8595 (9661^24631-1)/9660 98152 Serge Batalov 06/2022 8596 (4175^27109-1)/4174 98149 Serge Batalov 06/2022 8597 (57801^20611-1)/57800 98144 Serge Batalov 06/2022 8598 2^325973+1185 98128 Lelio R Paula 07/2016 8599 (25*2^325949-1)/17 98121 Lelio R Paula 02/2014 8600 2^325945-1847269 98120 Enzo Doria 07/2015 8601 8*10^98111-67 98112 Robert Price 10/2017 8602 (2^325902+1138)/2 98106 Stefano Morozzi 09/2020 8603 (215^42061-1)/214 98103 Serge Batalov 06/2022 8604 (6775^25609-1)/6774 98102 Serge Batalov 06/2022 8605 (6718^25633-1)/6717 98100 Serge Batalov 06/2022 8606 2^325866+15 98096 Lelio R Paula 12/2012 8607 22591^21952+21952^22591 98079 Hans Havermann 02/2020 8608 2^325765+1974305 98066 Enzo Doria 06/2016 8609 2^325733-58695 98056 Lelio R Paula 07/2016 8610 (7*10^98055-529)/9 98055 Robert Price 08/2021 8611 2^325717-3645 98051 Lelio R Paula 07/2016 8612 (2^325704+718)/2 98047 Stefano Morozzi 09/2020 8613 (15679^23371-1)/15678 98045 Serge Batalov 06/2022 8614 (23342^22441-1)/23341 98022 Serge Batalov 06/2022 8615 23968^12293+12293^23968 98021 Hans Havermann 11/2019 8616 (23*2^325583-1)/21 98011 Lelio R Paula 02/2014 8617 (7*10^98007-13)/3 98008 Robert Price 06/2016 8618 (2^325544+1110)/2 97999 Stefano Morozzi 09/2020 8619 2^325512-459959 97989 Enzo Doria 05/2015 8620 (2^325492+682)/2 97983 Stefano Morozzi 09/2020 8621 (3^205354-8)/17 97978 Lelio R Paula 09/2013 8622 2^325433+76817 97966 Enzo Doria 05/2016 8623 5*10^97963+81 97964 Robert Price 08/2017 8624 (13208^23773-1)/13207 97961 Serge Batalov 06/2022 8625 2^325390-109061 97953 Enzo Doria 04/2014 8626 (55*10^97940+323)/9 97941 Robert Price 10/2021 8627 13^87921+24 97940 Lelio R Paula 08/2016 8628 10^97930+188277 97931 Patrick De Geest 09/2022 8630 10^97930-7000001 97930 Robert Price 06/2021 8629 10^97930-66951 97930 Patrick De Geest 09/2022 8631 961^32831-960^32831 97926 Jean-Louis Charton 02/2011 8632 (17968^23017-1)/17967 97922 Serge Batalov 06/2022 8633 (3337^27793-1)/3336 97922 Serge Batalov 06/2022 8635 22600^21499+21499^22600 97913 Hans Havermann 05/2020 8634 (18703^22921-1)/18702 97913 Serge Batalov 06/2022 8636 2^325215+12909 97900 Lelio R Paula 07/2016 8637 22619^21286+21286^22619 97898 Hans Havermann 04/2020 8638 (85*10^97876-49)/9 97877 Robert Price 12/2020 8639 7*10^97874-69 97875 Robert Price 01/2017 8640 5*10^97869-63 97870 Robert Price 04/2021 8642 (17^79537+5^79537)/22 97865 Robert Price 06/2013 8641 15^83212+22 97865 Lelio R Paula 08/2016 8643 2^325087-109057 97861 Enzo Doria 04/2014 8644 2^325074+1870657 97858 Enzo Doria 05/2016 8646 2^325066-2111 97855 Yves Minet 08/2013 8645 CopelandErdos(97855) 97855 Eric W. Weisstein 10/2015 8647 (8694^24841-1)/8693 97851 Serge Batalov 06/2022 8648 (21159^22621-1)/21158 97843 Serge Batalov 06/2022 8649 26660^4677+4677^26660 97842 Hans Havermann 12/2019 8650 18^77944-89 97841 Lelio R Paula 07/2016 8651 119^47136+118 97833 Norbert Schneider 09/2018 8652 6^125720-17663 97830 Enzo Doria 02/2013 8653 (73640^20101-1)/73639 97829 Serge Batalov 06/2022 8654 2^324972-2069 97827 Yves Minet 05/2013 8655 2^324958-4691 97823 Yves Minet 05/2019 8656 (8087^25033-1)/8086 97820 Serge Batalov 06/2022 8657 2^324944-2788319 97818 Enzo Doria 03/2016 8658 22845^19112+19112^22845 97807 Hans Havermann 10/2019 8659 (2^324898+1270)/2 97804 Stefano Morozzi 09/2020 8661 4*10^97799-9 97800 Erik Branger 11/2013 8660 2^324882+577294575 97800 Lelio R Paula 09/2016 8662 2^324863-1867921 97794 Enzo Doria 04/2016 8663 6^125662-18473 97785 Enzo Doria 03/2013 8664 12^90604+11 97779 Lelio R Paula 07/2016 8665 (29*10^97751+49)/3 97752 Robert Price 09/2021 8666 (37108^21391-1)/37107 97741 Serge Batalov 06/2022 8667 5^139830+24 97737 Lelio R Paula 04/2016 8668 (2^324672+1198)/2 97736 Stefano Morozzi 09/2020 8669 (101*10^97724+7)/9 97726 Robert Price 02/2022 8670 2^324612+1155 97718 Lelio R Paula 07/2016 8671 (2^324597+3542)/2 97714 Stefano Morozzi 09/2020 8672 19^76404-44 97702 Lelio R Paula 07/2016 8673 (5939^25889-1)/5938 97694 Serge Batalov 06/2022 8675 2^324505-2983 97686 Yves Minet 04/2011 8674 (7740^25121-1)/7739 97686 Serge Batalov 06/2022 8676 (144^45259+1)/145 97684 Paul Bourdelais 08/2019 8677 (31*2^324496-1)/45 97683 Lelio R Paula 02/2014 8678 (11234^24109-1)/11233 97651 Serge Batalov 06/2022 8679 6^125488-17843 97649 Enzo Doria 02/2013 8680 (2^324350+3198)/2 97639 Stefano Morozzi 09/2020 8681 (75638^20011-1)/75637 97624 Serge Batalov 06/2022 8682 7^115515-2 97622 Lelio R Paula 09/2013 8683 (15672^23269-1)/15671 97613 Serge Batalov 06/2022 8684 (89^50069-1)/88 97603 Paul Bourdelais 08/2017 8685 6^125418-5 97595 Lelio R Paula 11/2014 8686 (2^324193+3522)/2 97592 Stefano Morozzi 09/2020 8687 (2422^28837-1)/2421 97587 Serge Batalov 06/2022 8688 (2^324172+666)/2 97586 Stefano Morozzi 09/2020 8689 2^324091+111546435 97562 Paul Bourdelais 10/2021 8690 2^324076+1155 97557 Lelio R Paula 07/2016 8691 (2^324074+9)/13 97555 Lelio R Paula 10/2013 8692 (11*10^97539-71)/3 97540 Robert Price 04/2022 8693 (55459*2^323993+1)/21 97536 Lelio R Paula 07/2014 8694 13^87557-12^87557 97534 Jean-Louis Charton 12/2008 8695 2^323946+73939 97518 Enzo Doria 04/2016 8696 2^323937+1866947 97515 Enzo Doria 03/2016 8697 (98339^19531-1)/98338 97508 Serge Batalov 06/2022 8699 6^125290-18533 97495 Enzo Doria 03/2013 8698 (2^323870+1650)/2 97495 Stefano Morozzi 09/2020 8700 2^323845+101 97488 Lelio R Paula 12/2012 8701 18^77662+65 97487 Lelio R Paula 07/2016 8702 22634^20265+20265^22634 97479 Hans Havermann 04/2020 8703 (5533^26041-1)/5532 97467 Serge Batalov 06/2022 8704 2^323772+76771 97466 Enzo Doria 05/2016 8705 2^323765-112213 97463 Enzo Doria 06/2014 8706 22730^19389+19389^22730 97457 Hans Havermann 02/2020 8707 2^323720-6555 97450 Lelio R Paula 07/2016 8708 2^323694-1860401 97442 Enzo Doria 03/2016 8709 20^74886+3 97429 Lelio R Paula 06/2016 8710 24476^9561+9561^24476 97427 Hans Havermann 01/2020 8711 (2^323623+1766)/2 97420 Stefano Morozzi 09/2020 8712 (3250^27739-1)/3249 97413 Serge Batalov 06/2022 8714 3*10^97399+73 97400 Robert Price 04/2016 8713 7^115252-50 97400 Lelio R Paula 07/2016 8715 (4715^26513-1)/4714 97392 Serge Batalov 06/2022 8716 224737#+393581 97389 Nicolas PALAU 12/2016 8717 (2^323468+3186)/2 97374 Stefano Morozzi 09/2020 8718 (2^323456+538)/2 97370 Stefano Morozzi 09/2020 8719 23277^15236+15236^23277 97365 Hans Havermann 07/2020 8721 (26*10^97353+31)/3 97354 Robert Price 07/2016 8720 (2^323403+3510)/2 97354 Stefano Morozzi 09/2020 8722 23756^12519+12519^23756 97342 Hans Havermann 07/2020 8723 10^97335+271641 97336 Patrick De Geest 09/2022 8725 10^97335-4000001 97335 Robert Price 07/2021 8724 10^97335-98193 97335 Patrick De Geest 09/2022 8726 (637*10^97331+11)/9 97333 Robert Price 10/2021 8727 23991^11402+11402^23991 97332 Hans Havermann 07/2020 8728 61^54517-60^54517 97331 Jean-Louis Charton 09/2005 8729 (38*10^97329+187)/9 97330 Robert Price 11/2017 8730 (31147^21661-1)/31146 97328 Serge Batalov 06/2022 8731 86455!4+8 97319 Robert Price 09/2019 8732 22591^20310+20310^22591 97316 Hans Havermann 06/2020 8733 2^323261-431173 97312 Harrison Mesh 06/2022 8734 (3996^27017-1)/3995 97302 Serge Batalov 06/2022 8735 25101^7520+7520^25101 97297 Hans Havermann 05/2020 8736 (233*10^97294+7)/3 97296 Robert Price 03/2022 8737 p(19982)#/2-1024 97293 Robert Price 09/2017 8738 (65*10^97288+277)/9 97289 Robert Price 08/2021 8739 6^125021-85 97286 Lelio R Paula 08/2016 8740 2^323164-47355 97283 Lelio R Paula 07/2016 8741 (3^203902+4)/36051015157 97276 Lelio R Paula 09/2013 8742 2^323054-6555 97249 Lelio R Paula 07/2016 8743 22822^18247+18247^22822 97249 Hans Havermann 02/2020 8744 9*10^97247-29 97248 Robert Price 05/2017 8745 24382^9735+9735^24382 97244 Hans Havermann 02/2020 8746 (31*10^97242+41)/9 97243 Robert Price 04/2015 8747 GoldenRatioPrime[97241] 97241 Eric W. Weisstein 06/2009 8748 12^90098-41 97233 Lelio R Paula 07/2016 8749 2^322928-216929 97212 Enzo Doria 05/2014 8750 (16731^23017-1)/16730 97209 Serge Batalov 06/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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