## PRP Records

### Probable Primes Top 10000

#### (291910 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 ? 8501 22619^21286+21286^22619 97898 Hans Havermann 04/2020 8502 (85*10^97876-49)/9 97877 Robert Price 12/2020 8503 7*10^97874-69 97875 Robert Price 01/2017 8504 5*10^97869-63 97870 Robert Price 04/2021 8506 (17^79537+5^79537)/22 97865 Robert Price 06/2013 8505 15^83212+22 97865 Lelio R Paula 08/2016 8507 2^325087-109057 97861 Enzo Doria 04/2014 8508 2^325074+1870657 97858 Enzo Doria 05/2016 8510 2^325066-2111 97855 Yves Minet 08/2013 8509 CopelandErdos(97855) 97855 Eric W. Weisstein 10/2015 8511 (8694^24841-1)/8693 97851 Serge Batalov 06/2022 8512 (21159^22621-1)/21158 97843 Serge Batalov 06/2022 8513 26660^4677+4677^26660 97842 Hans Havermann 12/2019 8514 18^77944-89 97841 Lelio R Paula 07/2016 8515 119^47136+118 97833 Norbert Schneider 09/2018 8516 6^125720-17663 97830 Enzo Doria 02/2013 8517 (73640^20101-1)/73639 97829 Serge Batalov 06/2022 8518 2^324972-2069 97827 Yves Minet 05/2013 8519 2^324958-4691 97823 Yves Minet 05/2019 8520 (8087^25033-1)/8086 97820 Serge Batalov 06/2022 8521 2^324944-2788319 97818 Enzo Doria 03/2016 8522 22845^19112+19112^22845 97807 Hans Havermann 10/2019 8523 (2^324898+1270)/2 97804 Stefano Morozzi 09/2020 8525 4*10^97799-9 97800 Erik Branger 11/2013 8524 2^324882+577294575 97800 Lelio R Paula 09/2016 8526 2^324863-1867921 97794 Enzo Doria 04/2016 8527 6^125662-18473 97785 Enzo Doria 03/2013 8528 12^90604+11 97779 Lelio R Paula 07/2016 8529 (29*10^97751+49)/3 97752 Robert Price 09/2021 8530 (37108^21391-1)/37107 97741 Serge Batalov 06/2022 8531 5^139830+24 97737 Lelio R Paula 04/2016 8532 (2^324672+1198)/2 97736 Stefano Morozzi 09/2020 8533 (101*10^97724+7)/9 97726 Robert Price 02/2022 8534 2^324612+1155 97718 Lelio R Paula 07/2016 8535 (2^324597+3542)/2 97714 Stefano Morozzi 09/2020 8536 19^76404-44 97702 Lelio R Paula 07/2016 8537 (5939^25889-1)/5938 97694 Serge Batalov 06/2022 8539 2^324505-2983 97686 Yves Minet 04/2011 8538 (7740^25121-1)/7739 97686 Serge Batalov 06/2022 8540 (144^45259+1)/145 97684 Paul Bourdelais 08/2019 8541 (31*2^324496-1)/45 97683 Lelio R Paula 02/2014 8542 (11234^24109-1)/11233 97651 Serge Batalov 06/2022 8543 6^125488-17843 97649 Enzo Doria 02/2013 8544 (2^324350+3198)/2 97639 Stefano Morozzi 09/2020 8545 (75638^20011-1)/75637 97624 Serge Batalov 06/2022 8546 7^115515-2 97622 Lelio R Paula 09/2013 8547 (15672^23269-1)/15671 97613 Serge Batalov 06/2022 8548 (89^50069-1)/88 97603 Paul Bourdelais 08/2017 8549 6^125418-5 97595 Lelio R Paula 11/2014 8550 (2^324193+3522)/2 97592 Stefano Morozzi 09/2020 8551 (2422^28837-1)/2421 97587 Serge Batalov 06/2022 8552 (2^324172+666)/2 97586 Stefano Morozzi 09/2020 8553 2^324091+111546435 97562 Paul Bourdelais 10/2021 8554 2^324076+1155 97557 Lelio R Paula 07/2016 8555 (2^324074+9)/13 97555 Lelio R Paula 10/2013 8556 (11*10^97539-71)/3 97540 Robert Price 04/2022 8557 (55459*2^323993+1)/21 97536 Lelio R Paula 07/2014 8558 13^87557-12^87557 97534 Jean-Louis Charton 12/2008 8559 2^323946+73939 97518 Enzo Doria 04/2016 8560 2^323937+1866947 97515 Enzo Doria 03/2016 8561 (98339^19531-1)/98338 97508 Serge Batalov 06/2022 8563 6^125290-18533 97495 Enzo Doria 03/2013 8562 (2^323870+1650)/2 97495 Stefano Morozzi 09/2020 8564 2^323845+101 97488 Lelio R Paula 12/2012 8565 18^77662+65 97487 Lelio R Paula 07/2016 8566 22634^20265+20265^22634 97479 Hans Havermann 04/2020 8567 (5533^26041-1)/5532 97467 Serge Batalov 06/2022 8568 2^323772+76771 97466 Enzo Doria 05/2016 8569 2^323765-112213 97463 Enzo Doria 06/2014 8570 22730^19389+19389^22730 97457 Hans Havermann 02/2020 8571 2^323720-6555 97450 Lelio R Paula 07/2016 8572 2^323694-1860401 97442 Enzo Doria 03/2016 8573 20^74886+3 97429 Lelio R Paula 06/2016 8574 24476^9561+9561^24476 97427 Hans Havermann 01/2020 8575 (2^323623+1766)/2 97420 Stefano Morozzi 09/2020 8576 (3250^27739-1)/3249 97413 Serge Batalov 06/2022 8578 3*10^97399+73 97400 Robert Price 04/2016 8577 7^115252-50 97400 Lelio R Paula 07/2016 8579 (4715^26513-1)/4714 97392 Serge Batalov 06/2022 8580 224737#+393581 97389 Nicolas PALAU 12/2016 8581 (2^323468+3186)/2 97374 Stefano Morozzi 09/2020 8582 (2^323456+538)/2 97370 Stefano Morozzi 09/2020 8583 23277^15236+15236^23277 97365 Hans Havermann 07/2020 8585 (26*10^97353+31)/3 97354 Robert Price 07/2016 8584 (2^323403+3510)/2 97354 Stefano Morozzi 09/2020 8586 23756^12519+12519^23756 97342 Hans Havermann 07/2020 8587 10^97335+271641 97336 Patrick De Geest 09/2022 8589 10^97335-4000001 97335 Robert Price 07/2021 8588 10^97335-98193 97335 Patrick De Geest 09/2022 8590 (637*10^97331+11)/9 97333 Robert Price 10/2021 8591 23991^11402+11402^23991 97332 Hans Havermann 07/2020 8592 61^54517-60^54517 97331 Jean-Louis Charton 09/2005 8593 (38*10^97329+187)/9 97330 Robert Price 11/2017 8594 (31147^21661-1)/31146 97328 Serge Batalov 06/2022 8595 86455!4+8 97319 Robert Price 09/2019 8596 22591^20310+20310^22591 97316 Hans Havermann 06/2020 8597 2^323261-431173 97312 Harrison Mesh 06/2022 8598 (3996^27017-1)/3995 97302 Serge Batalov 06/2022 8599 25101^7520+7520^25101 97297 Hans Havermann 05/2020 8600 (233*10^97294+7)/3 97296 Robert Price 03/2022 8601 p(19982)#/2-1024 97293 Robert Price 09/2017 8602 (65*10^97288+277)/9 97289 Robert Price 08/2021 8603 6^125021-85 97286 Lelio R Paula 08/2016 8604 2^323164-47355 97283 Lelio R Paula 07/2016 8605 (3^203902+4)/36051015157 97276 Lelio R Paula 09/2013 8606 2^323054-6555 97249 Lelio R Paula 07/2016 8607 22822^18247+18247^22822 97249 Hans Havermann 02/2020 8608 9*10^97247-29 97248 Robert Price 05/2017 8609 24382^9735+9735^24382 97244 Hans Havermann 02/2020 8610 (31*10^97242+41)/9 97243 Robert Price 04/2015 8611 GoldenRatioPrime[97241] 97241 Eric W. Weisstein 06/2009 8612 12^90098-41 97233 Lelio R Paula 07/2016 8613 2^322928-216929 97212 Enzo Doria 05/2014 8614 (16731^23017-1)/16730 97209 Serge Batalov 06/2022 8615 3*10^97205-61 97206 Robert Price 04/2021 8616 (7*2^322896-1)/57 97201 Lelio R Paula 02/2014 8617 (35*10^97194-341)/9 97195 Robert Price 08/2021 8618 (4872^26357-1)/4871 97194 Serge Batalov 06/2022 8619 (2^322897+5)/3146107489 97193 Lelio R Paula 10/2013 8620 (796*10^97183-31)/9 97185 Robert Price 07/2022 8621 (2^322789+2214)/2 97169 Stefano Morozzi 09/2020 8622 2^322725+75761 97150 Enzo Doria 04/2016 8623 (13*2^322686+1)/119 97138 Lelio R Paula 11/2013 8624 (2175^29101-1)/2174 97121 Serge Batalov 06/2022 8625 22402^21639+21639^22402 97118 Hans Havermann 07/2020 8626 23399^14128+14128^23399 97108 Hans Havermann 06/2020 8627 (2892^28057-1)/2891 97108 Serge Batalov 06/2022 8628 (9578^24391-1)/9577 97104 Serge Batalov 06/2022 8629 (2^322525+2606)/2 97090 Stefano Morozzi 09/2020 8630 (9563^24391-1)/9562 97087 Serge Batalov 06/2022 8631 (41*10^97085+373)/9 97086 Robert Price 04/2017 8632 (2^322473+854)/2 97074 Stefano Morozzi 02/2021 8633 2^322413+77 97056 Lelio R Paula 12/2012 8634 2^322406+177 97054 Lelio R Paula 12/2012 8635 (349^38167-1)/348 97050 Serge Batalov 06/2022 8636 (14*10^97044+31)/9 97045 Robert Price 02/2015 8637 2^322302+255255 97023 Lelio R Paula 07/2016 8638 (1302^31147-1)/1301 97008 Serge Batalov 06/2022 8639 2^322196-113093 96991 Enzo Doria 07/2014 8640 (2^322169+2690)/2 96983 Stefano Morozzi 09/2020 8641 (49*10^96980+221)/9 96981 Robert Price 02/2022 8642 9*10^96968-47 96969 Robert Price 11/2021 8643 (5895^25717-1)/5894 96962 Serge Batalov 06/2022 8644 (27473^21841-1)/27472 96946 Serge Batalov 06/2022 8645 23109^15668+15668^23109 96943 Hans Havermann 07/2020 8646 2^322000-1861469 96932 Enzo Doria 03/2016 8647 2^321971-112747 96923 Enzo Doria 06/2014 8648 23754^12023+12023^23754 96917 Hans Havermann 07/2020 8649 11^93062-92 96915 Lelio R Paula 06/2016 8650 (37871^21169-1)/37870 96914 Serge Batalov 06/2022 8651 (2^321922+2214)/2 96908 Stefano Morozzi 09/2020 8652 (2^321900+2086)/2 96902 Stefano Morozzi 09/2020 8653 (11*2^321841-7)/15 96884 Renaud Lifchitz 03/2011 8654 3^203051+34 96880 Lelio R Paula 05/2016 8655 2*10^96867-51 96868 Robert Price 11/2017 8656 (2^321779+2618)/2 96865 Stefano Morozzi 09/2020 8657 (64*10^96863-1)/27 96864 Serge Batalov 05/2010 8658 2^321716-2786939 96847 Enzo Doria 03/2016 8659 22496^20181+20181^22496 96844 Hans Havermann 03/2020 8660 2^321701-113053 96842 Enzo Doria 07/2014 8661 2^321700-28635 96842 Lelio R Paula 06/2016 8662 (5*2^321691-1)/27 96838 Lelio R Paula 02/2014 8663 6*10^96835+13 96836 Robert Price 10/2021 8664 6^124433-124433 96828 Robert Price 01/2014 8665 2^321631+69 96821 Lelio R Paula 12/2012 8666 (27109^21841-1)/27108 96820 Serge Batalov 06/2022 8667 (13*2^321606+1)/119 96813 Lelio R Paula 11/2013 8668 (5052^26141-1)/5051 96809 Serge Batalov 06/2022 8669 (46*10^96798-1)/9 96799 Serge Batalov 10/2014 8670 (59*10^96798+31)/9 96799 Robert Price 09/2015 8671 (2^321536+2062)/2 96792 Stefano Morozzi 09/2020 8672 223319#+231223 96790 Makoto Morimoto 02/2016 8673 2^321519-28635 96787 Lelio R Paula 06/2016 8674 2^321487-1867237 96778 Enzo Doria 03/2016 8675 2^321461-63 96770 Lelio R Paula 12/2012 8676 (16053^23011-1)/16052 96770 Serge Batalov 06/2022 8677 2^321439+123 96763 Lelio R Paula 12/2012 8678 2^321434+709 96762 Lelio R Paula 02/2013 8679 (2^321415+554)/2 96756 Stefano Morozzi 09/2020 8680 14^84413+89 96749 Lelio R Paula 07/2016 8681 (28*10^96743+71)/9 96744 Serge Batalov 12/2008 8682 13^86847+96 96743 Lelio R Paula 06/2016 8683 9*2^321336-7 96733 Lelio R Paula 08/2014 8684 (209*10^96722-17)/3 96724 Robert Price 05/2017 8685 (54163^20431-1)/54162 96710 Serge Batalov 06/2022 8686 2^321237-4615 96702 Yves Minet 05/2019 8687 (27273^21799-1)/27272 96691 Serge Batalov 06/2022 8688 2^321187-1159 96687 Yves Minet 11/2012 8689 2^321182-1850081 96686 Enzo Doria 08/2015 8691 23359^13768+13768^23359 96680 Hans Havermann 06/2020 8690 (65630^20071-1)/65629 96680 Serge Batalov 06/2022 8692 2^321116-112829 96666 Enzo Doria 06/2014 8693 2^321108-109499 96664 Enzo Doria 04/2014 8694 2^321098+2793859 96661 Enzo Doria 03/2016 8695 (2^321100+1170)/2 96661 Stefano Morozzi 09/2020 8696 2^321057+4097 96648 Lelio R Paula 06/2016 8697 (4435*29^66081-4)/7 96640 Curtis Bright 05/2015 8698 22743^17750+17750^22743 96640 Hans Havermann 04/2020 8699 22882^16679+16679^22882 96612 Hans Havermann 02/2020 8700 23452^13163+13163^23452 96608 Hans Havermann 02/2020 8701 (1042^32009-1)/1041 96596 Serge Batalov 06/2022 8702 (85*10^96594-373)/9 96595 Robert Price 05/2021 8703 (2^320863+666)/2 96590 Stefano Morozzi 09/2020 8704 p(19849)#/2-64 96581 Robert Price 04/2017 8705 2^320817+189 96576 Lelio R Paula 12/2012 8706 2^320816-4685 96576 Yves Minet 05/2019 8708 (361*10^96567-163)/9 96569 Robert Price 10/2017 8707 (19*10^96568+137)/3 96569 Robert Price 03/2022 8709 2^320788-110327 96567 Enzo Doria 05/2014 8710 (3065^27697-1)/3064 96561 Serge Batalov 06/2022 8711 2^320764+793 96560 Lelio R Paula 02/2013 8712 (2^320752+1842)/2 96556 Stefano Morozzi 02/2021 8713 (48331^20611-1)/48330 96542 Serge Batalov 06/2022 8714 (50595^20521-1)/50594 96529 Serge Batalov 06/2022 8715 (9179*2^320652-1)/221 96528 Lelio R Paula 05/2015 8716 23288^13947+13947^23288 96517 Hans Havermann 07/2020 8718 2^320616-78795 96516 Lelio R Paula 03/2016 8717 (19*10^96520+287)/9/109/409 96516 Alfred Reich 11/2022 8719 2^320612-461939 96514 Enzo Doria 07/2015 8720 (21245^22303-1)/21244 96507 Serge Batalov 06/2022 8721 10^96504+987654321 96505 Robert Price 12/2019 8722 10^96504+71887 96505 Patrick De Geest 02/2020 8723 22654^18195+18195^22654 96505 Hans Havermann 07/2020 8724 10^96504-139277 96504 Patrick De Geest 02/2020 8725 (218^41263-1)/217 96490 Serge Batalov 06/2022 8726 (47220^20641-1)/47219 96474 Serge Batalov 06/2022 8727 5*2^320431+7 96461 Lelio R Paula 08/2014 8728 19^75431-90 96458 Lelio R Paula 06/2016 8729 (11853^23677-1)/11852 96452 Serge Batalov 06/2022 8730 (2^320386+2814)/2 96446 Stefano Morozzi 02/2021 8731 (2^320370+3)/67 96440 Lelio R Paula 10/2013 8732 3*10^96431-17 96432 Robert Price 03/2021 8733 2^320309+1871477 96423 Enzo Doria 05/2016 8734 (10412^24001-1)/10411 96421 Serge Batalov 06/2022 8735 tau(809^6028) 96410 Nik Lygeros / Olivier Rozier / LR team 10/2013 8736 (29*10^96407-23)/3 96408 Robert Price 03/2022 8737 (21*2^320252-1)/1895 96404 Lelio R Paula 02/2014 8738 2^320232-173 96400 Lelio R Paula 12/2012 8739 175^42975-2 96395 Lelio R Paula 10/2017 8740 (2^320170+2718)/2 96381 Stefano Morozzi 09/2020 8741 10^96377+199911 96378 Patrick De Geest 12/2016 8742 10^96377-20001 96377 Robert Price 11/2016 8743 (18079^22639-1)/18078 96374 Serge Batalov 06/2022 8745 2^320124-2790449 96367 Enzo Doria 03/2016 8744 10^96366+19197 96367 Patrick De Geest 08/2021 8747 10^96366-10000000001 96366 Robert Price 04/2021 8746 10^96366-287367 96366 Patrick De Geest 08/2021 8748 (26351^21799-1)/26350 96365 Serge Batalov 06/2022 8749 22488^19255+19255^22488 96351 Hans Havermann 11/2019 8750 23248^13939+13939^23248 96346 Hans Havermann 11/2019

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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