## 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) !!!

See the Top discoverers
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 ? 9501 2^321716-2786939 96847 Enzo Doria 03/2016 9502 22496^20181+20181^22496 96844 Hans Havermann 03/2020 9503 2^321701-113053 96842 Enzo Doria 07/2014 9504 2^321700-28635 96842 Lelio R Paula 06/2016 9505 (5*2^321691-1)/27 96838 Lelio R Paula 02/2014 9506 6*10^96835+13 96836 Robert Price 10/2021 9507 6^124433-124433 96828 Robert Price 01/2014 9508 2^321631+69 96821 Lelio R Paula 12/2012 9509 (27109^21841-1)/27108 96820 Serge Batalov 06/2022 9510 (13*2^321606+1)/119 96813 Lelio R Paula 11/2013 9511 (5052^26141-1)/5051 96809 Serge Batalov 06/2022 9512 (46*10^96798-1)/9 96799 Serge Batalov 10/2014 9513 (59*10^96798+31)/9 96799 Robert Price 09/2015 9514 (2^321536+2062)/2 96792 Stefano Morozzi 09/2020 9515 223319#+231223 96790 Makoto Morimoto 02/2016 9516 2^321519-28635 96787 Lelio R Paula 06/2016 9517 2^321487-1867237 96778 Enzo Doria 03/2016 9518 2^321461-63 96770 Lelio R Paula 12/2012 9519 (16053^23011-1)/16052 96770 Serge Batalov 06/2022 9520 2^321439+123 96763 Lelio R Paula 12/2012 9521 2^321434+709 96762 Lelio R Paula 02/2013 9522 2^321419+22703 96757 Enzo Doria 09/2023 9523 (2^321415+554)/2 96756 Stefano Morozzi 09/2020 9524 14^84413+89 96749 Lelio R Paula 07/2016 9525 (28*10^96743+71)/9 96744 Serge Batalov 12/2008 9526 13^86847+96 96743 Lelio R Paula 06/2016 9527 9*2^321336-7 96733 Lelio R Paula 08/2014 9528 (209*10^96722-17)/3 96724 Robert Price 05/2017 9529 (54163^20431-1)/54162 96710 Serge Batalov 06/2022 9530 2^321237-4615 96702 Yves Minet 05/2019 9531 (27273^21799-1)/27272 96691 Serge Batalov 06/2022 9532 2^321187-1159 96687 Yves Minet 11/2012 9533 2^321182-1850081 96686 Enzo Doria 08/2015 9535 23359^13768+13768^23359 96680 Hans Havermann 06/2020 9534 (65630^20071-1)/65629 96680 Serge Batalov 06/2022 9536 2^321116-112829 96666 Enzo Doria 06/2014 9537 2^321108-109499 96664 Enzo Doria 04/2014 9538 2^321098+2793859 96661 Enzo Doria 03/2016 9539 (2^321100+1170)/2 96661 Stefano Morozzi 09/2020 9540 2^321057+4097 96648 Lelio R Paula 06/2016 9541 (4435*29^66081-4)/7 96640 Curtis Bright 05/2015 9542 22743^17750+17750^22743 96640 Hans Havermann 04/2020 9543 22882^16679+16679^22882 96612 Hans Havermann 02/2020 9544 23452^13163+13163^23452 96608 Hans Havermann 02/2020 9545 (1042^32009-1)/1041 96596 Serge Batalov 06/2022 9546 (85*10^96594-373)/9 96595 Robert Price 05/2021 9547 (2^320863+666)/2 96590 Stefano Morozzi 09/2020 9548 p(19849)#/2-64 96581 Robert Price 04/2017 9549 2^320817+189 96576 Lelio R Paula 12/2012 9550 2^320816-4685 96576 Yves Minet 05/2019 9552 (361*10^96567-163)/9 96569 Robert Price 10/2017 9551 (19*10^96568+137)/3 96569 Robert Price 03/2022 9553 2^320788-110327 96567 Enzo Doria 05/2014 9554 (3065^27697-1)/3064 96561 Serge Batalov 06/2022 9555 2^320764+793 96560 Lelio R Paula 02/2013 9556 (2^320752+1842)/2 96556 Stefano Morozzi 02/2021 9557 (48331^20611-1)/48330 96542 Serge Batalov 06/2022 9558 (107746^19321-1)/(107746^139-1) 96532 Ryan Propper 11/2023 9559 (50595^20521-1)/50594 96529 Serge Batalov 06/2022 9560 (9179*2^320652-1)/221 96528 Lelio R Paula 05/2015 9561 23288^13947+13947^23288 96517 Hans Havermann 07/2020 9563 2^320616-78795 96516 Lelio R Paula 03/2016 9562 (19*10^96520+287)/9/109/409 96516 Alfred Reich 11/2022 9564 2^320612-461939 96514 Enzo Doria 07/2015 9565 (21245^22303-1)/21244 96507 Serge Batalov 06/2022 9566 10^96504+987654321 96505 Robert Price 12/2019 9567 10^96504+71887 96505 Patrick De Geest 02/2020 9568 22654^18195+18195^22654 96505 Hans Havermann 07/2020 9569 10^96504-139277 96504 Patrick De Geest 02/2020 9570 (218^41263-1)/217 96490 Serge Batalov 06/2022 9571 (47220^20641-1)/47219 96474 Serge Batalov 06/2022 9572 5*2^320431+7 96461 Lelio R Paula 08/2014 9573 19^75431-90 96458 Lelio R Paula 06/2016 9574 (11853^23677-1)/11852 96452 Serge Batalov 06/2022 9575 (2^320386+2814)/2 96446 Stefano Morozzi 02/2021 9576 (2^320370+3)/67 96440 Lelio R Paula 10/2013 9577 3*10^96431-17 96432 Robert Price 03/2021 9578 2^320309+1871477 96423 Enzo Doria 05/2016 9579 (10412^24001-1)/10411 96421 Serge Batalov 06/2022 9580 tau(809^6028) 96410 Nik Lygeros / Olivier Rozier / LR team 10/2013 9581 (29*10^96407-23)/3 96408 Robert Price 03/2022 9582 (21*2^320252-1)/1895 96404 Lelio R Paula 02/2014 9583 2^320232-173 96400 Lelio R Paula 12/2012 9584 175^42975-2 96395 Lelio R Paula 10/2017 9585 (2^320170+2718)/2 96381 Stefano Morozzi 09/2020 9586 10^96377+199911 96378 Patrick De Geest 12/2016 9587 10^96377-20001 96377 Robert Price 11/2016 9588 (18079^22639-1)/18078 96374 Serge Batalov 06/2022 9590 2^320124-2790449 96367 Enzo Doria 03/2016 9589 10^96366+19197 96367 Patrick De Geest 08/2021 9592 10^96366-10000000001 96366 Robert Price 04/2021 9591 10^96366-287367 96366 Patrick De Geest 08/2021 9593 (26351^21799-1)/26350 96365 Serge Batalov 06/2022 9594 22488^19255+19255^22488 96351 Hans Havermann 11/2019 9595 23248^13939+13939^23248 96346 Hans Havermann 11/2019 9596 (5928^25537-1)/5927 96345 Serge Batalov 06/2022 9598 2^320043-108775 96343 Enzo Doria 04/2014 9597 24989^7168+7168^24989 96343 Hans Havermann 11/2019 9599 10^96338+424939 96339 Patrick De Geest 03/2016 9600 10^96338-9281 96338 Robert Price 09/2015 9601 (8527^24509-1)/8526 96336 Serge Batalov 06/2022 9602 (3*2^320008+1)/7 96332 Lelio R Paula 09/2013 9603 (2444^28433-1)/2443 96331 Serge Batalov 06/2022 9604 (48690^20551-1)/48689 96327 Serge Batalov 06/2022 9605 (61935^20101-1)/61934 96318 Serge Batalov 06/2022 9606 25699^5596+5596^25699 96317 Hans Havermann 07/2020 9607 (7*10^96312+83)/9 96312 Tyler Busby 01/2023 9608 (11*10^96298+529)/9 96299 Robert Price 09/2021 9610 26502^4297+4297^26502 96287 Hans Havermann 07/2020 9609 (54180^20341-1)/54179 96287 Serge Batalov 06/2022 9611 2^319838+4257 96281 Lelio R Paula 03/2016 9612 2^319830-16995 96279 Lelio R Paula 03/2016 9613 6^123713+143 96268 Lelio R Paula 05/2016 9614 (28*10^96265-97)/3 96266 Robert Price 07/2016 9615 (3799^26893-1)/3798 96265 Serge Batalov 06/2022 9617 103^47825-102 96264 Norbert Schneider 10/2016 9616 (54041^20341-1)/54040 96264 Serge Batalov 06/2022 9618 (2^319777+2082)/2 96263 Stefano Morozzi 09/2020 9619 (2^319771+3686)/2 96261 Stefano Morozzi 09/2020 9620 2^319713-81 96244 Lelio R Paula 11/2012 9621 2^319711+213413 96243 Enzo Doria 09/2023 9622 (55459*2^319706+1)/20167 96242 Lelio R Paula 07/2014 9623 22834^16393+16393^22834 96238 Hans Havermann 05/2020 9624 8*10^96236+27 96237 Robert Price 09/2021 9625 12^89153-43 96213 Lelio R Paula 06/2016 9626 (25048^21871-1)/25047 96202 Serge Batalov 06/2022 9628 (2*10^96195-59)/3 96195 Robert Price 05/2017 9627 9*10^96194-77 96195 Robert Price 08/2020 9629 2^319545+147 96193 Lelio R Paula 11/2012 9630 23357^13128+13128^23357 96189 Hans Havermann 02/2020 9631 (19838^22381-1)/19837 96179 Serge Batalov 06/2022 9632 (221^41023-1)/220 96172 Serge Batalov 06/2022 9633 25952^5073+5073^25952 96160 Hans Havermann 12/2019 9634 (50891^20431-1)/50890 96157 Serge Batalov 06/2022 9635 (50^56597+1)/51 96155 Robert Price 03/2014 9636 22313^20374+20374^22313 96149 Hans Havermann 12/2019 9637 22279^20668+20668^22279 96141 Hans Havermann 11/2019 9638 (41*10^96137-59)/9 96138 Robert Price 10/2017 9639 2^319353-110343 96135 Enzo Doria 05/2014 9640 11^92309-42 96130 Lelio R Paula 05/2016 9641 (21675^22171-1)/21674 96129 Serge Batalov 06/2022 9642 14^83869-13^83869 96125 Jean-Louis Charton 01/2009 9643 (7*10^96112+143)/3 96113 Robert Price 04/2016 9644 26731^3940+3940^26731 96112 Hans Havermann 07/2020 9645 22640^17583+17583^22640 96109 Hans Havermann 07/2020 9646 (19178^22441-1)/19177 96107 Serge Batalov 06/2022 9647 2^319237+65835 96100 Lelio R Paula 03/2016 9648 2^319194-1841 96087 Yves Minet 03/2013 9649 23949^10280+10280^23949 96084 Hans Havermann 07/2020 9650 (1927^29251-1)/1926 96083 Serge Batalov 06/2022 9651 20^73847-31 96078 Lelio R Paula 05/2016 9652 (60229^20101-1)/60228 96075 Serge Batalov 06/2022 9653 (28044^21601-1)/28043 96074 Serge Batalov 06/2022 9654 50^56543-49 96065 Norbert Schneider 09/2018 9655 2^319107-109555 96061 Enzo Doria 04/2014 9656 (3*2^319114-1)/2627 96060 Lelio R Paula 02/2014 9657 2^319098-112157 96059 Enzo Doria 06/2014 9658 15^81673+94 96055 Lelio R Paula 07/2016 9659 (85761^19471-1)/85760 96052 Serge Batalov 06/2022 9660 2^319074+1871749 96051 Enzo Doria 05/2016 9661 25670^5517+5517^25670 96050 Hans Havermann 06/2020 9662 6*10^96037+19 96038 Robert Price 11/2021 9663 2^319007-112111 96031 Enzo Doria 06/2014 9664 (57987^20161-1)/57986 96029 Serge Batalov 06/2022 9666 2^318946-1421 96013 Yves Minet 01/2013 9665 (68310^19861-1)/68309 96013 Serge Batalov 06/2022 9667 (20294^22291-1)/20293 96012 Serge Batalov 06/2022 9668 (304^38669-1)/303 96008 Serge Batalov 06/2022 9669 (1840^29401-1)/1839 95986 Serge Batalov 06/2022 9670 22830^16003+16003^22830 95982 Hans Havermann 02/2020 9671 2^318834-110411 95979 Enzo Doria 05/2014 9672 2^318831-1965 95978 Lelio R Paula 03/2016 9673 (5*10^95976+7)/3 95977 Erik Branger 03/2014 9674 (12797^23369-1)/12796 95975 Serge Batalov 06/2022 9675 (10534^23857-1)/10533 95963 Serge Batalov 06/2022 9676 22871^15696+15696^22871 95962 Hans Havermann 01/2020 9677 (2^318760+858)/2 95957 Stefano Morozzi 02/2021 9678 23167^13860+13860^23167 95953 Hans Havermann 01/2020 9679 (823^32911-1)/822 95946 Serge Batalov 06/2022 9681 5*3^201089-8 95945 Lelio R Paula 08/2014 9680 (81783^19531-1)/81782 95945 Serge Batalov 06/2022 9682 2^318711-139 95942 Lelio R Paula 11/2012 9683 2^318635-1167 95919 Lelio R Paula 03/2016 9684 15^81555+16 95917 Lelio R Paula 07/2016 9685 (37*10^95895+377)/9 95896 Robert Price 10/2017 9686 (22699*2^318527+1)/21 95890 Lelio R Paula 07/2014 9687 45^57997+196072 95882 Enzo Doria 10/2023 9688 2^318496-97305 95877 Lelio R Paula 03/2016 9689 22129^21496+21496^22129 95871 Hans Havermann 07/2020 9691 2^318466+15015 95868 Lelio R Paula 03/2016 9690 24847^7216+7216^24847 95868 Hans Havermann 07/2020 9692 23706^11065+11065^23706 95866 Hans Havermann 07/2020 9693 (2863^27733-1)/2862 95865 Serge Batalov 06/2022 9694 6^123187-173129 95859 Mike Oakes 04/2011 9695 2^318423-487 95855 Yves Minet 03/2012 9696 10^95848+443709 95849 Patrick De Geest 10/2022 9697 10^95848-5000000001 95848 Robert Price 09/2022 9698 10^95848-61971 95848 Patrick De Geest 10/2022 9699 (2^318359+678)/2 95836 Stefano Morozzi 09/2020 9700 (10223*2^318350+1)/1563 95834 Lelio R Paula 07/2014 9701 (8060^24533-1)/8059 95831 Serge Batalov 06/2022 9702 (9853^23993-1)/9852 95814 Serge Batalov 06/2022 9704 (2^318267+2550)/2 95808 Stefano Morozzi 09/2020 9703 (5048^25873-1)/5047 95808 Serge Batalov 06/2022 9706 4*10^95799+13 95800 Robert Price 02/2021 9705 (65533^19891-1)/65532 95800 Serge Batalov 06/2022 9707 2^318203+211343 95789 Enzo Doria 08/2023 9708 45369!2+1024 95787 Robert Price 02/2015 9709 3^200758-86 95786 Lelio R Paula 05/2016 9710 (2^318271+1)/(3*46031404238891*654090604244843) 95781 Gord Palameta 12/2018 9711 (2^318171+2030)/2 95779 Stefano Morozzi 09/2020 9712 3*10^95776-59 95777 Robert Price 10/2017 9713 (82970^19471-1)/82969 95772 Serge Batalov 06/2022 9714 193^41901-2 95768 Lelio R Paula 10/2017 9715 (2^318124+2502)/2 95765 Stefano Morozzi 09/2020 9716 (12900^23297-1)/12899 95761 Serge Batalov 06/2022 9717 4*10^95752-71 95753 Robert Price 11/2017 9718 (16955^22639-1)/16954 95743 Serge Batalov 06/2022 9719 (81795^19489-1)/81794 95740 Serge Batalov 06/2022 9720 (2742^27847-1)/2741 95737 Serge Batalov 06/2022 9721 (6072^25303-1)/6071 95726 Serge Batalov 06/2022 9722 23640^11197+11197^23640 95721 Hans Havermann 12/2019 9723 10^95712+89329 95713 Patrick De Geest 09/2022 9725 10^95712-4000001 95712 Robert Price 07/2021 9724 10^95712-989313 95712 Patrick De Geest 09/2022 9726 (60657^20011-1)/60656 95706 Serge Batalov 06/2022 9727 ((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/9 95704 Hans Havermann 05/2019 9728 (509203*2^317881-1)/52805 95693 Lelio R Paula 04/2015 9729 (26161^21661-1)/26160 95687 Serge Batalov 06/2022 9730 (2^317853+1086)/2 95683 Stefano Morozzi 09/2020 9731 4*10^95672+91 95673 Robert Price 11/2017 9732 6*10^95665+43 95666 Robert Price 07/2020 9733 (20819^22153-1)/20818 95663 Serge Batalov 06/2022 9734 (64464^19891-1)/64463 95658 Serge Batalov 06/2022 9735 (934^32203-1)/933 95652 Serge Batalov 06/2022 9736 (11*10^95641-113)/3 95642 Robert Price 01/2017 9737 (72330^19681-1)/72329 95632 Serge Batalov 06/2022 9738 (13224^23203-1)/13223 95624 Serge Batalov 06/2022 9739 (18211^22441-1)/18210 95602 Serge Batalov 06/2022 9740 (71975^19681-1)/71974 95590 Serge Batalov 06/2022 9741 (13*10^95588+11)/3 95589 Robert Price 05/2015 9742 Phi(191188,10)/191189 95587 Maksym Voznyy 11/2015 9743 (13368^23167-1)/13367 95585 Serge Batalov 06/2022 9744 (25874^21661-1)/25873 95583 Serge Batalov 06/2022 9745 3^200325+70 95580 Lelio R Paula 05/2016 9746 (25*10^95574-7)/9 95575 Robert Price 12/2014 9747 (2^317485-3)/21313 95569 Lelio R Paula 06/2013 9748 2^317464+31 95567 Lelio R Paula 11/2012 9749 (2^317451+2114)/2 95562 Stefano Morozzi 09/2020 9750 7^113073+82 95558 Lelio R Paula 04/2016

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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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