## 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 ? 8751 (5928^25537-1)/5927 96345 Serge Batalov 06/2022 8753 2^320043-108775 96343 Enzo Doria 04/2014 8752 24989^7168+7168^24989 96343 Hans Havermann 11/2019 8754 10^96338+424939 96339 Patrick De Geest 03/2016 8755 10^96338-9281 96338 Robert Price 09/2015 8756 (8527^24509-1)/8526 96336 Serge Batalov 06/2022 8757 (3*2^320008+1)/7 96332 Lelio R Paula 09/2013 8758 (2444^28433-1)/2443 96331 Serge Batalov 06/2022 8759 (48690^20551-1)/48689 96327 Serge Batalov 06/2022 8760 (61935^20101-1)/61934 96318 Serge Batalov 06/2022 8761 25699^5596+5596^25699 96317 Hans Havermann 07/2020 8762 (7*10^96312+83)/9 96312 Tyler Busby 01/2023 8763 (11*10^96298+529)/9 96299 Robert Price 09/2021 8765 26502^4297+4297^26502 96287 Hans Havermann 07/2020 8764 (54180^20341-1)/54179 96287 Serge Batalov 06/2022 8766 2^319838+4257 96281 Lelio R Paula 03/2016 8767 2^319830-16995 96279 Lelio R Paula 03/2016 8768 6^123713+143 96268 Lelio R Paula 05/2016 8769 (28*10^96265-97)/3 96266 Robert Price 07/2016 8770 (3799^26893-1)/3798 96265 Serge Batalov 06/2022 8772 103^47825-102 96264 Norbert Schneider 10/2016 8771 (54041^20341-1)/54040 96264 Serge Batalov 06/2022 8773 (2^319777+2082)/2 96263 Stefano Morozzi 09/2020 8774 (2^319771+3686)/2 96261 Stefano Morozzi 09/2020 8775 2^319713-81 96244 Lelio R Paula 11/2012 8776 (55459*2^319706+1)/20167 96242 Lelio R Paula 07/2014 8777 22834^16393+16393^22834 96238 Hans Havermann 05/2020 8778 8*10^96236+27 96237 Robert Price 09/2021 8779 12^89153-43 96213 Lelio R Paula 06/2016 8780 (25048^21871-1)/25047 96202 Serge Batalov 06/2022 8782 (2*10^96195-59)/3 96195 Robert Price 05/2017 8781 9*10^96194-77 96195 Robert Price 08/2020 8783 2^319545+147 96193 Lelio R Paula 11/2012 8784 23357^13128+13128^23357 96189 Hans Havermann 02/2020 8785 (19838^22381-1)/19837 96179 Serge Batalov 06/2022 8786 (221^41023-1)/220 96172 Serge Batalov 06/2022 8787 25952^5073+5073^25952 96160 Hans Havermann 12/2019 8788 (50891^20431-1)/50890 96157 Serge Batalov 06/2022 8789 (50^56597+1)/51 96155 Robert Price 03/2014 8790 22313^20374+20374^22313 96149 Hans Havermann 12/2019 8791 22279^20668+20668^22279 96141 Hans Havermann 11/2019 8792 (41*10^96137-59)/9 96138 Robert Price 10/2017 8793 2^319353-110343 96135 Enzo Doria 05/2014 8794 11^92309-42 96130 Lelio R Paula 05/2016 8795 (21675^22171-1)/21674 96129 Serge Batalov 06/2022 8796 14^83869-13^83869 96125 Jean-Louis Charton 01/2009 8797 (7*10^96112+143)/3 96113 Robert Price 04/2016 8798 26731^3940+3940^26731 96112 Hans Havermann 07/2020 8799 22640^17583+17583^22640 96109 Hans Havermann 07/2020 8800 (19178^22441-1)/19177 96107 Serge Batalov 06/2022 8801 2^319237+65835 96100 Lelio R Paula 03/2016 8802 2^319194-1841 96087 Yves Minet 03/2013 8803 23949^10280+10280^23949 96084 Hans Havermann 07/2020 8804 (1927^29251-1)/1926 96083 Serge Batalov 06/2022 8805 20^73847-31 96078 Lelio R Paula 05/2016 8806 (60229^20101-1)/60228 96075 Serge Batalov 06/2022 8807 (28044^21601-1)/28043 96074 Serge Batalov 06/2022 8808 50^56543-49 96065 Norbert Schneider 09/2018 8809 2^319107-109555 96061 Enzo Doria 04/2014 8810 (3*2^319114-1)/2627 96060 Lelio R Paula 02/2014 8811 2^319098-112157 96059 Enzo Doria 06/2014 8812 15^81673+94 96055 Lelio R Paula 07/2016 8813 (85761^19471-1)/85760 96052 Serge Batalov 06/2022 8814 2^319074+1871749 96051 Enzo Doria 05/2016 8815 25670^5517+5517^25670 96050 Hans Havermann 06/2020 8816 6*10^96037+19 96038 Robert Price 11/2021 8817 2^319007-112111 96031 Enzo Doria 06/2014 8818 (57987^20161-1)/57986 96029 Serge Batalov 06/2022 8820 2^318946-1421 96013 Yves Minet 01/2013 8819 (68310^19861-1)/68309 96013 Serge Batalov 06/2022 8821 (20294^22291-1)/20293 96012 Serge Batalov 06/2022 8822 (304^38669-1)/303 96008 Serge Batalov 06/2022 8823 (1840^29401-1)/1839 95986 Serge Batalov 06/2022 8824 22830^16003+16003^22830 95982 Hans Havermann 02/2020 8825 2^318834-110411 95979 Enzo Doria 05/2014 8826 2^318831-1965 95978 Lelio R Paula 03/2016 8827 (5*10^95976+7)/3 95977 Erik Branger 03/2014 8828 (12797^23369-1)/12796 95975 Serge Batalov 06/2022 8829 (10534^23857-1)/10533 95963 Serge Batalov 06/2022 8830 22871^15696+15696^22871 95962 Hans Havermann 01/2020 8831 (2^318760+858)/2 95957 Stefano Morozzi 02/2021 8832 23167^13860+13860^23167 95953 Hans Havermann 01/2020 8833 (823^32911-1)/822 95946 Serge Batalov 06/2022 8835 5*3^201089-8 95945 Lelio R Paula 08/2014 8834 (81783^19531-1)/81782 95945 Serge Batalov 06/2022 8836 2^318711-139 95942 Lelio R Paula 11/2012 8837 2^318635-1167 95919 Lelio R Paula 03/2016 8838 15^81555+16 95917 Lelio R Paula 07/2016 8839 (37*10^95895+377)/9 95896 Robert Price 10/2017 8840 (22699*2^318527+1)/21 95890 Lelio R Paula 07/2014 8841 2^318496-97305 95877 Lelio R Paula 03/2016 8842 22129^21496+21496^22129 95871 Hans Havermann 07/2020 8844 2^318466+15015 95868 Lelio R Paula 03/2016 8843 24847^7216+7216^24847 95868 Hans Havermann 07/2020 8845 23706^11065+11065^23706 95866 Hans Havermann 07/2020 8846 (2863^27733-1)/2862 95865 Serge Batalov 06/2022 8847 6^123187-173129 95859 Mike Oakes 04/2011 8848 2^318423-487 95855 Yves Minet 03/2012 8849 10^95848+443709 95849 Patrick De Geest 10/2022 8850 10^95848-5000000001 95848 Robert Price 09/2022 8851 10^95848-61971 95848 Patrick De Geest 10/2022 8852 (2^318359+678)/2 95836 Stefano Morozzi 09/2020 8853 (10223*2^318350+1)/1563 95834 Lelio R Paula 07/2014 8854 (8060^24533-1)/8059 95831 Serge Batalov 06/2022 8855 (9853^23993-1)/9852 95814 Serge Batalov 06/2022 8857 (2^318267+2550)/2 95808 Stefano Morozzi 09/2020 8856 (5048^25873-1)/5047 95808 Serge Batalov 06/2022 8859 4*10^95799+13 95800 Robert Price 02/2021 8858 (65533^19891-1)/65532 95800 Serge Batalov 06/2022 8860 45369!2+1024 95787 Robert Price 02/2015 8861 3^200758-86 95786 Lelio R Paula 05/2016 8862 (2^318271+1)/(3*46031404238891*654090604244843) 95781 Gord Palameta 12/2018 8863 (2^318171+2030)/2 95779 Stefano Morozzi 09/2020 8864 3*10^95776-59 95777 Robert Price 10/2017 8865 (82970^19471-1)/82969 95772 Serge Batalov 06/2022 8866 193^41901-2 95768 Lelio R Paula 10/2017 8867 (2^318124+2502)/2 95765 Stefano Morozzi 09/2020 8868 (12900^23297-1)/12899 95761 Serge Batalov 06/2022 8869 4*10^95752-71 95753 Robert Price 11/2017 8870 (16955^22639-1)/16954 95743 Serge Batalov 06/2022 8871 (81795^19489-1)/81794 95740 Serge Batalov 06/2022 8872 (2742^27847-1)/2741 95737 Serge Batalov 06/2022 8873 (6072^25303-1)/6071 95726 Serge Batalov 06/2022 8874 23640^11197+11197^23640 95721 Hans Havermann 12/2019 8875 10^95712+89329 95713 Patrick De Geest 09/2022 8877 10^95712-4000001 95712 Robert Price 07/2021 8876 10^95712-989313 95712 Patrick De Geest 09/2022 8878 (60657^20011-1)/60656 95706 Serge Batalov 06/2022 8879 ((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/9 95704 Hans Havermann 05/2019 8880 (509203*2^317881-1)/52805 95693 Lelio R Paula 04/2015 8881 (26161^21661-1)/26160 95687 Serge Batalov 06/2022 8882 (2^317853+1086)/2 95683 Stefano Morozzi 09/2020 8883 4*10^95672+91 95673 Robert Price 11/2017 8884 6*10^95665+43 95666 Robert Price 07/2020 8885 (20819^22153-1)/20818 95663 Serge Batalov 06/2022 8886 (64464^19891-1)/64463 95658 Serge Batalov 06/2022 8887 (934^32203-1)/933 95652 Serge Batalov 06/2022 8888 (11*10^95641-113)/3 95642 Robert Price 01/2017 8889 (72330^19681-1)/72329 95632 Serge Batalov 06/2022 8890 (13224^23203-1)/13223 95624 Serge Batalov 06/2022 8891 (18211^22441-1)/18210 95602 Serge Batalov 06/2022 8892 (71975^19681-1)/71974 95590 Serge Batalov 06/2022 8893 (13*10^95588+11)/3 95589 Robert Price 05/2015 8894 Phi(191188,10)/191189 95587 Maksym Voznyy 11/2015 8895 (13368^23167-1)/13367 95585 Serge Batalov 06/2022 8896 (25874^21661-1)/25873 95583 Serge Batalov 06/2022 8897 3^200325+70 95580 Lelio R Paula 05/2016 8898 (25*10^95574-7)/9 95575 Robert Price 12/2014 8899 (2^317485-3)/21313 95569 Lelio R Paula 06/2013 8900 2^317464+31 95567 Lelio R Paula 11/2012 8901 (2^317451+2114)/2 95562 Stefano Morozzi 09/2020 8902 7^113073+82 95558 Lelio R Paula 04/2016 8903 (24728^21751-1)/24727 95552 Serge Batalov 06/2022 8904 (49764^20341-1)/49763 95536 Serge Batalov 06/2022 8905 (36155^20959-1)/36154 95531 Serge Batalov 06/2022 8906 (7725^24571-1)/7724 95526 Serge Batalov 06/2022 8907 (20546^22147-1)/20545 95510 Serge Batalov 06/2022 8908 2^317251+465 95503 Lelio R Paula 03/2016 8909 19^74684+58 95503 Lelio R Paula 06/2016 8910 (2^317250-7)/339 95500 Lelio R Paula 07/2013 8911 5*10^95498-21 95499 Robert Price 12/2021 8912 (21615^22031-1)/21614 95495 Serge Batalov 06/2022 8913 6^122718-79 95494 Lelio R Paula 05/2016 8914 22168^20291+20291^22168 95485 Hans Havermann 10/2019 8915 (77427^19531-1)/77426 95481 Serge Batalov 06/2022 8916 (13026^23203-1)/13025 95472 Serge Batalov 06/2022 8917 2^317141-110491 95469 Enzo Doria 05/2014 8918 (2^317097+3014)/2 95456 Stefano Morozzi 09/2020 8919 2^317094+76309 95455 Enzo Doria 05/2016 8920 2^317085+95 95453 Lelio R Paula 11/2012 8921 (17*10^95451-377)/9 95452 Robert Price 11/2017 8922 2^317057-109551 95444 Enzo Doria 04/2014 8923 3^200026+28 95437 Lelio R Paula 05/2016 8924 2^317024+93 95434 Donovan Johnson 06/2008 8925 (86*10^95428-437)/9 95429 Robert Price 03/2021 8926 10^95427+192591 95428 Patrick De Geest 05/2021 8929 2^316999+1605 95427 Lelio R Paula 03/2016 8928 (2^317000+3210)/2 95427 Stefano Morozzi 09/2020 8927 10^95427-10001 95427 Robert Price 02/2021 8930 2^316995-110427 95426 Enzo Doria 05/2014 8931 (69841^19699-1)/69840 95420 Serge Batalov 06/2022 8932 (59242^19993-1)/59241 95415 Serge Batalov 06/2022 8934 22300^18987+18987^22300 95410 Hans Havermann 06/2020 8933 (9478^23993-1)/9477 95410 Serge Batalov 06/2022 8935 2^316937+177 95408 Lelio R Paula 11/2012 8936 4*10^95407+91 95408 Robert Price 11/2017 8937 2^316908+1915 95399 Lelio R Paula 03/2016 8938 2^316894+99 95395 Lelio R Paula 11/2012 8939 (2^316887+2546)/2 95393 Stefano Morozzi 09/2020 8940 2*10^95374-21 95375 Robert Price 09/2020 8941 6^122547+11 95361 Lelio R Paula 05/2016 8942 2^316771+82875 95358 Lelio R Paula 03/2016 8943 (15609^22741-1)/15608 95358 Serge Batalov 06/2022 8944 (2^316765+3102)/2 95356 Stefano Morozzi 09/2020 8945 (2267^28411-1)/2266 95329 Serge Batalov 06/2022 8946 (824^32693-1)/823 95328 Serge Batalov 06/2022 8947 (23*10^95326+1)/3 95327 Serge Batalov 05/2009 8948 1*10^95326+57 95327 Robert Price 03/2011 8949 10^95326-393687 95326 Patrick De Geest 09/2013 8950 (3^199803+4)/479539 95325 Lelio R Paula 04/2013 8951 2^316654-109481 95323 Enzo Doria 04/2014 8952 8*10^95316+51 95317 Robert Price 05/2017 8953 (50^56099+43^56099)/93 95309 Serge Batalov 12/2016 8954 (23*2^316559+1)/3925 95292 Lelio R Paula 09/2013 8956 (71*10^95277-539)/9 95278 Robert Price 11/2017 8955 23422^11691+11691^23422 95278 Hans Havermann 10/2019 8957 19^74503-56 95271 Lelio R Paula 06/2016 8958 (5038^25733-1)/5037 95267 Serge Batalov 06/2022 8959 11^91475-4380 95262 Enzo Doria 01/2013 8960 (62*10^95251-611)/9 95252 Robert Price 05/2017 8961 (160090^18301-1)/160089 95240 Serge Batalov 06/2022 8962 (173205^18181-1)/173204 95238 Serge Batalov 06/2022 8963 (158710^18313-1)/158709 95234 Serge Batalov 06/2022 8964 (9979^23813-1)/9978 95227 Serge Batalov 06/2022 8965 (57376^20011-1)/57375 95223 Serge Batalov 06/2022 8966 (2^316321-509203)/69377 95218 Lelio R Paula 06/2013 8967 26541^3868+3868^26541 95216 Hans Havermann 07/2020 8968 (79*10^95214-43)/9 95215 Erik Branger 11/2013 8969 (7176^24691-1)/7175 95202 Anonymous 11/2020 8970 (9*2^316233-1)/1751 95194 Lelio R Paula 02/2014 8971 5*2^316213+9 95191 Lelio R Paula 08/2014 8972 2*10^95188-91 95189 Robert Price 04/2020 8973 2^316205-1848163 95188 Enzo Doria 07/2015 8974 2^316185-2787913 95182 Enzo Doria 04/2016 8975 (2^316174+3538)/2 95178 Stefano Morozzi 09/2020 8976 (9787*2^316142-1)/3 95172 Lelio R Paula 04/2015 8977 2^316140-5 95168 Henri Lifchitz 02/2006 8978 (15185*2^316117-1)/3 95165 Lelio R Paula 04/2015 8979 (34*10^95153-7)/9/19/19157 95149 Makoto Morimoto 05/2016 8980 2^316069+76817 95147 Enzo Doria 05/2016 8981 (199*10^95134-7)/3 95136 Robert Price 02/2017 8982 2^316027-97305 95134 Lelio R Paula 03/2016 8983 2^316006-2798051 95128 Enzo Doria 04/2016 8984 24994^6397+6397^24994 95127 Hans Havermann 02/2020 8986 2^315921-2797603 95102 Enzo Doria 04/2016 8985 (2^315921+1314)/2 95102 Stefano Morozzi 02/2021 8987 2*10^95095+63 95096 Robert Price 10/2017 8988 2^315857+1299 95083 Lelio R Paula 03/2016 8989 (2^315858+2598)/2 95083 Stefano Morozzi 09/2020 8991 14^82955-43 95078 Lelio R Paula 06/2016 8990 (8*10^95078-269)/9 95078 Robert Price 09/2021 8992 (23*10^95074-101)/3 95075 Robert Price 04/2021 8993 2^315827-933075 95074 Paul Bourdelais 04/2021 8994 (2*10^95072-17)/3 95072 Robert Price 08/2014 8995 (286*10^95059-1)/3 95061 Robert Price 11/2020 8996 (2^315779+1610)/2 95059 Stefano Morozzi 09/2020 8997 2^315775-111546435 95058 Paul Bourdelais 10/2021 8998 21938^21513+21513^21938 95051 Hans Havermann 09/2020 8999 2^315727+65 95044 Lelio R Paula 11/2012 9000 2^315725+1885757 95043 Enzo Doria 03/2017

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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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