## PRP Records

### Probable Primes Top 10000

#### (290751 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 ? 7751 9*10^97247-29 97248 Robert Price 05/2017 7752 24382^9735+9735^24382 97244 Hans Havermann 02/2020 7753 (31*10^97242+41)/9 97243 Robert Price 04/2015 7754 GoldenRatioPrime[97241] 97241 Eric W. Weisstein 06/2009 7755 12^90098-41 97233 Lelio R Paula 07/2016 7756 2^322928-216929 97212 Enzo Doria 05/2014 7757 (16731^23017-1)/16730 97209 Serge Batalov 06/2022 7758 3*10^97205-61 97206 Robert Price 04/2021 7759 (7*2^322896-1)/57 97201 Lelio R Paula 02/2014 7760 (35*10^97194-341)/9 97195 Robert Price 08/2021 7761 (4872^26357-1)/4871 97194 Serge Batalov 06/2022 7762 (2^322897+5)/3146107489 97193 Lelio R Paula 10/2013 7763 (2^322789+2214)/2 97169 Stefano Morozzi 09/2020 7764 2^322725+75761 97150 Enzo Doria 04/2016 7765 (13*2^322686+1)/119 97138 Lelio R Paula 11/2013 7766 (2175^29101-1)/2174 97121 Serge Batalov 06/2022 7767 22402^21639+21639^22402 97118 Hans Havermann 07/2020 7768 23399^14128+14128^23399 97108 Hans Havermann 06/2020 7769 (2892^28057-1)/2891 97108 Serge Batalov 06/2022 7770 (9578^24391-1)/9577 97104 Serge Batalov 06/2022 7771 (2^322525+2606)/2 97090 Stefano Morozzi 09/2020 7772 (9563^24391-1)/9562 97087 Serge Batalov 06/2022 7773 (41*10^97085+373)/9 97086 Robert Price 04/2017 7774 (2^322473+854)/2 97074 Stefano Morozzi 02/2021 7775 2^322413+77 97056 Lelio R Paula 12/2012 7776 2^322406+177 97054 Lelio R Paula 12/2012 7777 (349^38167-1)/348 97050 Serge Batalov 06/2022 7778 (14*10^97044+31)/9 97045 Robert Price 02/2015 7779 2^322302+255255 97023 Lelio R Paula 07/2016 7780 (1302^31147-1)/1301 97008 Serge Batalov 06/2022 7781 2^322196-113093 96991 Enzo Doria 07/2014 7782 (2^322169+2690)/2 96983 Stefano Morozzi 09/2020 7783 (49*10^96980+221)/9 96981 Robert Price 02/2022 7784 9*10^96968-47 96969 Robert Price 11/2021 7785 (5895^25717-1)/5894 96962 Serge Batalov 06/2022 7786 (27473^21841-1)/27472 96946 Serge Batalov 06/2022 7787 23109^15668+15668^23109 96943 Hans Havermann 07/2020 7788 2^322000-1861469 96932 Enzo Doria 03/2016 7789 2^321971-112747 96923 Enzo Doria 06/2014 7790 23754^12023+12023^23754 96917 Hans Havermann 07/2020 7791 11^93062-92 96915 Lelio R Paula 06/2016 7792 (37871^21169-1)/37870 96914 Serge Batalov 06/2022 7793 (2^321922+2214)/2 96908 Stefano Morozzi 09/2020 7794 (2^321900+2086)/2 96902 Stefano Morozzi 09/2020 7795 (11*2^321841-7)/15 96884 Renaud Lifchitz 03/2011 7796 3^203051+34 96880 Lelio R Paula 05/2016 7797 2*10^96867-51 96868 Robert Price 11/2017 7798 (2^321779+2618)/2 96865 Stefano Morozzi 09/2020 7799 (64*10^96863-1)/27 96864 Serge Batalov 05/2010 7800 2^321716-2786939 96847 Enzo Doria 03/2016 7801 22496^20181+20181^22496 96844 Hans Havermann 03/2020 7802 2^321701-113053 96842 Enzo Doria 07/2014 7803 2^321700-28635 96842 Lelio R Paula 06/2016 7804 (5*2^321691-1)/27 96838 Lelio R Paula 02/2014 7805 6*10^96835+13 96836 Robert Price 10/2021 7806 6^124433-124433 96828 Robert Price 01/2014 7807 2^321631+69 96821 Lelio R Paula 12/2012 7808 (27109^21841-1)/27108 96820 Serge Batalov 06/2022 7809 (13*2^321606+1)/119 96813 Lelio R Paula 11/2013 7810 (5052^26141-1)/5051 96809 Serge Batalov 06/2022 7811 (46*10^96798-1)/9 96799 Serge Batalov 10/2014 7812 (59*10^96798+31)/9 96799 Robert Price 09/2015 7813 (2^321536+2062)/2 96792 Stefano Morozzi 09/2020 7814 223319#+231223 96790 Makoto Morimoto 02/2016 7815 2^321519-28635 96787 Lelio R Paula 06/2016 7816 2^321487-1867237 96778 Enzo Doria 03/2016 7817 2^321461-63 96770 Lelio R Paula 12/2012 7818 (16053^23011-1)/16052 96770 Serge Batalov 06/2022 7819 2^321439+123 96763 Lelio R Paula 12/2012 7820 2^321434+709 96762 Lelio R Paula 02/2013 7821 (2^321415+554)/2 96756 Stefano Morozzi 09/2020 7822 14^84413+89 96749 Lelio R Paula 07/2016 7823 (28*10^96743+71)/9 96744 Serge Batalov 12/2008 7824 13^86847+96 96743 Lelio R Paula 06/2016 7825 9*2^321336-7 96733 Lelio R Paula 08/2014 7826 (209*10^96722-17)/3 96724 Robert Price 05/2017 7827 (54163^20431-1)/54162 96710 Serge Batalov 06/2022 7828 2^321237-4615 96702 Yves Minet 05/2019 7829 (27273^21799-1)/27272 96691 Serge Batalov 06/2022 7830 2^321187-1159 96687 Yves Minet 11/2012 7831 2^321182-1850081 96686 Enzo Doria 08/2015 7833 23359^13768+13768^23359 96680 Hans Havermann 06/2020 7832 (65630^20071-1)/65629 96680 Serge Batalov 06/2022 7834 2^321116-112829 96666 Enzo Doria 06/2014 7835 2^321108-109499 96664 Enzo Doria 04/2014 7836 2^321098+2793859 96661 Enzo Doria 03/2016 7837 (2^321100+1170)/2 96661 Stefano Morozzi 09/2020 7838 2^321057+4097 96648 Lelio R Paula 06/2016 7839 (4435*29^66081-4)/7 96640 Curtis Bright 05/2015 7840 22743^17750+17750^22743 96640 Hans Havermann 04/2020 7841 22882^16679+16679^22882 96612 Hans Havermann 02/2020 7842 23452^13163+13163^23452 96608 Hans Havermann 02/2020 7843 (1042^32009-1)/1041 96596 Serge Batalov 06/2022 7844 (85*10^96594-373)/9 96595 Robert Price 05/2021 7845 (2^320863+666)/2 96590 Stefano Morozzi 09/2020 7846 p(19849)#/2-64 96581 Robert Price 04/2017 7847 2^320817+189 96576 Lelio R Paula 12/2012 7848 2^320816-4685 96576 Yves Minet 05/2019 7850 (361*10^96567-163)/9 96569 Robert Price 10/2017 7849 (19*10^96568+137)/3 96569 Robert Price 03/2022 7851 2^320788-110327 96567 Enzo Doria 05/2014 7852 (3065^27697-1)/3064 96561 Serge Batalov 06/2022 7853 2^320764+793 96560 Lelio R Paula 02/2013 7854 (2^320752+1842)/2 96556 Stefano Morozzi 02/2021 7855 (48331^20611-1)/48330 96542 Serge Batalov 06/2022 7856 (50595^20521-1)/50594 96529 Serge Batalov 06/2022 7857 (9179*2^320652-1)/221 96528 Lelio R Paula 05/2015 7858 23288^13947+13947^23288 96517 Hans Havermann 07/2020 7859 2^320616-78795 96516 Lelio R Paula 03/2016 7860 2^320612-461939 96514 Enzo Doria 07/2015 7861 (21245^22303-1)/21244 96507 Serge Batalov 06/2022 7862 10^96504+987654321 96505 Robert Price 12/2019 7863 10^96504+71887 96505 Patrick De Geest 02/2020 7864 22654^18195+18195^22654 96505 Hans Havermann 07/2020 7865 10^96504-139277 96504 Patrick De Geest 02/2020 7866 (218^41263-1)/217 96490 Serge Batalov 06/2022 7867 (47220^20641-1)/47219 96474 Serge Batalov 06/2022 7868 5*2^320431+7 96461 Lelio R Paula 08/2014 7869 19^75431-90 96458 Lelio R Paula 06/2016 7870 (11853^23677-1)/11852 96452 Serge Batalov 06/2022 7871 (2^320386+2814)/2 96446 Stefano Morozzi 02/2021 7872 (2^320370+3)/67 96440 Lelio R Paula 10/2013 7873 3*10^96431-17 96432 Robert Price 03/2021 7874 2^320309+1871477 96423 Enzo Doria 05/2016 7875 (10412^24001-1)/10411 96421 Serge Batalov 06/2022 7876 tau(809^6028) 96410 Nik Lygeros / Olivier Rozier / LR team 10/2013 7877 (29*10^96407-23)/3 96408 Robert Price 03/2022 7878 (21*2^320252-1)/1895 96404 Lelio R Paula 02/2014 7879 2^320232-173 96400 Lelio R Paula 12/2012 7880 175^42975-2 96395 Lelio R Paula 10/2017 7881 (2^320170+2718)/2 96381 Stefano Morozzi 09/2020 7882 10^96377+199911 96378 Patrick De Geest 12/2016 7883 10^96377-20001 96377 Robert Price 11/2016 7884 (18079^22639-1)/18078 96374 Serge Batalov 06/2022 7886 2^320124-2790449 96367 Enzo Doria 03/2016 7885 10^96366+19197 96367 Patrick De Geest 08/2021 7888 10^96366-10000000001 96366 Robert Price 04/2021 7887 10^96366-287367 96366 Patrick De Geest 08/2021 7889 (26351^21799-1)/26350 96365 Serge Batalov 06/2022 7890 22488^19255+19255^22488 96351 Hans Havermann 11/2019 7891 23248^13939+13939^23248 96346 Hans Havermann 11/2019 7892 (5928^25537-1)/5927 96345 Serge Batalov 06/2022 7894 2^320043-108775 96343 Enzo Doria 04/2014 7893 24989^7168+7168^24989 96343 Hans Havermann 11/2019 7895 10^96338+424939 96339 Patrick De Geest 03/2016 7896 10^96338-9281 96338 Robert Price 09/2015 7897 (8527^24509-1)/8526 96336 Serge Batalov 06/2022 7898 (3*2^320008+1)/7 96332 Lelio R Paula 09/2013 7899 (2444^28433-1)/2443 96331 Serge Batalov 06/2022 7900 (48690^20551-1)/48689 96327 Serge Batalov 06/2022 7901 (61935^20101-1)/61934 96318 Serge Batalov 06/2022 7902 25699^5596+5596^25699 96317 Hans Havermann 07/2020 7903 (11*10^96298+529)/9 96299 Robert Price 09/2021 7905 26502^4297+4297^26502 96287 Hans Havermann 07/2020 7904 (54180^20341-1)/54179 96287 Serge Batalov 06/2022 7906 2^319838+4257 96281 Lelio R Paula 03/2016 7907 2^319830-16995 96279 Lelio R Paula 03/2016 7908 6^123713+143 96268 Lelio R Paula 05/2016 7909 (28*10^96265-97)/3 96266 Robert Price 07/2016 7910 (3799^26893-1)/3798 96265 Serge Batalov 06/2022 7912 103^47825-102 96264 Norbert Schneider 10/2016 7911 (54041^20341-1)/54040 96264 Serge Batalov 06/2022 7913 (2^319777+2082)/2 96263 Stefano Morozzi 09/2020 7914 (2^319771+3686)/2 96261 Stefano Morozzi 09/2020 7915 2^319713-81 96244 Lelio R Paula 11/2012 7916 (55459*2^319706+1)/20167 96242 Lelio R Paula 07/2014 7917 22834^16393+16393^22834 96238 Hans Havermann 05/2020 7918 8*10^96236+27 96237 Robert Price 09/2021 7919 12^89153-43 96213 Lelio R Paula 06/2016 7920 (25048^21871-1)/25047 96202 Serge Batalov 06/2022 7922 (2*10^96195-59)/3 96195 Robert Price 05/2017 7921 9*10^96194-77 96195 Robert Price 08/2020 7923 2^319545+147 96193 Lelio R Paula 11/2012 7924 23357^13128+13128^23357 96189 Hans Havermann 02/2020 7925 (19838^22381-1)/19837 96179 Serge Batalov 06/2022 7926 (221^41023-1)/220 96172 Serge Batalov 06/2022 7927 25952^5073+5073^25952 96160 Hans Havermann 12/2019 7928 (50891^20431-1)/50890 96157 Serge Batalov 06/2022 7929 (50^56597+1)/51 96155 Robert Price 03/2014 7930 22313^20374+20374^22313 96149 Hans Havermann 12/2019 7931 22279^20668+20668^22279 96141 Hans Havermann 11/2019 7932 (41*10^96137-59)/9 96138 Robert Price 10/2017 7933 2^319353-110343 96135 Enzo Doria 05/2014 7934 11^92309-42 96130 Lelio R Paula 05/2016 7935 (21675^22171-1)/21674 96129 Serge Batalov 06/2022 7936 14^83869-13^83869 96125 Jean-Louis Charton 01/2009 7937 (7*10^96112+143)/3 96113 Robert Price 04/2016 7938 26731^3940+3940^26731 96112 Hans Havermann 07/2020 7939 22640^17583+17583^22640 96109 Hans Havermann 07/2020 7940 (19178^22441-1)/19177 96107 Serge Batalov 06/2022 7941 2^319237+65835 96100 Lelio R Paula 03/2016 7942 2^319194-1841 96087 Yves Minet 03/2013 7943 23949^10280+10280^23949 96084 Hans Havermann 07/2020 7944 (1927^29251-1)/1926 96083 Serge Batalov 06/2022 7945 20^73847-31 96078 Lelio R Paula 05/2016 7946 (60229^20101-1)/60228 96075 Serge Batalov 06/2022 7947 (28044^21601-1)/28043 96074 Serge Batalov 06/2022 7948 50^56543-49 96065 Norbert Schneider 09/2018 7949 2^319107-109555 96061 Enzo Doria 04/2014 7950 (3*2^319114-1)/2627 96060 Lelio R Paula 02/2014 7951 2^319098-112157 96059 Enzo Doria 06/2014 7952 15^81673+94 96055 Lelio R Paula 07/2016 7953 (85761^19471-1)/85760 96052 Serge Batalov 06/2022 7954 2^319074+1871749 96051 Enzo Doria 05/2016 7955 25670^5517+5517^25670 96050 Hans Havermann 06/2020 7956 6*10^96037+19 96038 Robert Price 11/2021 7957 2^319007-112111 96031 Enzo Doria 06/2014 7958 (57987^20161-1)/57986 96029 Serge Batalov 06/2022 7960 2^318946-1421 96013 Yves Minet 01/2013 7959 (68310^19861-1)/68309 96013 Serge Batalov 06/2022 7961 (20294^22291-1)/20293 96012 Serge Batalov 06/2022 7962 (304^38669-1)/303 96008 Serge Batalov 06/2022 7963 (1840^29401-1)/1839 95986 Serge Batalov 06/2022 7964 22830^16003+16003^22830 95982 Hans Havermann 02/2020 7965 2^318834-110411 95979 Enzo Doria 05/2014 7966 2^318831-1965 95978 Lelio R Paula 03/2016 7967 (5*10^95976+7)/3 95977 Erik Branger 03/2014 7968 (12797^23369-1)/12796 95975 Serge Batalov 06/2022 7969 (10534^23857-1)/10533 95963 Serge Batalov 06/2022 7970 22871^15696+15696^22871 95962 Hans Havermann 01/2020 7971 (2^318760+858)/2 95957 Stefano Morozzi 02/2021 7972 23167^13860+13860^23167 95953 Hans Havermann 01/2020 7973 (823^32911-1)/822 95946 Serge Batalov 06/2022 7975 5*3^201089-8 95945 Lelio R Paula 08/2014 7974 (81783^19531-1)/81782 95945 Serge Batalov 06/2022 7976 2^318711-139 95942 Lelio R Paula 11/2012 7977 2^318635-1167 95919 Lelio R Paula 03/2016 7978 15^81555+16 95917 Lelio R Paula 07/2016 7979 (37*10^95895+377)/9 95896 Robert Price 10/2017 7980 (22699*2^318527+1)/21 95890 Lelio R Paula 07/2014 7981 2^318496-97305 95877 Lelio R Paula 03/2016 7982 22129^21496+21496^22129 95871 Hans Havermann 07/2020 7984 2^318466+15015 95868 Lelio R Paula 03/2016 7983 24847^7216+7216^24847 95868 Hans Havermann 07/2020 7985 23706^11065+11065^23706 95866 Hans Havermann 07/2020 7986 (2863^27733-1)/2862 95865 Serge Batalov 06/2022 7987 6^123187-173129 95859 Mike Oakes 04/2011 7988 2^318423-487 95855 Yves Minet 03/2012 7989 (2^318359+678)/2 95836 Stefano Morozzi 09/2020 7990 (10223*2^318350+1)/1563 95834 Lelio R Paula 07/2014 7991 (8060^24533-1)/8059 95831 Serge Batalov 06/2022 7992 (9853^23993-1)/9852 95814 Serge Batalov 06/2022 7994 (2^318267+2550)/2 95808 Stefano Morozzi 09/2020 7993 (5048^25873-1)/5047 95808 Serge Batalov 06/2022 7996 4*10^95799+13 95800 Robert Price 02/2021 7995 (65533^19891-1)/65532 95800 Serge Batalov 06/2022 7997 45369!2+1024 95787 Robert Price 02/2015 7998 3^200758-86 95786 Lelio R Paula 05/2016 7999 (2^318271+1)/(3*46031404238891*654090604244843) 95781 Gord Palameta 12/2018 8000 (2^318171+2030)/2 95779 Stefano Morozzi 09/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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