## PRP Records

### Probable Primes Top 10000

#### (294613 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 13^90809-96 101157 Lelio R Paula 10/2016 8752 26199^7258+7258^26199 101150 Hans Havermann 11/2018 8753 19^79098-30 101147 Lelio R Paula 10/2016 8754 19^79095+88 101144 Lelio R Paula 10/2016 8755 (30826*34^66040-59)/11 101143 Eric Chen 03/2023 8756 12401^24702-24702^12401 101117 Norbert Schneider 07/2022 8757 15^85976+32 101116 Lelio R Paula 10/2016 8758 2^335872-2776215 101108 Tony Prest / Never Odd Or Even 01/2019 8759 (3^211950+7)/28854513015920697088 101107 Lelio R Paula 11/2013 8760 (4^167933+17)/3 101106 Robert Price 02/2017 8761 2^335858+153 101104 Lelio R Paula 10/2009 8762 (2^335872-2776871)/5/5/479 101104 Tony Prest / Never Odd Or Even 01/2019 8763 (2^335872-2758787)/23/31/20809 101101 Tony Prest / Never Odd Or Even 01/2019 8764 (2^335839+2114)/2 101098 Stefano Morozzi 09/2020 8765 (2^335872-2795083)/3/3/113/283/148367 101097 Tony Prest / Never Odd Or Even 01/2019 8767 6^129918-35 101096 Lelio R Paula 10/2016 8766 (2*10^101096-107)/3 101096 Robert Price 11/2020 8768 3^211885-70 101095 Lelio R Paula 09/2016 8769 (29*2^335835-1)/550599 101093 Lelio R Paula 03/2014 8770 (2^335872-2794771)/3/5/5/61/232312440293 101093 Tony Prest / Never Odd Or Even 01/2019 8771 2^335818-20033 101092 Enzo Doria 06/2013 8772 2^335813-110083 101090 Enzo Doria 04/2014 8773 2^335804+2155 101088 Lelio R Paula 09/2016 8774 (2^335872-2756679)/7/7/7/13/31/4987/437653/8734021 101087 Tony Prest / Never Odd Or Even 01/2019 8775 2^335784-16145 101082 Enzo Doria 04/2013 8776 11^97051+62 101069 Lelio R Paula 10/2016 8777 3*10^101065+11 101066 Robert Price 07/2018 8778 27820^4293+4293^27820 101064 Hans Havermann 10/2018 8779 (2^335714+3750)/2 101060 Stefano Morozzi 01/2021 8780 (2^335690+1038)/2 101053 Stefano Morozzi 09/2020 8781 (2^335691-3)/26515 101049 Lelio R Paula 12/2013 8782 2^335658-94395 101044 Lelio R Paula 09/2016 8783 24514^13215+13215^24514 101024 Hans Havermann 11/2018 8784 2^335586+169 101022 Lelio R Paula 10/2009 8785 (56^57787-1)/55 101021 Paul Bourdelais 08/2017 8786 (2^335562+1258)/2 101014 Stefano Morozzi 09/2020 8787 2^335541+4849845 101008 Paul Bourdelais 04/2022 8788 (38*10^100999+169)/9 101000 Robert Price 11/2021 8789 (19*10^100997+737)/9 100998 Robert Price 07/2018 8790 47599!2+1024 100991 Robert Price 02/2015 8791 2^335468-18629 100986 Enzo Doria 05/2013 8792 2^335454-20961 100982 Enzo Doria 06/2013 8793 (2^335454+3258)/2 100982 Stefano Morozzi 02/2021 8794 10^100978+61 100979 Lelio R Paula 09/2016 8795 10^100978-156437 100978 Patrick De Geest 11/2016 8796 (2^335422+3114)/2 100972 Stefano Morozzi 09/2020 8797 (35*10^100970-89)/9 100971 Robert Price 02/2022 8798 (15*2^335417+1)/481 100970 Lelio R Paula 12/2013 8799 2^335403-1859167 100967 Enzo Doria 03/2016 8800 23599^18976+18976^23599 100962 Hans Havermann 10/2018 8801 6*10^100958+43 100959 Robert Price 07/2020 8802 9*2^335364-5 100956 Lelio R Paula 08/2014 8803 (7998^25867-1)/7997 100955 Serge Batalov 06/2022 8804 2^335349+72287 100951 Enzo Doria 04/2016 8805 2^335329+16095 100945 Lelio R Paula 09/2016 8806 232823#+233663 100937 Makoto Morimoto 10/2017 8807 (232823#+10141)/(10141*1674461) 100927 Makoto Morimoto 06/2019 8808 2^335237-20893 100917 Enzo Doria 06/2013 8809 2^335222-19337 100912 Enzo Doria 05/2013 8810 2^335222-109985 100912 Enzo Doria 04/2014 8811 2^335182-17237 100900 Enzo Doria 05/2013 8812 (2^335107+1634)/2 100877 Stefano Morozzi 09/2020 8813 2^335043-16737 100858 Enzo Doria 05/2013 8814 (21181*2^335049+1)/1343811 100858 Lelio R Paula 07/2014 8815 2^335038-20633 100857 Enzo Doria 06/2013 8816 2^335031+1873373 100855 Enzo Doria 06/2016 8817 23489^19650+19650^23489 100847 Hans Havermann 10/2018 8818 3^211354-8816 100842 Enzo Doria 05/2014 8819 2^334984-112757 100841 Enzo Doria 06/2014 8820 (746*10^100827+1)/9 100829 Robert Price 03/2020 8821 29451^2648+2648^29451 100809 Hans Havermann 09/2018 8822 25583^8716+8716^25583 100806 Hans Havermann 08/2018 8824 2^334857+48527 100803 Lelio R Paula 08/2011 8823 12^93406+29 100803 Lelio R Paula 10/2016 8825 28780^3179+3179^28780 100796 Hans Havermann 09/2018 8826 (5*2^334825+1)/47 100792 Lelio R Paula 12/2013 8827 (328^40063-1)/327 100791 Serge Batalov 06/2022 8828 2^334809-13 100788 Lelio R Paula 04/2011 8829 (3552^28387-1)/3551 100784 Serge Batalov 06/2022 8830 (82*10^100780-1)/9 100781 Robert Price 12/2014 8831 31395^1622+1622^31395 100780 Hans Havermann 09/2018 8832 (2^334779+47)/5 100778 Lelio R Paula 12/2013 8833 2^334751+2049 100771 Lelio R Paula 09/2016 8834 13^90443-98 100749 Lelio R Paula 10/2016 8835 (2^334674+3190)/2 100747 Stefano Morozzi 09/2020 8836 (2^334651+1050)/2 100740 Stefano Morozzi 09/2020 8837 (7*10^100737+71)/3 100738 Robert Price 05/2018 8838 (24737*2^334628+1)/3 100737 Lelio R Paula 07/2014 8839 15^85639-28 100720 Lelio R Paula 10/2016 8840 27068^5259+5259^27068 100718 Hans Havermann 08/2018 8841 2^334562+577294575 100711 Lelio R Paula 09/2016 8842 4*3^211077-5 100710 Lelio R Paula 08/2014 8843 2^334524+145 100702 Lelio R Paula 07/2009 8844 (2^334451+714)/2 100680 Stefano Morozzi 09/2020 8845 27648^4375+4375^27648 100666 Hans Havermann 09/2018 8846 (1017*2^334391-1)/3535 100662 Lelio R Paula 05/2015 8847 (2^334309+3122)/2 100637 Stefano Morozzi 09/2020 8848 2^334294-113111 100633 Enzo Doria 07/2014 8849 25581^8582+8582^25581 100626 Hans Havermann 08/2018 8851 6^129308-17723 100622 Enzo Doria 03/2013 8850 (19*10^100627+287)/9/292157 100622 Alfred Reich 11/2022 8852 6^129305+95 100619 Lelio R Paula 10/2016 8853 2^334244-1167 100618 Lelio R Paula 09/2016 8854 (2^334233+3066)/2 100614 Stefano Morozzi 09/2020 8855 (76*10^100611+77)/9 100612 Robert Price 10/2019 8856 7*10^100606-93 100607 Robert Price 08/2020 8857 (26*10^100566+49)/3 100567 Robert Price 08/2019 8858 (21*2^334050+1)/935 100558 Lelio R Paula 12/2013 8859 24885^10984+10984^24885 100555 Hans Havermann 07/2018 8860 (1351^32119-1)/1350 100551 Serge Batalov 06/2022 8861 (78557*2^334018+1)/4326021 100548 Lelio R Paula 07/2014 8862 (35*10^100542+1)/9 100543 Serge Batalov 11/2010 8863 23578^18367+18367^23578 100538 Hans Havermann 07/2018 8864 13^90251+24 100535 Lelio R Paula 10/2016 8865 2^333963+789 100533 Lelio R Paula 08/2011 8866 2^333919-1840087 100520 Enzo Doria 06/2015 8867 (2^333916+1698)/2 100519 Stefano Morozzi 09/2020 8868 2^333911+72623 100518 Enzo Doria 04/2016 8869 24605^12168+12168^24605 100517 Hans Havermann 08/2018 8870 66*10^100502+7 100504 Robert Price 07/2020 8871 18^80064-67 100503 Lelio R Paula 10/2016 8872 (13*10^100487+137)/3 100488 Robert Price 06/2021 8873 5^143742-48 100472 Lelio R Paula 10/2016 8874 24095^14784+14784^24095 100472 Hans Havermann 08/2018 8875 2^333757-112123 100471 Enzo Doria 06/2014 8876 (7953^25759-1)/7952 100470 Serge Batalov 06/2022 8877 7*10^100457-57 100458 Robert Price 06/2020 8878 27358^4693+4693^27358 100444 Hans Havermann 07/2018 8879 8*10^100439-51 100440 Robert Price 08/2019 8880 2^333603-108861 100425 Enzo Doria 03/2014 8881 9*7^118818-2 100414 Lelio R Paula 11/2014 8882 2^333546-17097 100408 Enzo Doria 05/2013 8883 (19*10^100403+287)/9/3 100403 Alfred Reich 11/2022 8884 17^81597+72 100401 Lelio R Paula 10/2016 8885 (3613^28219-1)/3612 100396 Serge Batalov 06/2022 8886 p(20559)#/2+8 100384 Robert Price 01/2017 8887 11^96390-24 100380 Lelio R Paula 10/2016 8888 (2^333385+2730)/2 100359 Stefano Morozzi 09/2020 8889 4832563059*2^333333+30029 100353 Donovan Johnson 01/2008 8890 23565^18136+18136^23565 100353 Hans Havermann 07/2018 8891 2^333354+763 100350 Lelio R Paula 08/2011 8892 (1608961*2^333333+1)/3 100349 Alex_soldier 09/2022 8893 (424517*2^333333+1)/5 100349 Alex_soldier 09/2022 8894 (887087*2^333333+1)/5 100349 Alex_soldier 09/2022 8895 (1159703*2^333333+1)/7 100349 Alex_soldier 09/2022 8896 (25*10^100343-67)/3 100344 Robert Price 06/2019 8897 2^333289-109483 100330 Enzo Doria 04/2014 8898 2^333240-2790209 100316 Enzo Doria 03/2016 8899 23601^17798+17798^23601 100314 Hans Havermann 05/2018 8901 (2^333227-2^166614+1)/5 100311 11/2006 8900 2^333225+719 100311 Lelio R Paula 08/2011 8902 2^333221-2785333 100310 Enzo Doria 10/2015 8903 76^53332-75 100308 Norbert Schneider 02/2015 8904 (29*10^100302+583)/9 100303 Robert Price 06/2021 8905 6^128892-17573 100298 Enzo Doria 03/2013 8906 (47*10^100283-119)/9 100284 Robert Price 05/2019 8907 2^333105-113215 100275 Enzo Doria 07/2014 8908 (31*2^333102+1)/2375 100272 Lelio R Paula 11/2013 8909 4*10^100257-83 100258 Robert Price 10/2018 8910 17^81476-74 100253 Lelio R Paula 10/2016 8911 23392^19207+19207^23392 100199 Hans Havermann 06/2018 8912 (2^332830+750)/2 100192 Stefano Morozzi 09/2020 8913 (206*10^100189-17)/9 100191 Robert Price 01/2020 8914 17^81417-16 100180 Theodore Burton 11/2005 8915 (2^332773+590)/2 100175 Stefano Morozzi 09/2020 8916 2*23^73562+215 100172 Eric Chen 08/2023 8917 2^332739-113215 100165 Enzo Doria 07/2014 8918 2^332730-1865621 100162 Enzo Doria 03/2016 8919 91^51127-2 100160 Lelio R Paula 09/2013 8920 15^85159-32 100155 Lelio R Paula 10/2016 8921 6^128661+97 100118 Lelio R Paula 10/2016 8922 19^78285+40 100108 Lelio R Paula 07/2016 8923 6^128640+5 100102 Lelio R Paula 11/2014 8924 10^100095+89973 100096 Patrick De Geest 10/2022 8925 10^100095-400001 100095 Robert Price 09/2021 8926 10^100095-203693 100095 Patrick De Geest 10/2022 8927 22779^22970-22970^22779 100093 Norbert Schneider 08/2020 8928 (2^332468+3130)/2 100083 Stefano Morozzi 09/2020 8929 (14*10^100075+61)/3 100076 Robert Price 12/2018 8930 (2^332435+3098)/2 100073 Stefano Morozzi 09/2020 8931 28562^3189+3189^28562 100072 Hans Havermann 05/2018 8932 6^128565-127 100044 Lelio R Paula 08/2016 8933 (2^332317+2106)/2 100038 Stefano Morozzi 09/2020 8935 2^332309-133 100035 Lelio R Paula 02/2011 8936 2^332307+731 100035 Lelio R Paula 07/2011 8934 937^33662-33662^937 100035 Norbert Schneider 05/2023 8937 2^332301+12927 100033 Lelio R Paula 04/2013 8938 23406^18781+18781^23406 100031 Hans Havermann 04/2018 8939 2^332277-4573 100026 Yves Minet 03/2019 8940 12^92684-13 100023 Lelio R Paula 07/2016 8941 70^54207-54207^70 100018 Norbert Schneider 04/2023 8942 78557*2^332193+55669 100005 Jorge Menendez 04/2019 8943 78557*2^332192+72689 100005 Jorge Menendez 04/2019 8944 10^100003+45799 100004 Stefano Morozzi 04/2019 8945 10^100003+155461 100004 Stefano Morozzi 04/2019 8946 10^100003+211389 100004 Stefano Morozzi 04/2019 8947 10^100003+381027 100004 Stefano Morozzi 04/2019 8948 10^100003+540703 100004 Stefano Morozzi 04/2019 8949 10^100003+823977 100004 Stefano Morozzi 04/2019 8961 10^100002+236023 100003 Stefano Morozzi 05/2018 8962 10^100002+433741 100003 Stefano Morozzi 05/2018 8950 2^332202+104659 100003 Stefano Morozzi 04/2019 8951 2^332202+857539 100003 Stefano Morozzi 04/2019 8952 2^332202+181773 100003 Stefano Morozzi 04/2019 8953 2^332202+687543 100003 Stefano Morozzi 04/2019 8954 2^332202+941595 100003 Stefano Morozzi 04/2019 8955 2^332202+445813 100003 Stefano Morozzi 04/2019 8956 2^332202+1599727 100003 Stefano Morozzi 04/2019 8957 2^332202+1389567 100003 Stefano Morozzi 04/2019 8958 2^332202+1206315 100003 Stefano Morozzi 04/2019 8959 2^332202+1958647 100003 Stefano Morozzi 04/2019 8960 10^100003-562857 100003 Patrick De Geest 07/2019 8963 (10^100002-1)/9-10^33441 100002 Akihiko Yoshida 03/2018 8964 (10^100002-1)/9-10^44692 100002 Akihiko Yoshida 03/2018 8965 10^100002-249519 100002 Patrick De Geest 07/2018 8966 10^100001+314199 100002 Patrick De Geest 07/2018 8986 10^100000+3938473 100001 Robert Price 05/2015 8987 10^100000+3979761 100001 Robert Price 05/2015 8988 10^100000+4293973 100001 Robert Price 09/2015 8983 10^100000+4858267 100001 Robert Price 12/2015 8984 10^100000+5113299 100001 Robert Price 02/2016 8985 10^100000+5169411 100001 Robert Price 02/2016 8975 10^100000+5354043 100001 Robert Price 05/2016 8976 10^100000+5717979 100001 Robert Price 05/2016 8977 10^100000+6080631 100001 Robert Price 07/2016 8978 10^100000+6308469 100001 Robert Price 07/2016 8979 10^100000+6512023 100001 Robert Price 08/2016 8980 10^100000+6596557 100001 Robert Price 08/2016 8981 10^100000+7115409 100001 Robert Price 10/2016 8982 10^100000+7235803 100001 Robert Price 10/2016 8992 10^100000+7867333 100001 Robert Price 12/2016 8993 10^100000+8743093 100001 Robert Price 02/2017 8994 10^100000+8955391 100001 Robert Price 03/2017 8995 10^100000+9180019 100001 Robert Price 03/2017 8996 10^100000+9225987 100001 Robert Price 04/2017 8997 10^100000+9265587 100001 Robert Price 04/2017 8998 10^100000+9287049 100001 Robert Price 04/2017 8999 10^100000+9425053 100001 Robert Price 05/2017 9000 10^100000+9450769 100001 Robert Price 05/2017 8967 10^100000+11187931 100001 Robert Price 03/2018 8968 10^100000+11264721 100001 Robert Price 04/2018 8969 10^100000+11477661 100001 Robert Price 05/2018 8970 10^100000+11644653 100001 Robert Price 07/2018 8971 10^100001-431439 100001 Patrick De Geest 07/2018 8972 10^100000+11769399 100001 Robert Price 08/2018 8973 10^100000+11848159 100001 Robert Price 08/2018 8974 10^100000+11863467 100001 Robert Price 08/2018 8989 10^100000+11992051 100001 Robert Price 09/2018 8990 2^332196-1-2*29696 100001 Matt Stath 11/2018 8991 10^100000+12363957 100001 Robert Price 11/2018

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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