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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
8751 | 10^90983+1393 | 90984 | Patrick De Geest | 01/2019 |
8752 | 11*10^90982+9 | 90984 | Robert Price | 08/2020 |
8753 | 10^90983-562383 | 90983 | Patrick De Geest | 07/2019 |
8754 | (311^36497-1)/310 | 90976 | Eric Chen | 09/2017 |
8755 | (2^302210+1014)/2 | 90974 | Stefano Morozzi | 09/2020 |
8756 | (3^190668+2)/89 | 90970 | Lelio R Paula | 04/2013 |
8757 | 2^302188+90195 | 90968 | Lelio R Paula | 02/2016 |
8758 | (53*10^90965-71)/9 | 90966 | Robert Price | 09/2015 |
8759 | 10^90965+573987 | 90966 | Patrick De Geest | 07/2019 |
8760 | 10^90965-6833 | 90965 | Patrick De Geest | 01/2019 |
8761 | 10^90964+48789 | 90965 | Patrick De Geest | 07/2019 |
8762 | 10^90964-52103 | 90964 | Patrick De Geest | 07/2019 |
8763 | 10^90963+191889 | 90964 | Patrick De Geest | 07/2019 |
8764 | 10^90963-3659 | 90963 | Patrick De Geest | 01/2019 |
8765 | 10^90962+7657 | 90963 | Patrick De Geest | 01/2019 |
8766 | 10^90962-215633 | 90962 | Patrick De Geest | 07/2019 |
8767 | 10^90961+67471 | 90962 | Patrick De Geest | 07/2019 |
8768 | 10^90961-211043 | 90961 | Patrick De Geest | 07/2019 |
8769 | 10^90960+1072117 | 90961 | Patrick De Geest | 07/2019 |
8770 | 10^90959+8791 | 90960 | Patrick De Geest | 01/2019 |
8771 | 10^90960-610659 | 90960 | Patrick De Geest | 07/2019 |
8772 | 10^90959-275213 | 90959 | Patrick De Geest | 07/2019 |
8773 | (2^302129+3110)/2 | 90950 | Stefano Morozzi | 09/2020 |
8775 | 10^90948+9867 | 90949 | Patrick De Geest | 01/2019 |
8774 | 21665^15774+15774^21665 | 90949 | Hans Havermann | 04/2020 |
8776 | 10^90948-109239 | 90948 | Patrick De Geest | 07/2019 |
8777 | 2^302113+74105 | 90946 | Enzo Doria | 04/2016 |
8778 | 2^302102-6555 | 90942 | Lelio R Paula | 02/2016 |
8779 | 10^90930+95223 | 90931 | Patrick De Geest | 07/2019 |
8780 | 10^90930-3623 | 90930 | Patrick De Geest | 01/2019 |
8781 | 156*(10^(4*22731)-1)/101-1 | 90925 | Robert Price | 05/2014 |
8782 | 3^190568+38 | 90925 | Lelio R Paula | 04/2016 |
8783 | 10^90917+179863 | 90918 | Patrick De Geest | 07/2019 |
8784 | 10^90917-6693 | 90917 | Patrick De Geest | 01/2019 |
8785 | 2^302009-16449 | 90914 | Enzo Doria | 04/2013 |
8786 | 10^90908+3181 | 90909 | Patrick De Geest | 01/2019 |
8787 | 10^90908-139511 | 90908 | Patrick De Geest | 07/2019 |
8788 | 10^90904+106947 | 90905 | Patrick De Geest | 07/2019 |
8789 | 10^90904-5169 | 90904 | Patrick De Geest | 01/2019 |
8790 | 10^90903+120963 | 90904 | Patrick De Geest | 07/2019 |
8791 | 10^90902+2613 | 90903 | Patrick De Geest | 01/2019 |
8792 | 10^90903-190737 | 90903 | Patrick De Geest | 07/2019 |
8793 | 25174^4083+4083^25174 | 90903 | Hans Havermann | 08/2020 |
8794 | 10^90902-952329 | 90902 | Patrick De Geest | 07/2019 |
8795 | (17*2^301951-1)/165 | 90896 | Lelio R Paula | 02/2014 |
8796 | 3^190497+74 | 90891 | Lelio R Paula | 04/2016 |
8797 | (24737*2^301896+1)/399 | 90882 | Lelio R Paula | 06/2014 |
8798 | 10^90880+5707 | 90881 | Patrick De Geest | 01/2019 |
8799 | 10^90880-152993 | 90880 | Patrick De Geest | 07/2019 |
8800 | 18^72397+89 | 90878 | Lelio R Paula | 06/2016 |
8801 | (2^301876+762)/2 | 90874 | Stefano Morozzi | 09/2020 |
8802 | 134^42719-133 | 90868 | Norbert Schneider | 03/2019 |
8803 | 6^116769-47 | 90864 | Lelio R Paula | 05/2016 |
8804 | 10^90858+233433 | 90859 | Patrick De Geest | 07/2019 |
8805 | 10^90858-8301 | 90858 | Patrick De Geest | 01/2019 |
8806 | 24298^5483+5483^24298 | 90851 | Hans Havermann | 08/2020 |
8807 | 10^90849+40141 | 90850 | Patrick De Geest | 07/2019 |
8808 | 10^90849-4721 | 90849 | Patrick De Geest | 01/2019 |
8809 | 2^301712-465 | 90825 | Lelio R Paula | 02/2016 |
8810 | 2^301693-69 | 90819 | Lelio R Paula | 11/2012 |
8811 | 2^301683-301683^2 | 90816 | Henri Lifchitz | 05/2005 |
8812 | 10^90807+7279 | 90808 | Patrick De Geest | 01/2019 |
8813 | 10^90807-162263 | 90807 | Patrick De Geest | 07/2019 |
8814 | 6*10^90803+79 | 90804 | Robert Price | 09/2020 |
8815 | 10^90800-6453 | 90800 | Patrick De Geest | 11/2018 |
8816 | 11^87187-1710 | 90796 | Enzo Doria | 12/2012 |
8817 | 5*10^90793+21 | 90794 | Robert Price | 01/2017 |
8818 | (22*10^90792-13)/9 | 90793 | Robert Price | 03/2015 |
8819 | 2^301591-1615 | 90788 | Lelio R Paula | 02/2016 |
8820 | (52^52901+1)/53 | 90777 | Paul Bourdelais | 08/2017 |
8821 | 2^301546-109037 | 90775 | Enzo Doria | 04/2014 |
8822 | 10^90772+4029 | 90773 | Patrick De Geest | 11/2018 |
8823 | 10^90772-36627 | 90772 | Patrick De Geest | 07/2019 |
8824 | 10^90771+67737 | 90772 | Patrick De Geest | 07/2019 |
8825 | 10^90771-441003 | 90771 | Patrick De Geest | 07/2019 |
8826 | 10^90770+28941 | 90771 | Patrick De Geest | 07/2019 |
8827 | 10^90770-431 | 90770 | Patrick De Geest | 11/2018 |
8828 | 14^79195-3 | 90768 | Lelio R Paula | 06/2016 |
8829 | 10^90766+877 | 90767 | Patrick De Geest | 11/2018 |
8830 | 2^301517-1861693 | 90766 | Enzo Doria | 11/2015 |
8831 | 10^90766-109241 | 90766 | Patrick De Geest | 07/2019 |
8832 | 10^90765+485361 | 90766 | Patrick De Geest | 07/2019 |
8833 | 10^90765-4797 | 90765 | Patrick De Geest | 11/2018 |
8834 | 10^90757+7573 | 90758 | Patrick De Geest | 11/2018 |
8835 | 10^90757-554979 | 90757 | Patrick De Geest | 07/2019 |
8836 | 10^90756+438109 | 90757 | Patrick De Geest | 07/2019 |
8837 | 10^90756-8727 | 90756 | Patrick De Geest | 11/2018 |
8838 | 10^90749+823 | 90750 | Patrick De Geest | 11/2018 |
8841 | 2^301460-173 | 90749 | Lelio R Paula | 11/2012 |
8839 | 10^90748+4213 | 90749 | Patrick De Geest | 11/2018 |
8840 | 10^90749-130413 | 90749 | Patrick De Geest | 07/2019 |
8842 | 10^90748-75411 | 90748 | Patrick De Geest | 07/2019 |
8843 | 10^90747+438471 | 90748 | Patrick De Geest | 07/2019 |
8844 | 10^90747-9279 | 90747 | Patrick De Geest | 11/2018 |
8845 | (85*10^90745-103)/9 | 90746 | Robert Price | 10/2017 |
8846 | (2^301439+1206)/2 | 90742 | Stefano Morozzi | 09/2020 |
8847 | 10^90726+4077 | 90727 | Patrick De Geest | 11/2018 |
8848 | 10^90726-504951 | 90726 | Patrick De Geest | 07/2019 |
8850 | 10^90721+181 | 90722 | Patrick De Geest | 11/2018 |
8849 | (2^301372+2722)/2 | 90722 | Stefano Morozzi | 09/2020 |
8851 | 10^90721-177149 | 90721 | Patrick De Geest | 07/2019 |
8852 | (2^301317+1146)/2 | 90706 | Stefano Morozzi | 09/2020 |
8853 | 2^301312-89 | 90704 | Lelio R Paula | 11/2012 |
8854 | 10^90696+6349 | 90697 | Patrick De Geest | 11/2018 |
8855 | 2^301285-129 | 90696 | Lelio R Paula | 11/2012 |
8856 | 10^90696-635049 | 90696 | Patrick De Geest | 07/2019 |
8857 | 2^301282-109991 | 90695 | Enzo Doria | 04/2014 |
8858 | 10^90690+8877 | 90691 | Patrick De Geest | 11/2018 |
8859 | 10^90690-227433 | 90690 | Patrick De Geest | 07/2019 |
8860 | 10^90683+61411 | 90684 | Patrick De Geest | 07/2019 |
8861 | (2^301244+1738)/2 | 90684 | Stefano Morozzi | 09/2020 |
8862 | 10^90683-2577 | 90683 | Patrick De Geest | 11/2018 |
8863 | 2^301228-1854269 | 90679 | Enzo Doria | 09/2015 |
8864 | 10^90674-5000001 | 90674 | Robert Price | 12/2021 |
8866 | (151*10^90669-1)/3 | 90671 | Robert Price | 04/2017 |
8865 | (2^301201+2046)/2 | 90671 | Stefano Morozzi | 09/2020 |
8868 | (32*10^90669+13)/9 | 90670 | Robert Price | 04/2015 |
8867 | 10^90669+9793 | 90670 | Patrick De Geest | 11/2018 |
8869 | 10^90669-223931 | 90669 | Patrick De Geest | 07/2019 |
8870 | (2^301191+2510)/2 | 90668 | Stefano Morozzi | 09/2020 |
8871 | 5*10^90666-63 | 90667 | Robert Price | 04/2021 |
8872 | 10^90665+10989 | 90666 | Patrick De Geest | 07/2019 |
8873 | 10^90665-3087 | 90665 | Patrick De Geest | 11/2018 |
8874 | 2^301177-227713 | 90664 | Harrison Mesh | 06/2022 |
8875 | 10^90662+89637 | 90663 | Patrick De Geest | 07/2019 |
8876 | 10^90662-9519 | 90662 | Patrick De Geest | 11/2018 |
8877 | 10^90661+2373 | 90662 | Patrick De Geest | 11/2018 |
8878 | 10^90661-194781 | 90661 | Patrick De Geest | 07/2019 |
8879 | 3*5^129698+8 | 90656 | Lelio R Paula | 10/2014 |
8880 | F(433781) | 90655 | Henri Lifchitz | 09/2003 |
8881 | 19^70891+82 | 90653 | Lelio R Paula | 06/2016 |
8882 | (29*2^301124-1)/13 | 90648 | Lelio R Paula | 02/2014 |
8883 | 10^90636+64159 | 90637 | Patrick De Geest | 07/2019 |
8884 | 10^90636-3101 | 90636 | Patrick De Geest | 11/2018 |
8885 | 7*3^189953-8 | 90632 | Lelio R Paula | 08/2014 |
8886 | 10^90626+339289 | 90627 | Patrick De Geest | 07/2019 |
8887 | 10^90626-1131 | 90626 | Patrick De Geest | 11/2018 |
8888 | 11^87022-1800 | 90625 | Enzo Doria | 12/2012 |
8889 | 10^90623+861 | 90624 | Patrick De Geest | 11/2018 |
8890 | 10^90623-305841 | 90623 | Patrick De Geest | 07/2019 |
8891 | (2^301042+47)/12036969 | 90616 | Lelio R Paula | 06/2013 |
8892 | 2^301004-2786939 | 90612 | Enzo Doria | 03/2016 |
8893 | 10^90611+169977 | 90612 | Patrick De Geest | 07/2019 |
8895 | 10^90611-9737 | 90611 | Patrick De Geest | 11/2018 |
8894 | 10^90610+36747 | 90611 | Patrick De Geest | 07/2019 |
8896 | 10^90609+6823 | 90610 | Patrick De Geest | 11/2018 |
8897 | 10^90610-26573 | 90610 | Patrick De Geest | 07/2019 |
8898 | 10^90609-228173 | 90609 | Patrick De Geest | 07/2019 |
8899 | 2^300980-27 | 90605 | Lelio R Paula | 11/2012 |
8900 | 2*10^90597-7 | 90598 | Dmitry Domanov | 11/2010 |
8901 | 197^39485+2 | 90597 | Lelio R Paula | 06/2013 |
8902 | 7^107198+48 | 90593 | Lelio R Paula | 04/2016 |
8903 | (86*10^90588+121)/9 | 90589 | Robert Price | 03/2017 |
8904 | 2^300923+53 | 90587 | Lelio R Paula | 11/2012 |
8905 | 2^300874+7 | 90573 | Lelio R Paula | 10/2012 |
8906 | 10^90567+9489 | 90568 | Patrick De Geest | 11/2018 |
8907 | 10^90567-231353 | 90567 | Patrick De Geest | 07/2019 |
8908 | (2^300857+2214)/2 | 90567 | Stefano Morozzi | 01/2020 |
8909 | 5^129568-56 | 90565 | Lelio R Paula | 04/2016 |
8910 | 2^300847-112831 | 90564 | Enzo Doria | 06/2014 |
8911 | 10^90562+790197 | 90563 | Patrick De Geest | 07/2019 |
8912 | 10^90562-2981 | 90562 | Patrick De Geest | 11/2018 |
8913 | (7796^23269-1)/7795 | 90557 | Serge Batalov | 08/2020 |
8914 | (31*10^90554+257)/9 | 90555 | Robert Price | 12/2021 |
8915 | 10^90549+3811 | 90550 | Patrick De Geest | 11/2018 |
8916 | 10^90549-630303 | 90549 | Patrick De Geest | 07/2019 |
8917 | 2^300790-4541 | 90547 | Yves Minet | 03/2019 |
8918 | 10^90532+8169 | 90533 | Patrick De Geest | 11/2018 |
8919 | 10^90531+9831 | 90532 | Patrick De Geest | 11/2018 |
8920 | 10^90532-154889 | 90532 | Patrick De Geest | 07/2019 |
8921 | 10^90531-1060589 | 90531 | Patrick De Geest | 07/2019 |
8923 | 2^300718+255255 | 90526 | Lelio R Paula | 02/2016 |
8922 | (2^300719+938)/2 | 90526 | Stefano Morozzi | 01/2020 |
8924 | 10^90516+215917 | 90517 | Patrick De Geest | 07/2019 |
8925 | 10^90516-6783 | 90516 | Patrick De Geest | 11/2018 |
8926 | 10^90511+30177 | 90512 | Patrick De Geest | 07/2019 |
8927 | 10^90511-6977 | 90511 | Patrick De Geest | 11/2018 |
8928 | (8573^23011-1)/8572 | 90502 | Serge Batalov | 08/2020 |
8929 | 2^300637+95 | 90501 | Lelio R Paula | 11/2012 |
8930 | 7^107087-24 | 90500 | Lelio R Paula | 04/2016 |
8931 | 10^90499+191547 | 90500 | Patrick De Geest | 07/2019 |
8932 | 10^90499-5823 | 90499 | Patrick De Geest | 11/2018 |
8934 | (10^90499+3^90499)/13 | 90498 | Robert Price | 01/2013 |
8933 | 13^81241+90 | 90498 | Lelio R Paula | 06/2016 |
8935 | (2^300600+1222)/2 | 90490 | Stefano Morozzi | 01/2020 |
8936 | 10^90480+5131 | 90481 | Patrick De Geest | 11/2018 |
8937 | 10^90480-85721 | 90480 | Patrick De Geest | 07/2019 |
8938 | (34*10^90478-547)/9 | 90479 | Robert Price | 03/2021 |
8939 | 6^116273-85 | 90478 | Lelio R Paula | 05/2016 |
8940 | 10^90473+3139 | 90474 | Patrick De Geest | 11/2018 |
8941 | 10^90473-150599 | 90473 | Patrick De Geest | 07/2019 |
8942 | 10^90470+2319 | 90471 | Patrick De Geest | 11/2018 |
8943 | 10^90470-71637 | 90470 | Patrick De Geest | 07/2019 |
8944 | 6^116256-17573 | 90465 | Enzo Doria | 02/2013 |
8945 | 2^300502+54615 | 90461 | Lelio R Paula | 02/2016 |
8946 | (13*2^300487+1)/45 | 90456 | Lelio R Paula | 09/2013 |
8947 | 10^90453+141843 | 90454 | Patrick De Geest | 07/2019 |
8949 | 10^90453-3969 | 90453 | Patrick De Geest | 11/2018 |
8948 | 10^90452+59317 | 90453 | Patrick De Geest | 05/2021 |
8950 | 10^90452-80000001 | 90452 | Robert Price | 04/2021 |
8951 | 10^90452-84713 | 90452 | Patrick De Geest | 05/2021 |
8952 | 10^90440+1359 | 90441 | Patrick De Geest | 11/2018 |
8953 | 10^90440-18821 | 90440 | Patrick De Geest | 07/2019 |
8954 | (3^189545-8)/5 | 90436 | Lelio R Paula | 01/2013 |
8955 | (7*2^300406-1)/3 | 90432 | Lelio R Paula | 02/2014 |
8956 | 10^90430+3339 | 90431 | Patrick De Geest | 11/2018 |
8957 | 10^90430-63477 | 90430 | Patrick De Geest | 07/2019 |
8958 | (5408^24223-1)/5407 | 90422 | Serge Batalov | 08/2020 |
8959 | 10^90414+229593 | 90415 | Patrick De Geest | 07/2019 |
8960 | 10^90414-1547 | 90414 | Patrick De Geest | 11/2018 |
8961 | 10^90404+47041 | 90405 | Patrick De Geest | 07/2019 |
8962 | 10^90404-6429 | 90404 | Patrick De Geest | 11/2018 |
8963 | 10^90401+2077 | 90402 | Patrick De Geest | 11/2018 |
8964 | 10^90401-368637 | 90401 | Patrick De Geest | 07/2019 |
8965 | 24900^4271+4271^24900 | 90401 | Hans Havermann | 08/2020 |
8966 | 4*5^129332+3 | 90400 | Lelio R Paula | 10/2014 |
8968 | 10^90397+19783 | 90398 | Patrick De Geest | 07/2019 |
8967 | 23380^7353+7353^23380 | 90398 | Hans Havermann | 08/2020 |
8970 | 10^90397-323 | 90397 | Patrick De Geest | 11/2018 |
8969 | (2^300293+2762)/2 | 90397 | Stefano Morozzi | 01/2020 |
8971 | 24058^5719+5719^24058 | 90394 | Hans Havermann | 08/2020 |
8972 | 2^300249-16245 | 90384 | Enzo Doria | 04/2013 |
8973 | 24414^5035+5035^24414 | 90381 | Hans Havermann | 08/2020 |
8974 | (7*10^90371-313)/9 | 90371 | Robert Price | 11/2016 |
8975 | 10^90363+58677 | 90364 | Patrick De Geest | 07/2019 |
8976 | 10^90363-3557 | 90363 | Patrick De Geest | 11/2018 |
8977 | 10^90358+104641 | 90359 | Patrick De Geest | 07/2019 |
8980 | 2*6^116118+7 | 90358 | Lelio R Paula | 10/2014 |
8979 | 10^90358-4979 | 90358 | Patrick De Geest | 11/2018 |
8978 | 10^90357+112837 | 90358 | Patrick De Geest | 07/2019 |
8981 | 10^90357-189593 | 90357 | Patrick De Geest | 07/2019 |
8982 | 10^90356+53113 | 90357 | Patrick De Geest | 07/2019 |
8983 | 10^90356-7197 | 90356 | Patrick De Geest | 11/2018 |
8984 | 10^90353+603211 | 90354 | Patrick De Geest | 07/2019 |
8985 | 10^90353-1089 | 90353 | Patrick De Geest | 11/2018 |
8986 | (24737*2^300101+1)/25 | 90343 | Lelio R Paula | 06/2014 |
8987 | 4*10^90334-21 | 90335 | Robert Price | 04/2016 |
8988 | (4546^24697-1)/4545 | 90329 | Serge Batalov | 08/2020 |
8989 | 10^90322+137691 | 90323 | Patrick De Geest | 07/2019 |
8990 | 10^90322-9551 | 90322 | Patrick De Geest | 11/2018 |
8991 | 10^90316+9991 | 90317 | Patrick De Geest | 11/2018 |
8992 | (4550^24691-1)/4549 | 90317 | Serge Batalov | 08/2020 |
8993 | 10^90316-45627 | 90316 | Patrick De Geest | 07/2019 |
8994 | 10^90315+32889 | 90316 | Patrick De Geest | 07/2019 |
8996 | 2^300019-110335 | 90315 | Enzo Doria | 05/2014 |
8995 | 10^90315-8561 | 90315 | Patrick De Geest | 11/2018 |
8997 | FAB2(300001,5032) | 90310 | Robert Price | 05/2019 |
8998 | FAB2(300001,29405) | 90310 | Robert Price | 05/2019 |
8999 | (2^299965+2774)/2 | 90299 | Stefano Morozzi | 01/2020 |
9000 | 23679^6506+6506^23679 | 90296 | Hans Havermann | 08/2020 |