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 ? |
6751 | 10^90930+95223 | 90931 | Patrick De Geest | 07/2019 |
6752 | 10^90930-3623 | 90930 | Patrick De Geest | 01/2019 |
6753 | 156*(10^(4*22731)-1)/101-1 | 90925 | Robert Price | 05/2014 |
6754 | 3^190568+38 | 90925 | Lelio R Paula | 04/2016 |
6755 | 10^90917+179863 | 90918 | Patrick De Geest | 07/2019 |
6756 | 10^90917-6693 | 90917 | Patrick De Geest | 01/2019 |
6757 | 2^302009-16449 | 90914 | Enzo Doria | 04/2013 |
6758 | 10^90908+3181 | 90909 | Patrick De Geest | 01/2019 |
6759 | 10^90908-139511 | 90908 | Patrick De Geest | 07/2019 |
6760 | 10^90904+106947 | 90905 | Patrick De Geest | 07/2019 |
6761 | 10^90904-5169 | 90904 | Patrick De Geest | 01/2019 |
6762 | 10^90903+120963 | 90904 | Patrick De Geest | 07/2019 |
6763 | 10^90902+2613 | 90903 | Patrick De Geest | 01/2019 |
6764 | 10^90903-190737 | 90903 | Patrick De Geest | 07/2019 |
6765 | 25174^4083+4083^25174 | 90903 | Hans Havermann | 08/2020 |
6766 | 10^90902-952329 | 90902 | Patrick De Geest | 07/2019 |
6767 | (17*2^301951-1)/165 | 90896 | Lelio R Paula | 02/2014 |
6768 | 3^190497+74 | 90891 | Lelio R Paula | 04/2016 |
6769 | (24737*2^301896+1)/399 | 90882 | Lelio R Paula | 06/2014 |
6770 | 10^90880+5707 | 90881 | Patrick De Geest | 01/2019 |
6771 | 10^90880-152993 | 90880 | Patrick De Geest | 07/2019 |
6772 | 18^72397+89 | 90878 | Lelio R Paula | 06/2016 |
6773 | (2^301876+762)/2 | 90874 | Stefano Morozzi | 09/2020 |
6774 | 134^42719-133 | 90868 | Norbert Schneider | 03/2019 |
6775 | 6^116769-47 | 90864 | Lelio R Paula | 05/2016 |
6776 | 10^90858+233433 | 90859 | Patrick De Geest | 07/2019 |
6777 | 10^90858-8301 | 90858 | Patrick De Geest | 01/2019 |
6778 | 24298^5483+5483^24298 | 90851 | Hans Havermann | 08/2020 |
6779 | 10^90849+40141 | 90850 | Patrick De Geest | 07/2019 |
6780 | 10^90849-4721 | 90849 | Patrick De Geest | 01/2019 |
6781 | 2^301712-465 | 90825 | Lelio R Paula | 02/2016 |
6782 | 2^301693-69 | 90819 | Lelio R Paula | 11/2012 |
6783 | 2^301683-301683^2 | 90816 | Henri Lifchitz | 05/2005 |
6784 | 10^90807+7279 | 90808 | Patrick De Geest | 01/2019 |
6785 | 10^90807-162263 | 90807 | Patrick De Geest | 07/2019 |
6786 | 6*10^90803+79 | 90804 | Robert Price | 09/2020 |
6787 | 10^90800-6453 | 90800 | Patrick De Geest | 11/2018 |
6788 | 11^87187-1710 | 90796 | Enzo Doria | 12/2012 |
6789 | 5*10^90793+21 | 90794 | Robert Price | 01/2017 |
6790 | (22*10^90792-13)/9 | 90793 | Robert Price | 03/2015 |
6791 | 2^301591-1615 | 90788 | Lelio R Paula | 02/2016 |
6792 | (52^52901+1)/53 | 90777 | Paul Bourdelais | 08/2017 |
6793 | 2^301546-109037 | 90775 | Enzo Doria | 04/2014 |
6794 | 10^90772+4029 | 90773 | Patrick De Geest | 11/2018 |
6795 | 10^90772-36627 | 90772 | Patrick De Geest | 07/2019 |
6796 | 10^90771+67737 | 90772 | Patrick De Geest | 07/2019 |
6797 | 10^90771-441003 | 90771 | Patrick De Geest | 07/2019 |
6798 | 10^90770+28941 | 90771 | Patrick De Geest | 07/2019 |
6799 | 10^90770-431 | 90770 | Patrick De Geest | 11/2018 |
6800 | 14^79195-3 | 90768 | Lelio R Paula | 06/2016 |
6801 | 10^90766+877 | 90767 | Patrick De Geest | 11/2018 |
6804 | 2^301517-1861693 | 90766 | Enzo Doria | 11/2015 |
6802 | 10^90766-109241 | 90766 | Patrick De Geest | 07/2019 |
6803 | 10^90765+485361 | 90766 | Patrick De Geest | 07/2019 |
6805 | 10^90765-4797 | 90765 | Patrick De Geest | 11/2018 |
6806 | 10^90757+7573 | 90758 | Patrick De Geest | 11/2018 |
6807 | 10^90757-554979 | 90757 | Patrick De Geest | 07/2019 |
6808 | 10^90756+438109 | 90757 | Patrick De Geest | 07/2019 |
6809 | 10^90756-8727 | 90756 | Patrick De Geest | 11/2018 |
6810 | 10^90749+823 | 90750 | Patrick De Geest | 11/2018 |
6813 | 2^301460-173 | 90749 | Lelio R Paula | 11/2012 |
6811 | 10^90748+4213 | 90749 | Patrick De Geest | 11/2018 |
6812 | 10^90749-130413 | 90749 | Patrick De Geest | 07/2019 |
6814 | 10^90748-75411 | 90748 | Patrick De Geest | 07/2019 |
6815 | 10^90747+438471 | 90748 | Patrick De Geest | 07/2019 |
6816 | 10^90747-9279 | 90747 | Patrick De Geest | 11/2018 |
6817 | (85*10^90745-103)/9 | 90746 | Robert Price | 10/2017 |
6818 | (2^301439+1206)/2 | 90742 | Stefano Morozzi | 09/2020 |
6819 | 10^90726+4077 | 90727 | Patrick De Geest | 11/2018 |
6820 | 10^90726-504951 | 90726 | Patrick De Geest | 07/2019 |
6822 | 10^90721+181 | 90722 | Patrick De Geest | 11/2018 |
6821 | (2^301372+2722)/2 | 90722 | Stefano Morozzi | 09/2020 |
6823 | 10^90721-177149 | 90721 | Patrick De Geest | 07/2019 |
6824 | (2^301317+1146)/2 | 90706 | Stefano Morozzi | 09/2020 |
6825 | 2^301312-89 | 90704 | Lelio R Paula | 11/2012 |
6826 | 10^90696+6349 | 90697 | Patrick De Geest | 11/2018 |
6828 | 2^301285-129 | 90696 | Lelio R Paula | 11/2012 |
6827 | 10^90696-635049 | 90696 | Patrick De Geest | 07/2019 |
6829 | 2^301282-109991 | 90695 | Enzo Doria | 04/2014 |
6830 | 10^90690+8877 | 90691 | Patrick De Geest | 11/2018 |
6831 | 10^90690-227433 | 90690 | Patrick De Geest | 07/2019 |
6832 | 10^90683+61411 | 90684 | Patrick De Geest | 07/2019 |
6833 | (2^301244+1738)/2 | 90684 | Stefano Morozzi | 09/2020 |
6834 | 10^90683-2577 | 90683 | Patrick De Geest | 11/2018 |
6835 | 2^301228-1854269 | 90679 | Enzo Doria | 09/2015 |
6837 | (151*10^90669-1)/3 | 90671 | Robert Price | 04/2017 |
6836 | (2^301201+2046)/2 | 90671 | Stefano Morozzi | 09/2020 |
6838 | (32*10^90669+13)/9 | 90670 | Robert Price | 04/2015 |
6839 | 10^90669+9793 | 90670 | Patrick De Geest | 11/2018 |
6840 | 10^90669-223931 | 90669 | Patrick De Geest | 07/2019 |
6841 | (2^301191+2510)/2 | 90668 | Stefano Morozzi | 09/2020 |
6842 | 5*10^90666-63 | 90667 | Robert Price | 04/2021 |
6843 | 10^90665+10989 | 90666 | Patrick De Geest | 07/2019 |
6844 | 10^90665-3087 | 90665 | Patrick De Geest | 11/2018 |
6845 | 10^90662+89637 | 90663 | Patrick De Geest | 07/2019 |
6846 | 10^90662-9519 | 90662 | Patrick De Geest | 11/2018 |
6847 | 10^90661+2373 | 90662 | Patrick De Geest | 11/2018 |
6848 | 10^90661-194781 | 90661 | Patrick De Geest | 07/2019 |
6849 | 3*5^129698+8 | 90656 | Lelio R Paula | 10/2014 |
6850 | F(433781) | 90655 | Henri Lifchitz | 09/2003 |
6851 | 19^70891+82 | 90653 | Lelio R Paula | 06/2016 |
6852 | (29*2^301124-1)/13 | 90648 | Lelio R Paula | 02/2014 |
6853 | 10^90636+64159 | 90637 | Patrick De Geest | 07/2019 |
6854 | 10^90636-3101 | 90636 | Patrick De Geest | 11/2018 |
6855 | 7*3^189953-8 | 90632 | Lelio R Paula | 08/2014 |
6856 | 10^90626+339289 | 90627 | Patrick De Geest | 07/2019 |
6857 | 10^90626-1131 | 90626 | Patrick De Geest | 11/2018 |
6858 | 11^87022-1800 | 90625 | Enzo Doria | 12/2012 |
6859 | 10^90623+861 | 90624 | Patrick De Geest | 11/2018 |
6860 | 10^90623-305841 | 90623 | Patrick De Geest | 07/2019 |
6861 | (2^301042+47)/12036969 | 90616 | Lelio R Paula | 06/2013 |
6863 | 2^301004-2786939 | 90612 | Enzo Doria | 03/2016 |
6862 | 10^90611+169977 | 90612 | Patrick De Geest | 07/2019 |
6865 | 10^90611-9737 | 90611 | Patrick De Geest | 11/2018 |
6864 | 10^90610+36747 | 90611 | Patrick De Geest | 07/2019 |
6866 | 10^90609+6823 | 90610 | Patrick De Geest | 11/2018 |
6867 | 10^90610-26573 | 90610 | Patrick De Geest | 07/2019 |
6868 | 10^90609-228173 | 90609 | Patrick De Geest | 07/2019 |
6869 | 2^300980-27 | 90605 | Lelio R Paula | 11/2012 |
6870 | 2*10^90597-7 | 90598 | Dmitry Domanov | 11/2010 |
6871 | 197^39485+2 | 90597 | Lelio R Paula | 06/2013 |
6872 | 7^107198+48 | 90593 | Lelio R Paula | 04/2016 |
6873 | (86*10^90588+121)/9 | 90589 | Robert Price | 03/2017 |
6874 | 2^300923+53 | 90587 | Lelio R Paula | 11/2012 |
6875 | 2^300874+7 | 90573 | Lelio R Paula | 10/2012 |
6876 | 10^90567+9489 | 90568 | Patrick De Geest | 11/2018 |
6877 | 10^90567-231353 | 90567 | Patrick De Geest | 07/2019 |
6878 | (2^300857+2214)/2 | 90567 | Stefano Morozzi | 01/2020 |
6879 | 5^129568-56 | 90565 | Lelio R Paula | 04/2016 |
6880 | 2^300847-112831 | 90564 | Enzo Doria | 06/2014 |
6881 | 10^90562+790197 | 90563 | Patrick De Geest | 07/2019 |
6882 | 10^90562-2981 | 90562 | Patrick De Geest | 11/2018 |
6883 | (7796^23269-1)/7795 | 90557 | Serge Batalov | 08/2020 |
6884 | 10^90549+3811 | 90550 | Patrick De Geest | 11/2018 |
6885 | 10^90549-630303 | 90549 | Patrick De Geest | 07/2019 |
6886 | 2^300790-4541 | 90547 | Yves Minet | 03/2019 |
6887 | 10^90532+8169 | 90533 | Patrick De Geest | 11/2018 |
6888 | 10^90531+9831 | 90532 | Patrick De Geest | 11/2018 |
6889 | 10^90532-154889 | 90532 | Patrick De Geest | 07/2019 |
6890 | 10^90531-1060589 | 90531 | Patrick De Geest | 07/2019 |
6892 | 2^300718+255255 | 90526 | Lelio R Paula | 02/2016 |
6891 | (2^300719+938)/2 | 90526 | Stefano Morozzi | 01/2020 |
6893 | 10^90516+215917 | 90517 | Patrick De Geest | 07/2019 |
6894 | 10^90516-6783 | 90516 | Patrick De Geest | 11/2018 |
6895 | 10^90511+30177 | 90512 | Patrick De Geest | 07/2019 |
6896 | 10^90511-6977 | 90511 | Patrick De Geest | 11/2018 |
6897 | (8573^23011-1)/8572 | 90502 | Serge Batalov | 08/2020 |
6898 | 2^300637+95 | 90501 | Lelio R Paula | 11/2012 |
6899 | 7^107087-24 | 90500 | Lelio R Paula | 04/2016 |
6900 | 10^90499+191547 | 90500 | Patrick De Geest | 07/2019 |
6901 | 10^90499-5823 | 90499 | Patrick De Geest | 11/2018 |
6903 | (10^90499+3^90499)/13 | 90498 | Robert Price | 01/2013 |
6902 | 13^81241+90 | 90498 | Lelio R Paula | 06/2016 |
6904 | (2^300600+1222)/2 | 90490 | Stefano Morozzi | 01/2020 |
6905 | 10^90480+5131 | 90481 | Patrick De Geest | 11/2018 |
6906 | 10^90480-85721 | 90480 | Patrick De Geest | 07/2019 |
6907 | (34*10^90478-547)/9 | 90479 | Robert Price | 03/2021 |
6908 | 6^116273-85 | 90478 | Lelio R Paula | 05/2016 |
6909 | 10^90473+3139 | 90474 | Patrick De Geest | 11/2018 |
6910 | 10^90473-150599 | 90473 | Patrick De Geest | 07/2019 |
6911 | 10^90470+2319 | 90471 | Patrick De Geest | 11/2018 |
6912 | 10^90470-71637 | 90470 | Patrick De Geest | 07/2019 |
6913 | 6^116256-17573 | 90465 | Enzo Doria | 02/2013 |
6914 | 2^300502+54615 | 90461 | Lelio R Paula | 02/2016 |
6915 | (13*2^300487+1)/45 | 90456 | Lelio R Paula | 09/2013 |
6916 | 10^90453+141843 | 90454 | Patrick De Geest | 07/2019 |
6917 | 10^90453-3969 | 90453 | Patrick De Geest | 11/2018 |
6918 | 10^90452-80000001 | 90452 | Robert Price | 04/2021 |
6919 | 10^90440+1359 | 90441 | Patrick De Geest | 11/2018 |
6920 | 10^90440-18821 | 90440 | Patrick De Geest | 07/2019 |
6921 | (3^189545-8)/5 | 90436 | Lelio R Paula | 01/2013 |
6922 | (7*2^300406-1)/3 | 90432 | Lelio R Paula | 02/2014 |
6923 | 10^90430+3339 | 90431 | Patrick De Geest | 11/2018 |
6924 | 10^90430-63477 | 90430 | Patrick De Geest | 07/2019 |
6925 | (5408^24223-1)/5407 | 90422 | Serge Batalov | 08/2020 |
6926 | 10^90414+229593 | 90415 | Patrick De Geest | 07/2019 |
6927 | 10^90414-1547 | 90414 | Patrick De Geest | 11/2018 |
6928 | 10^90404+47041 | 90405 | Patrick De Geest | 07/2019 |
6929 | 10^90404-6429 | 90404 | Patrick De Geest | 11/2018 |
6930 | 10^90401+2077 | 90402 | Patrick De Geest | 11/2018 |
6931 | 10^90401-368637 | 90401 | Patrick De Geest | 07/2019 |
6932 | 24900^4271+4271^24900 | 90401 | Hans Havermann | 08/2020 |
6933 | 4*5^129332+3 | 90400 | Lelio R Paula | 10/2014 |
6934 | 10^90397+19783 | 90398 | Patrick De Geest | 07/2019 |
6935 | 23380^7353+7353^23380 | 90398 | Hans Havermann | 08/2020 |
6937 | 10^90397-323 | 90397 | Patrick De Geest | 11/2018 |
6936 | (2^300293+2762)/2 | 90397 | Stefano Morozzi | 01/2020 |
6938 | 24058^5719+5719^24058 | 90394 | Hans Havermann | 08/2020 |
6939 | 2^300249-16245 | 90384 | Enzo Doria | 04/2013 |
6940 | 24414^5035+5035^24414 | 90381 | Hans Havermann | 08/2020 |
6941 | (7*10^90371-313)/9 | 90371 | Robert Price | 11/2016 |
6942 | 10^90363+58677 | 90364 | Patrick De Geest | 07/2019 |
6943 | 10^90363-3557 | 90363 | Patrick De Geest | 11/2018 |
6944 | 10^90358+104641 | 90359 | Patrick De Geest | 07/2019 |
6947 | 2*6^116118+7 | 90358 | Lelio R Paula | 10/2014 |
6946 | 10^90358-4979 | 90358 | Patrick De Geest | 11/2018 |
6945 | 10^90357+112837 | 90358 | Patrick De Geest | 07/2019 |
6948 | 10^90357-189593 | 90357 | Patrick De Geest | 07/2019 |
6949 | 10^90356+53113 | 90357 | Patrick De Geest | 07/2019 |
6950 | 10^90356-7197 | 90356 | Patrick De Geest | 11/2018 |
6951 | 10^90353+603211 | 90354 | Patrick De Geest | 07/2019 |
6952 | 10^90353-1089 | 90353 | Patrick De Geest | 11/2018 |
6953 | (24737*2^300101+1)/25 | 90343 | Lelio R Paula | 06/2014 |
6954 | 4*10^90334-21 | 90335 | Robert Price | 04/2016 |
6955 | (4546^24697-1)/4545 | 90329 | Serge Batalov | 08/2020 |
6956 | 10^90322+137691 | 90323 | Patrick De Geest | 07/2019 |
6957 | 10^90322-9551 | 90322 | Patrick De Geest | 11/2018 |
6958 | 10^90316+9991 | 90317 | Patrick De Geest | 11/2018 |
6959 | (4550^24691-1)/4549 | 90317 | Serge Batalov | 08/2020 |
6960 | 10^90316-45627 | 90316 | Patrick De Geest | 07/2019 |
6961 | 10^90315+32889 | 90316 | Patrick De Geest | 07/2019 |
6962 | 2^300019-110335 | 90315 | Enzo Doria | 05/2014 |
6963 | 10^90315-8561 | 90315 | Patrick De Geest | 11/2018 |
6964 | FAB2(300001,5032) | 90310 | Robert Price | 05/2019 |
6965 | FAB2(300001,29405) | 90310 | Robert Price | 05/2019 |
6966 | (2^299965+2774)/2 | 90299 | Stefano Morozzi | 01/2020 |
6967 | 23679^6506+6506^23679 | 90296 | Hans Havermann | 08/2020 |
6968 | 2^299949-1005 | 90294 | Lelio R Paula | 11/2013 |
6969 | (2^299947+2054)/2 | 90293 | Stefano Morozzi | 01/2020 |
6970 | 21740^14229+14229^21740 | 90291 | Hans Havermann | 08/2020 |
6971 | 10^90279+62457 | 90280 | Patrick De Geest | 07/2019 |
6972 | 10^90279-1551 | 90279 | Patrick De Geest | 09/2018 |
6973 | (2^299892+1986)/2 | 90277 | Stefano Morozzi | 01/2020 |
6974 | (2^299893+3866)/2 | 90277 | Stefano Morozzi | 01/2020 |
6975 | 2^299868-109613 | 90270 | Enzo Doria | 04/2014 |
6976 | 10^90259+359299 | 90260 | Patrick De Geest | 07/2019 |
6977 | 10^90259-9443 | 90259 | Patrick De Geest | 09/2018 |
6978 | (2^299831+3786)/2 | 90258 | Stefano Morozzi | 01/2020 |
6979 | 10^90252+102873 | 90253 | Patrick De Geest | 07/2019 |
6980 | 10^90252-8103 | 90252 | Patrick De Geest | 09/2018 |
6982 | 5*2^299799-3 | 90250 | Lelio R Paula | 08/2014 |
6981 | (2^299803+3326)/2 | 90250 | Stefano Morozzi | 01/2020 |
6983 | 13^81008-2 | 90239 | Lelio R Paula | 09/2013 |
6984 | 80697!4-256 | 90234 | Robert Price | 11/2019 |
6986 | 64^49957-63^49957 | 90232 | Robert Price | 07/2013 |
6985 | (2^299745+2994)/2 | 90232 | Stefano Morozzi | 01/2020 |
6987 | 10^90227+56281 | 90228 | Patrick De Geest | 06/2016 |
6990 | 2^299725+315 | 90227 | Lelio R Paula | 11/2013 |
6988 | 10^90227-1000000001 | 90227 | Robert Price | 05/2016 |
6989 | 10^90227-68763 | 90227 | Patrick De Geest | 06/2016 |
6991 | 5^129082+48 | 90225 | Lelio R Paula | 03/2016 |
6992 | 2^299699+195 | 90219 | Lelio R Paula | 10/2012 |
6993 | (55*10^90211-1)/9 | 90212 | Ray Chandler | 02/2012 |
6994 | 22131^11918+11918^22131 | 90211 | Hans Havermann | 08/2020 |
6995 | 10^90209+8971 | 90210 | Patrick De Geest | 09/2018 |
6996 | 10^90209-724797 | 90209 | Patrick De Geest | 07/2019 |
6997 | 10^90208+189531 | 90209 | Patrick De Geest | 07/2019 |
6998 | 10^90208-2247 | 90208 | Patrick De Geest | 09/2018 |
6999 | (629^32233-1)/628 | 90207 | Michael Stocker | 05/2020 |
7000 | 116^43693-115 | 90203 | Norbert Schneider | 08/2018 |