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) !!!
Submit your PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3751 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
| 3752 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
| 3753 | (2^543398)/(543398^2) | 163568 | Henri Lifchitz | 05/2025 |
| 3754 | (2013^49729-1)/(2013^223-1) | 163561 | Ryan Propper | 11/2023 |
| 3755 | L(2*543272)%(2^543272) | 163541 | Henri Lifchitz | 07/2025 |
| 3756 | (23*10^163523+301)/9 | 163524 | Robert Price | 06/2021 |
| 3757 | (68*10^163521-329)/9 | 163522 | Robert Price | 03/2021 |
| 3758 | 35820^35899+35899^35820 | 163489 | Norbert Schneider | 11/2021 |
| 3759 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
| 3760 | 2^542502+24799 | 163310 | Enzo Doria | 10/2023 |
| 3761 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
| 3762 | 2^542258+216949 | 163236 | Enzo Doria | 12/2023 |
| 3763 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
| 3764 | fibonacci(780566)-4 | 163129 | Jon Grantham | 08/2023 |
| 3765 | (682*10^163106-7)/9 | 163108 | Robert Price | 08/2021 |
| 3766 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
| 3767 | (29*10^163056+313)/9 | 163057 | Robert Price | 04/2021 |
| 3768 | 2^541476+214743 | 163001 | Enzo Doria | 11/2023 |
| 3769 | 13^142159+14^142159-2 | 162933 | Harsh Aggarwal | 05/2024 |
| 3770 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
| 3771 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
| 3772 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
| 3773 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
| 3774 | (203*10^162689+1)/3 | 162691 | Robert Price | 03/2020 |
| 3775 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
| 3776 | 2^540180+26791 | 162611 | Enzo Doria | 12/2023 |
| 3777 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
| 3778 | 2^539925+81 | 162534 | Henri Lifchitz | 11/2024 |
| 3779 | 2^539807-114081 | 162499 | Enzo Doria | 12/2014 |
| 3780 | 414^62093+62093^414 | 162498 | Norbert Schneider | 03/2022 |
| 3781 | 2^539654-114893 | 162453 | Enzo Doria | 05/2015 |
| 3782 | 9*10^162449-71 | 162450 | Robert Price | 11/2020 |
| 3783 | 2^539617-1851583 | 162441 | Enzo Doria | 08/2015 |
| 3784 | (509*10^162422+31)/9 | 162424 | Robert Price | 08/2022 |
| 3785 | (91*10^162410+11)/3 | 162412 | Robert Price | 02/2020 |
| 3786 | 2^539346+81049 | 162360 | Enzo Doria | 07/2016 |
| 3787 | 2^539220-115499 | 162322 | Enzo Doria | 07/2015 |
| 3788 | 2^539217-113713 | 162321 | Enzo Doria | 09/2014 |
| 3789 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
| 3790 | 4*10^162263-39 | 162264 | Robert Price | 09/2020 |
| 3791 | 31243^36098-36098^31243 | 162252 | Frank Doornink | 01/2024 |
| 3792 | 31987^36000-36000^31987 | 162180 | Frank Doornink | 01/2024 |
| 3793 | (115*10^162153-1)/3 | 162155 | Serge Batalov | 12/2014 |
| 3794 | (10^162138+11)/3 | 162138 | Serge Batalov | 07/2015 |
| 3795 | (61*10^162100-403)/9 | 162101 | Robert Price | 10/2021 |
| 3796 | 2^538473-112723 | 162097 | Enzo Doria | 06/2014 |
| 3797 | 2^538157+79337 | 162002 | Enzo Doria | 06/2016 |
| 3798 | 2^538136-114749 | 161996 | Enzo Doria | 05/2015 |
| 3799 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
| 3800 | (9*29^110727-1199)/14 | 161927 | Curtis Bright | 05/2015 |
| 3801 | ((2^179294-1)^3+2)/11 | 161918 | Serge Batalov | 03/2023 |
| 3802 | 31198^36027-36027^31198 | 161910 | Frank Doornink | 01/2024 |
| 3803 | 2^537815-22737 | 161899 | Enzo Doria | 07/2013 |
| 3804 | 2^537804-39839 | 161896 | Enzo Doria | 09/2015 |
| 3805 | (754*10^161816-7)/9 | 161818 | Robert Price | 05/2020 |
| 3806 | 2^537461+29867 | 161792 | Enzo Doria | 03/2024 |
| 3807 | 2^537458-59201 | 161791 | Enzo Doria | 10/2015 |
| 3808 | 2*10^161766+51 | 161767 | Robert Price | 05/2018 |
| 3809 | (7*10^161760+131)/3 | 161761 | Robert Price | 06/2020 |
| 3810 | 2^537209-49849 | 161717 | Enzo Doria | 10/2015 |
| 3811 | (58*10^161691+329)/9 | 161692 | Robert Price | 05/2019 |
| 3812 | 23*10^161668-3 | 161670 | Robert Price | 10/2021 |
| 3813 | 2^536937+1879397 | 161635 | Enzo Doria | 09/2016 |
| 3814 | 3*2^536868-5 | 161614 | Jon Grantham | 07/2023 |
| 3815 | 34*10^161593-9 | 161595 | Robert Price | 06/2020 |
| 3816 | (31*10^161582-1)/3 | 161584 | Robert Price | 02/2020 |
| 3817 | 24494^36813+36813^24494 | 161575 | Norbert Schneider | 11/2023 |
| 3818 | 2^536569-22881 | 161524 | Enzo Doria | 07/2013 |
| 3819 | (46*10^161505+593)/9 | 161506 | Robert Price | 04/2022 |
| 3820 | 10^161253+573493 | 161254 | Patrick De Geest | 07/2018 |
| 3821 | 10^161253-8001 | 161253 | Robert Price | 03/2018 |
| 3822 | 97*10^161247-3 | 161249 | Robert Price | 05/2020 |
| 3823 | 7*10^161192-9 | 161193 | Robert Price | 10/2015 |
| 3824 | 2^535415-19 | 161176 | Stefano Morozzi | 07/2022 |
| 3825 | 2^535269-113803 | 161133 | Enzo Doria | 09/2014 |
| 3826 | 2^535205-23295 | 161113 | Enzo Doria | 08/2013 |
| 3827 | (49*10^161105+437)/9 | 161106 | Robert Price | 09/2021 |
| 3828 | 2^534961+6561 | 161040 | Henri Lifchitz | 11/2024 |
| 3829 | (89^82609+1)/90 | 161036 | Paul Bourdelais | 10/2017 |
| 3830 | 35385^35385-17692^17692 | 160960 | Henri Lifchitz | 10/2024 |
| 3831 | 2^534429-19 | 160880 | Stefano Morozzi | 07/2022 |
| 3832 | 2^534359-23229 | 160859 | Enzo Doria | 08/2013 |
| 3833 | 10^160836-1001 | 160836 | Robert Price | 10/2022 |
| 3834 | 457^60454+60454^457 | 160803 | Norbert Schneider | 07/2021 |
| 3835 | 8*10^160782+53 | 160783 | Robert Price | 08/2020 |
| 3836 | 67^88037-66^88037 | 160763 | Robert Price | 10/2013 |
| 3837 | (88*10^160761-637)/9 | 160762 | Robert Price | 11/2020 |
| 3838 | 2^533981+81 | 160745 | Henri Lifchitz | 11/2024 |
| 3839 | 2^533948-1852559 | 160735 | Enzo Doria | 08/2015 |
| 3840 | (2^769082)%F(769082) | 160728 | Henri Lifchitz | 05/2025 |
| 3841 | 2^533665-23335 | 160650 | Enzo Doria | 08/2013 |
| 3842 | 2^533600+217981 | 160630 | Enzo Doria | 01/2024 |
| 3843 | (19*10^160619+77)/3 | 160620 | Robert Price | 05/2019 |
| 3844 | 2^533350-5 | 160555 | Stefano Morozzi | 07/2022 |
| 3845 | (38*10^160508+151)/9 | 160509 | Robert Price | 03/2022 |
| 3846 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
| 3847 | 26134^36315-36315^26134 | 160411 | Frank Doornink | 03/2024 |
| 3848 | 25821^36358-36358^25821 | 160411 | Frank Doornink | 03/2024 |
| 3849 | 2*10^160339-63 | 160340 | Robert Price | 01/2022 |
| 3850 | 24419^36532+36532^24419 | 160293 | Norbert Schneider | 10/2023 |
| 3851 | (91*10^160249+11)/3 | 160251 | Robert Price | 02/2020 |
| 3852 | (772*10^160239-7)/9 | 160241 | Robert Price | 06/2022 |
| 3853 | (2*10^160226+187)/9 | 160226 | Robert Price | 06/2022 |
| 3854 | 2^532253+1868417 | 160225 | Enzo Doria | 04/2016 |
| 3855 | 2^532108-291989 | 160181 | Enzo Doria | 07/2015 |
| 3856 | (28*10^160171-79)/3 | 160172 | Robert Price | 02/2021 |
| 3857 | (26*10^160166-131)/3 | 160167 | Robert Price | 10/2019 |
| 3858 | 55*10^160145+9 | 160147 | Robert Price | 03/2022 |
| 3859 | (17*10^160143+67)/3 | 160144 | Robert Price | 01/2019 |
| 3860 | (394^61637-1)/393 | 159977 | Jinyuan Wang | 04/2023 |
| 3861 | (3^765357)%F(765357) | 159950 | Henri Lifchitz | 07/2025 |
| 3862 | (19*10^159921-49)/3 | 159922 | Robert Price | 05/2019 |
| 3863 | 2^531110-1853771 | 159881 | Enzo Doria | 09/2015 |
| 3864 | 2^531088+48451 | 159874 | Enzo Doria | 07/2025 |
| 3865 | (275^65536+53^65536)/2 | 159864 | Kellen Shenton | 11/2020 |
| 3866 | 2^530992-1845299 | 159845 | Enzo Doria | 07/2015 |
| 3867 | 2^530810+25 | 159790 | Stefano Morozzi | 04/2021 |
| 3868 | 25590^36241-36241^25590 | 159753 | Frank Doornink | 02/2024 |
| 3869 | (136*10^159736-1)/9 | 159738 | Serge Batalov | 12/2014 |
| 3870 | 2^530417-113833 | 159672 | Enzo Doria | 09/2014 |
| 3871 | 2^530406-69701 | 159669 | Enzo Doria | 02/2016 |
| 3872 | 5*10^159656+41 | 159657 | Robert Price | 03/2019 |
| 3873 | 8*10^159614+29 | 159615 | Robert Price | 11/2021 |
| 3874 | 7^188858-188858^7 | 159604 | Norbert Schneider | 05/2018 |
| 3875 | 28^110278+27 | 159590 | Alfred Reich | 02/2024 |
| 3876 | (45^96517-2^96517)/43 | 159562 | Robert Price | 11/2024 |
| 3877 | 7*10^159553-27 | 159554 | Robert Price | 11/2022 |
| 3878 | 3^334409-5*2^334409 | 159554 | Jon Grantham | 08/2023 |
| 3879 | (24^115597-1)/23 | 159547 | Paul Bourdelais | 09/2017 |
| 3880 | 25472^36209-36209^25472 | 159540 | Frank Doornink | 01/2024 |
| 3881 | (17*10^159438-377)/9 | 159439 | Robert Price | 03/2018 |
| 3882 | (49^94321+2^94321)/51 | 159420 | Robert Price | 06/2025 |
| 3883 | (203*10^159381+1)/3 | 159383 | Robert Price | 03/2020 |
| 3884 | 32282^35343-35343^32282 | 159361 | Frank Doornink | 02/2024 |
| 3885 | 2^529215+219383 | 159310 | Enzo Doria | 02/2024 |
| 3886 | 89*10^159258-9 | 159260 | Robert Price | 05/2020 |
| 3887 | 2^528944-461315 | 159229 | Enzo Doria | 07/2015 |
| 3888 | (13*10^159147+161)/3 | 159148 | Robert Price | 11/2018 |
| 3889 | 2^528620-113879 | 159131 | Enzo Doria | 10/2014 |
| 3890 | 32125^35306-35306^32125 | 159119 | Frank Doornink | 02/2024 |
| 3891 | (47*10^159083+259)/9 | 159084 | Robert Price | 03/2022 |
| 3892 | (861^54181-1)/860 | 159019 | Jinyuan Wang | 11/2023 |
| 3893 | 2^528000-23307 | 158944 | Enzo Doria | 08/2013 |
| 3894 | (29*10^158909+61)/9 | 158910 | Robert Price | 08/2018 |
| 3895 | 2^527817+1876817 | 158889 | Enzo Doria | 07/2016 |
| 3896 | 2^527774-49451 | 158876 | Enzo Doria | 10/2015 |
| 3897 | 2^527745-291553 | 158868 | Enzo Doria | 07/2015 |
| 3898 | (91*10^158862+11)/3 | 158864 | Robert Price | 02/2020 |
| 3899 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
| 3900 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
| 3901 | (17*10^158819+7)/3 | 158820 | Robert Price | 06/2023 |
| 3902 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
| 3903 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
| 3904 | (49*10^158783+437)/9 | 158784 | Robert Price | 09/2021 |
| 3905 | 10^158755+310207 | 158756 | Patrick De Geest | 08/2021 |
| 3906 | 10^158755-50001 | 158755 | Robert Price | 08/2020 |
| 3907 | (61*10^158748-619)/9 | 158749 | Robert Price | 03/2022 |
| 3908 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
| 3909 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
| 3910 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
| 3911 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
| 3912 | 24286^36161+36161^24286 | 158579 | Norbert Schneider | 08/2023 |
| 3913 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
| 3914 | (299*10^158544-17)/3 | 158546 | Robert Price | 04/2020 |
| 3915 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
| 3916 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
| 3917 | (7^187507-3^187507)/4 | 158462 | Jon Grantham | 08/2023 |
| 3918 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
| 3919 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
| 3920 | 31209^35242-35242^31209 | 158388 | Frank Doornink | 01/2024 |
| 3921 | 32071^35144-35144^32071 | 158363 | Frank Doornink | 01/2024 |
| 3922 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
| 3923 | (229*10^158339-1)/3 | 158341 | Robert Price | 07/2020 |
| 3924 | 32042^35123-35123^32042 | 158255 | Frank Doornink | 01/2024 |
| 3925 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
| 3926 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
| 3927 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
| 3928 | (56*10^158230+187)/9 | 158231 | Robert Price | 10/2021 |
| 3929 | 10^158209-7000000001 | 158209 | Robert Price | 12/2021 |
| 3930 | 31050^35207-35207^31050 | 158153 | Frank Doornink | 01/2024 |
| 3931 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
| 3932 | 31527^35108-35108^31527 | 157940 | Frank Doornink | 01/2024 |
| 3933 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
| 3934 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
| 3935 | 2^524384-219533 | 157856 | Enzo Doria | 03/2024 |
| 3937 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
| 3938 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
| 3936 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
| 3939 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
| 3940 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
| 3941 | 2^524154+25 | 157787 | Stefano Morozzi | 04/2021 |
| 3942 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
| 3943 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
| 3944 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
| 3945 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
| 3946 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
| 3947 | 2^523496+220141 | 157588 | Enzo Doria | 03/2024 |
| 3948 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
| 3949 | 8*10^157477+27 | 157478 | Robert Price | 09/2021 |
| 3950 | p(30987)#-p(30987+1) | 157417 | Henri Lifchitz | 11/2024 |
| 3951 | 32268^34909-34909^32268 | 157397 | Frank Doornink | 02/2024 |
| 3952 | (8*10^157368+49)/3 | 157369 | Robert Price | 05/2020 |
| 3953 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
| 3954 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
| 3955 | 25401^35704-35704^25401 | 157271 | Frank Doornink | 01/2024 |
| 3956 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
| 3957 | (134*10^157191-11)/3 | 157193 | Robert Price | 01/2022 |
| 3958 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
| 3959 | 9*10^157152+71 | 157153 | Robert Price | 08/2020 |
| 3960 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
| 3961 | 31227^34952-34952^31227 | 157093 | Frank Doornink | 01/2024 |
| 3962 | (32^104347+5^104347)/37 | 157057 | Anonymous | 12/2023 |
| 3963 | fibonacci(751442)-2 | 157042 | Jon Grantham | 08/2023 |
| 3964 | 2^521401-29593 | 156958 | Enzo Doria | 08/2015 |
| 3965 | 7*10^156956+87 | 156957 | Robert Price | 07/2019 |
| 3966 | 2^521348-23397 | 156942 | Enzo Doria | 08/2013 |
| 3967 | 10^156902+34509 | 156903 | Patrick De Geest | 08/2021 |
| 3969 | 10^156902-80000001 | 156902 | Robert Price | 04/2021 |
| 3968 | 10^156902-69789 | 156902 | Patrick De Geest | 08/2021 |
| 3970 | (98^78797+1)/99 | 156901 | Paul Bourdelais | 12/2017 |
| 3971 | 65^86522+64 | 156857 | Lelio R Paula | 04/2016 |
| 3972 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
| 3973 | 2^520977-1858183 | 156830 | Enzo Doria | 10/2015 |
| 3974 | (8*10^156718-101)/3 | 156719 | Robert Price | 08/2018 |
| 3975 | (10^156640+7)/53 | 156639 | Alfred Reich | 07/2021 |
| 3976 | 2^520314-1849481 | 156631 | Enzo Doria | 08/2015 |
| 3977 | (16*10^156563-637)/9 | 156564 | Robert Price | 09/2022 |
| 3978 | (13*10^156522+89)/3 | 156523 | Robert Price | 09/2018 |
| 3979 | (2^(6*86654+1)-5)/3 | 156513 | Kevin Acres | 12/2013 |
| 3980 | (2^519925-5)/3 | 156513 | Stefano Morozzi | 08/2022 |
| 3981 | (4*10^156501+119)/3 | 156502 | Robert Price | 12/2021 |
| 3982 | (83*10^156476-101)/9 | 156477 | Robert Price | 08/2021 |
| 3983 | 3*10^156435-97 | 156436 | Robert Price | 07/2018 |
| 3984 | 10^156428+111 | 156429 | Boyan Hu | 10/2024 |
| 3985 | (8*10^156371-77)/3 | 156372 | Robert Price | 07/2018 |
| 3986 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
| 3987 | 31267^34782-34782^31267 | 156349 | Frank Doornink | 01/2024 |
| 3988 | (418*10^156309-31)/9 | 156311 | Robert Price | 05/2022 |
| 3989 | 2^519106-59141 | 156267 | Enzo Doria | 10/2015 |
| 3990 | 25929^35404-35404^25929 | 156266 | Frank Doornink | 03/2024 |
| 3991 | 2^519053+6077 | 156251 | Enzo Doria | 02/2016 |
| 3992 | 31199^34764-34764^31199 | 156235 | Frank Doornink | 01/2024 |
| 3993 | 2^518968-1860989 | 156225 | Enzo Doria | 11/2015 |
| 3994 | (25*10^156221-7)/9 | 156222 | Robert Price | 05/2018 |
| 3995 | 2^518931-2782297 | 156214 | Enzo Doria | 09/2015 |
| 3996 | 2^518608-2939 | 156117 | Yves Minet | 09/2014 |
| 3997 | 10*27^109005+697 | 156027 | Curtis Bright | 05/2015 |
| 3998 | (49*10^155933-319)/9 | 155934 | Robert Price | 10/2021 |
| 3999 | 2^517967-113485 | 155924 | Enzo Doria | 08/2014 |
| 4000 | (103*10^155904+17)/3 | 155906 | Robert Price | 08/2020 |
