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 | (46*10^170932+143)/9 | 170933 | Robert Price | 01/2019 |
| 3752 | (79*10^170901-1)/3 | 170903 | Robert Price | 02/2020 |
| 3753 | 81^89526+80 | 170860 | Alfred Reich | 04/2026 |
| 3754 | (58*10^170842+221)/9 | 170843 | Robert Price | 02/2017 |
| 3755 | (29*10^170830+583)/9 | 170831 | Robert Price | 06/2021 |
| 3756 | 3*10^170800+73 | 170801 | Robert Price | 08/2018 |
| 3757 | (29*10^170799-119)/9 | 170800 | Robert Price | 12/2021 |
| 3758 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
| 3759 | 2*10^170767+41 | 170768 | Robert Price | 05/2018 |
| 3760 | 3^357706-112358 | 170670 | Enzo Doria | 07/2014 |
| 3761 | TheodorusPrime(170657) | 170657 | Eric W. Weisstein | 08/2013 |
| 3762 | 2^566871+1876163 | 170646 | Enzo Doria | 07/2016 |
| 3763 | (10657#+(404267#)/(10657#))/(1675379) | 170624 | Makoto Morimoto | 10/2017 |
| 3764 | 33^112337-32^112337 | 170586 | Alfred Reich | 11/2025 |
| 3765 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
| 3766 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
| 3767 | Phi(201653,-7) | 170416 | Henri Lifchitz | 12/2025 |
| 3768 | 32150^37807-37807^32150 | 170403 | Frank Doornink | 02/2024 |
| 3769 | 7*10^170348+33 | 170349 | Robert Price | 06/2020 |
| 3770 | 2^565799+216011 | 170323 | Enzo Doria | 12/2023 |
| 3771 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
| 3772 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
| 3773 | 3*2^565024-5 | 170090 | Jon Grantham | 07/2023 |
| 3774 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
| 3775 | 2^564561+225 | 169950 | Henri Lifchitz | 11/2024 |
| 3776 | (7*10^169944+23)/3 | 169945 | Robert Price | 06/2020 |
| 3777 | (37*10^169943+251)/9 | 169944 | Robert Price | 09/2021 |
| 3778 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
| 3779 | 3^355902+4 | 169809 | Aurel Gibier | 10/2024 |
| 3780 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
| 3781 | (2^563903-13)/5 | 169752 | Stefano Morozzi | 08/2022 |
| 3782 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
| 3783 | 2^563583+89 | 169656 | Stefano Morozzi | 04/2021 |
| 3784 | 2^563311+215813 | 169574 | Enzo Doria | 11/2023 |
| 3785 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
| 3786 | (194*10^169461-17)/3 | 169463 | Robert Price | 09/2020 |
| 3787 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
| 3788 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
| 3789 | (109*10^169337+11)/3 | 169339 | Robert Price | 06/2022 |
| 3790 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
| 3791 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
| 3792 | (17*10^169283+19)/9 | 169284 | Robert Price | 03/2021 |
| 3793 | 390151#-2322911 | 169082 | Hayden Chesnut | 07/2024 |
| 3794 | 10^169074-5000000001 | 169074 | Robert Price | 09/2022 |
| 3795 | 8*10^169071+59 | 169072 | Robert Price | 11/2021 |
| 3796 | (10^169044+173)/3 | 169044 | Robert Price | 05/2021 |
| 3797 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
| 3798 | (64*10^168935+143)/9 | 168936 | Robert Price | 05/2021 |
| 3799 | (22*10^168906+47)/3 | 168907 | Robert Price | 06/2021 |
| 3800 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
| 3801 | (77*10^168803-149)/9 | 168804 | Robert Price | 03/2022 |
| 3802 | 4*10^168788-47 | 168789 | Robert Price | 10/2021 |
| 3803 | (154*10^168781+17)/9 | 168783 | Robert Price | 06/2022 |
| 3804 | (418*10^168751-31)/9 | 168753 | Robert Price | 05/2022 |
| 3805 | (29*10^168711+691)/9 | 168712 | Robert Price | 08/2021 |
| 3806 | 2^560405-39943 | 168699 | Enzo Doria | 09/2015 |
| 3807 | (397*10^168634+17)/9 | 168636 | Robert Price | 03/2022 |
| 3808 | 2^560189+36587 | 168634 | Enzo Doria | 09/2024 |
| 3809 | 89*10^168614-7 | 168616 | Robert Price | 04/2020 |
| 3810 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
| 3811 | (94*10^168541+11)/3 | 168543 | Robert Price | 04/2020 |
| 3812 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
| 3813 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
| 3814 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
| 3815 | 2024^50920+3 | 168353 | Martin Hopf | 01/2024 |
| 3816 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
| 3817 | 2^558830+25009 | 168225 | Enzo Doria | 11/2023 |
| 3818 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
| 3819 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
| 3820 | (74*10^168170+529)/9 | 168171 | Robert Price | 02/2022 |
| 3821 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
| 3822 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
| 3823 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
| 3824 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
| 3825 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
| 3826 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
| 3827 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
| 3828 | (8*10^167965-11)/3 | 167966 | Robert Price | 07/2023 |
| 3829 | 2^557916+216151 | 167950 | Enzo Doria | 12/2023 |
| 3830 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
| 3831 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |
| 3832 | 36^107827-107827 | 167812 | Kellen Shenton | 06/2023 |
| 3833 | 32027^37242-37242^32027 | 167795 | Frank Doornink | 01/2024 |
| 3834 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
| 3835 | 2^557322+217519 | 167771 | Enzo Doria | 01/2024 |
| 3836 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
| 3837 | 6*10^167662-13 | 167663 | Robert Price | 07/2022 |
| 3838 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
| 3839 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
| 3840 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
| 3841 | (88*10^167522-637)/9 | 167523 | Robert Price | 11/2020 |
| 3842 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
| 3843 | 7*10^167437-93 | 167438 | Robert Price | 08/2020 |
| 3844 | (43^102451-1)/7138097213378082 | 167335 | Paul Vanderveen | 05/2025 |
| 3845 | 25455^37978-37978^25455 | 167323 | Frank Doornink | 01/2024 |
| 3846 | 11^160663+6 | 167314 | Paul Bourdelais | 02/2021 |
| 3847 | (7*10^167308-493)/9 | 167308 | Robert Price | 04/2021 |
| 3848 | 2^555759+74333 | 167301 | Enzo Doria | 07/2023 |
| 3849 | 26084^37871-37871^26084 | 167253 | Frank Doornink | 03/2024 |
| 3850 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
| 3851 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
| 3852 | 9*10^166996+59 | 166997 | Robert Price | 01/2020 |
| 3853 | (68*10^166976-329)/9 | 166977 | Robert Price | 03/2021 |
| 3854 | (64*10^166901+683)/9 | 166902 | Robert Price | 06/2022 |
| 3855 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
| 3856 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
| 3857 | (185*10^166837+7)/3 | 166839 | Robert Price | 03/2020 |
| 3858 | (14*10^166813+139)/9 | 166814 | Robert Price | 11/2021 |
| 3859 | 26084^37767-37767^26084 | 166794 | Frank Doornink | 03/2024 |
| 3860 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
| 3861 | 31861^37028-37028^31861 | 166747 | Frank Doornink | 01/2024 |
| 3862 | Phi(276951,2^3) | 166740 | Henri Lifchitz | 12/2025 |
| 3863 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
| 3864 | 2*10^166646+69 | 166647 | Robert Price | 06/2020 |
| 3865 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
| 3866 | (188*10^166611+7)/3 | 166613 | Robert Price | 03/2020 |
| 3867 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
| 3868 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
| 3869 | 2^553020+1152921504606846975 | 166476 | Alfred Reich | 05/2026 |
| 3870 | 25218^37819-37819^25218 | 166469 | Frank Doornink | 12/2023 |
| 3871 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
| 3872 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
| 3873 | Phi(556277,2) | 166404 | Henri Lifchitz | 12/2025 |
| 3874 | 25214^37799-37799^25214 | 166378 | Frank Doornink | 11/2023 |
| 3875 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
| 3876 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
| 3877 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
| 3878 | (19*10^166325+137)/3 | 166326 | Robert Price | 03/2022 |
| 3879 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
| 3880 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
| 3881 | (85*10^166297-1)/3 | 166299 | Robert Price | 02/2020 |
| 3882 | (19*10^166280-7)/3 | 166281 | Robert Price | 12/2023 |
| 3883 | 25533^37726-37726^25533 | 166263 | Frank Doornink | 02/2024 |
| 3884 | 8*10^166227+87 | 166228 | Robert Price | 10/2019 |
| 3885 | 2^552137+1879397 | 166210 | Enzo Doria | 09/2016 |
| 3886 | 262273205671539190984629()252475512364409752762433 | 166141 | Anonymous | 01/2025 |
| 3887 | 490079063773165613318095()218182139934160868002603 | 166141 | Anonymous | 01/2025 |
| 3888 | 140717254840416411192803()712689271538459396766869 | 166140 | Anonymous | 01/2025 |
| 3889 | 122398296040696255481419()271117913237372866926417 | 166140 | Anonymous | 01/2025 |
| 3890 | (103*10^166126+11)/3 | 166128 | Robert Price | 01/2021 |
| 3891 | (22*10^166077+179)/3 | 166078 | Robert Price | 02/2022 |
| 3892 | (23^121949-1)/22 | 166061 | Paul Bourdelais | 10/2017 |
| 3893 | 2^551576+236221 | 166041 | Enzo Doria | 05/2025 |
| 3894 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
| 3895 | 2^551535-23821 | 166029 | Enzo Doria | 08/2013 |
| 3896 | 2^551507-23557 | 166021 | Enzo Doria | 08/2013 |
| 3897 | 32030^36841-36841^32030 | 165990 | Frank Doornink | 01/2024 |
| 3898 | 10^165947-7000000001 | 165947 | Robert Price | 12/2021 |
| 3899 | 4*10^165938-47 | 165939 | Robert Price | 10/2021 |
| 3900 | 7*10^165916-3 | 165917 | Robert Price | 08/2015 |
| 3901 | (29*10^165796+67)/3 | 165797 | Robert Price | 12/2019 |
| 3902 | 81^86837-80^86837 | 165728 | Robert Price | 01/2015 |
| 3903 | (71*10^165716-17)/9 | 165717 | Serge Batalov | 01/2023 |
| 3904 | fibonacci(792909)+3 | 165708 | Jon Grantham | 08/2023 |
| 3905 | (71*10^165663-539)/9 | 165664 | Robert Price | 07/2019 |
| 3906 | 25682^37567-37567^25682 | 165657 | Frank Doornink | 02/2024 |
| 3907 | 2^550270-69551 | 165648 | Enzo Doria | 12/2015 |
| 3908 | 2^550250+29329 | 165642 | Enzo Doria | 03/2024 |
| 3909 | (202*10^165569-13)/9 | 165571 | Robert Price | 01/2020 |
| 3910 | 2^550000-23625 | 165567 | Enzo Doria | 08/2013 |
| 3911 | 31688^36783-36783^31688 | 165557 | Frank Doornink | 01/2024 |
| 3912 | 2^549675-1852057 | 165469 | Enzo Doria | 08/2015 |
| 3913 | 2^549663+212543 | 165466 | Enzo Doria | 08/2023 |
| 3914 | (3^549633)%(2^549633) | 165456 | Henri Lifchitz | 06/2025 |
| 3915 | Phi(125543,5#) | 165438 | Henri Lifchitz | 12/2025 |
| 3916 | (529*10^165394-7)/9 | 165396 | Robert Price | 08/2021 |
| 3917 | 26253^37424-37424^26253 | 165384 | Frank Doornink | 03/2024 |
| 3918 | -tau(103^14938) | 165374 | Nik Lygeros / Olivier Rozier | 10/2013 |
| 3919 | (28*10^165358-1)/9 | 165359 | Serge Batalov | 10/2014 |
| 3920 | 2^549278+1879669 | 165350 | Enzo Doria | 09/2016 |
| 3921 | (7*10^165350-439)/9 | 165350 | Robert Price | 02/2018 |
| 3922 | 2^549252-351269 | 165342 | Enzo Doria | 06/2015 |
| 3923 | 2^549221+335931 | 165332 | Enzo Doria | 09/2024 |
| 3924 | 67*10^165327-9 | 165329 | Robert Price | 03/2021 |
| 3925 | (14*10^165282+73)/3 | 165283 | Robert Price | 12/2018 |
| 3926 | (8*10^165283-629)/9 | 165283 | Robert Price | 01/2022 |
| 3927 | 2^549049+2797607 | 165281 | Enzo Doria | 04/2016 |
| 3928 | (218*10^165258+7)/9 | 165260 | Robert Price | 06/2022 |
| 3929 | (7*10^165239+107)/3 | 165240 | Robert Price | 02/2018 |
| 3930 | 2^548880+23961 | 165230 | Enzo Doria | 10/2023 |
| 3931 | 5*2^548778+3 | 165200 | Jon Grantham | 07/2023 |
| 3932 | (44^100511-1)/43 | 165184 | Paul Bourdelais | 11/2017 |
| 3933 | (7*10^165134+107)/3 | 165135 | Robert Price | 02/2018 |
| 3934 | (301*10^165082+23)/9 | 165084 | Robert Price | 06/2021 |
| 3935 | (23*10^165060-83)/3 | 165061 | Robert Price | 08/2019 |
| 3936 | 7*10^165023-27 | 165024 | Robert Price | 11/2022 |
| 3937 | (76*10^164984+77)/9 | 164985 | Robert Price | 10/2019 |
| 3938 | 31058^36715-36715^31058 | 164931 | Frank Doornink | 01/2024 |
| 3939 | (4*10^164929-211)/9 | 164929 | Robert Price | 03/2022 |
| 3940 | 10^164878-500001 | 164878 | Robert Price | 03/2022 |
| 3941 | Phi(175151,10)/25997097796891253 | 164816 | Anonymous | 02/2026 |
| 3942 | 9*10^164791-89 | 164792 | Robert Price | 04/2020 |
| 3943 | (2^788414)%F(788414) | 164769 | Henri Lifchitz | 05/2025 |
| 3944 | 2^547178-1856501 | 164717 | Enzo Doria | 10/2015 |
| 3945 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
| 3946 | (26*10^164643-167)/3 | 164644 | Robert Price | 10/2019 |
| 3947 | (10^164643+83)/3 | 164643 | Robert Price | 08/2021 |
| 3948 | 2^546398-59201 | 164483 | Enzo Doria | 10/2015 |
| 3949 | 2^546332-114893 | 164463 | Enzo Doria | 05/2015 |
| 3950 | 36087^36087-36080^36080 | 164462 | Henri Lifchitz | 08/2024 |
| 3951 | 32003^36504-36504^32003 | 164458 | Frank Doornink | 01/2024 |
| 3952 | (65*10^164427+277)/9 | 164428 | Robert Price | 08/2021 |
| 3953 | 2^545958+1876189 | 164350 | Enzo Doria | 07/2016 |
| 3954 | 2^545878-49841 | 164326 | Enzo Doria | 10/2015 |
| 3955 | (10^164284+77)/3 | 164284 | Robert Price | 01/2018 |
| 3956 | 2^545668-4019 | 164263 | Yves Minet | 04/2017 |
| 3957 | 10^164216+780639 | 164217 | Patrick De Geest | 08/2021 |
| 3959 | 10^164216-50000000001 | 164216 | Robert Price | 12/2020 |
| 3958 | 10^164216-891051 | 164216 | Patrick De Geest | 08/2021 |
| 3960 | (13*53^238539*617^9)/10^247183 | 164151 | Hans Havermann | 07/2017 |
| 3961 | (16*10^164122+197)/3 | 164123 | Robert Price | 04/2019 |
| 3962 | 2^545185+76757 | 164118 | Enzo Doria | 05/2016 |
| 3963 | 2^545076-114329 | 164085 | Enzo Doria | 01/2015 |
| 3964 | (2*10^164043-143)/3 | 164043 | Robert Price | 03/2018 |
| 3965 | (33085^36481-1)/(33085^191-1) | 164018 | Ryan Propper | 11/2023 |
| 3966 | (29^112153+1)/30 | 164011 | Lelio R Paula | 03/2017 |
| 3967 | 2^544757+1874777 | 163989 | Enzo Doria | 06/2016 |
| 3968 | 2^544723+211193 | 163978 | Enzo Doria | 08/2023 |
| 3969 | 2^544444-457199 | 163894 | Enzo Doria | 01/2015 |
| 3970 | (32804^36481-1)/(32804^191-1) | 163883 | Ryan Propper | 11/2023 |
| 3971 | 2^544264-343529 | 163840 | Enzo Doria | 07/2015 |
| 3972 | 7*10^163780+9 | 163781 | Robert Price | 09/2015 |
| 3973 | (2^783598)%L(783598) | 163761 | Henri Lifchitz | 05/2025 |
| 3974 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
| 3975 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
| 3976 | (2^543398)/(543398^2) | 163568 | Henri Lifchitz | 05/2025 |
| 3977 | (2013^49729-1)/(2013^223-1) | 163561 | Ryan Propper | 11/2023 |
| 3978 | L(2*543272)%(2^543272) | 163541 | Henri Lifchitz | 07/2025 |
| 3979 | (23*10^163523+301)/9 | 163524 | Robert Price | 06/2021 |
| 3980 | (68*10^163521-329)/9 | 163522 | Robert Price | 03/2021 |
| 3981 | 35820^35899+35899^35820 | 163489 | Norbert Schneider | 11/2021 |
| 3982 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
| 3983 | 2^542502+24799 | 163310 | Enzo Doria | 10/2023 |
| 3984 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
| 3985 | 2^542258+216949 | 163236 | Enzo Doria | 12/2023 |
| 3986 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
| 3987 | fibonacci(780566)-4 | 163129 | Jon Grantham | 08/2023 |
| 3988 | (682*10^163106-7)/9 | 163108 | Robert Price | 08/2021 |
| 3989 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
| 3990 | (29*10^163056+313)/9 | 163057 | Robert Price | 04/2021 |
| 3991 | 2^541476+214743 | 163001 | Enzo Doria | 11/2023 |
| 3992 | 13^142159+14^142159-2 | 162933 | Harsh Aggarwal | 05/2024 |
| 3993 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
| 3994 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
| 3995 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
| 3996 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
| 3997 | (203*10^162689+1)/3 | 162691 | Robert Price | 03/2020 |
| 3998 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
| 3999 | 2^540180+26791 | 162611 | Enzo Doria | 12/2023 |
| 4000 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
