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
See the Top discoverers
See the Latest PRPs
Search by form
Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
3751 | 2^476868-1859939 | 143552 | Enzo Doria | 11/2015 |
3752 | 40807^3294+3294^40807 | 143548 | Hans Havermann | 12/2020 |
3753 | 755^49878+49878^755 | 143547 | Norbert Schneider | 04/2019 |
3754 | (19^112247-4^112247)/15 | 143536 | Robert Price | 03/2021 |
3755 | 35561^10872+10872^35561 | 143536 | Hans Havermann | 06/2021 |
3756 | 37637^6492+6492^37637 | 143487 | Hans Havermann | 05/2021 |
3757 | 61567^214+214^61567 | 143477 | Hans Havermann | 05/2021 |
3758 | 25933^32504-32504^25933 | 143468 | Frank Doornink | 03/2024 |
3759 | 2^476558-113627 | 143459 | Enzo Doria | 08/2014 |
3760 | 2^476478-45 | 143435 | Lelio R Paula | 11/2017 |
3761 | 36380^8757+8757^36380 | 143423 | Hans Havermann | 06/2021 |
3762 | 32510^25707+25707^32510 | 143371 | Hans Havermann | 05/2021 |
3763 | 8*10^143361+17 | 143362 | Robert Price | 07/2021 |
3764 | (2^475854+9)/73 | 143245 | Lelio R Paula | 08/2015 |
3765 | 2^475813-113239 | 143234 | Enzo Doria | 07/2014 |
3766 | (19*10^143212+137)/3 | 143213 | Robert Price | 03/2022 |
3767 | 32218^27849+27849^32218 | 143203 | Hans Havermann | 04/2021 |
3768 | 580*33^94296+19 | 143193 | Eric Chen | 12/2023 |
3769 | 2^475624-114059 | 143178 | Enzo Doria | 11/2014 |
3770 | (11*2^475553-7)/15 | 143156 | Renaud Lifchitz | 03/2011 |
3771 | 2^475480-2786129 | 143134 | Enzo Doria | 10/2015 |
3772 | 33912^16621+16621^33912 | 143131 | Hans Havermann | 05/2021 |
3773 | (19*10^143129-43)/3 | 143130 | Robert Price | 05/2019 |
3774 | 31830^31373+31373^31830 | 143126 | Hans Havermann | 05/2021 |
3775 | 6*10^143105-53 | 143106 | Robert Price | 05/2021 |
3776 | (14*10^143097+73)/3 | 143098 | Robert Price | 12/2018 |
3777 | 2^475299-111937 | 143080 | Enzo Doria | 05/2014 |
3778 | 35488^10753+10753^35488 | 143071 | Hans Havermann | 04/2021 |
3779 | 29695^31986-31986^29695 | 143064 | Frank Doornink | 06/2024 |
3780 | 2^475160-2797859 | 143038 | Enzo Doria | 04/2016 |
3781 | (2^475069+3)/395 | 143008 | Lelio R Paula | 08/2015 |
3782 | 2^475027-461437 | 142998 | Enzo Doria | 07/2015 |
3783 | (2^474958+78557)/3 | 142977 | Lelio R Paula | 07/2015 |
3784 | (8*10^142932+43)/3 | 142933 | Robert Price | 06/2018 |
3785 | 35055^11942+11942^35055 | 142922 | Hans Havermann | 05/2021 |
3786 | 37650^6239+6239^37650 | 142887 | Hans Havermann | 05/2021 |
3787 | (54^82471-1)/53 | 142871 | Paul Bourdelais | 09/2017 |
3788 | 31205^31784-31784^31205 | 142845 | Frank Doornink | 01/2024 |
3789 | (11*2^474432-1)/95 | 142818 | Lelio R Paula | 09/2015 |
3790 | 2^474417-59923 | 142814 | Enzo Doria | 10/2015 |
3791 | 4*10^142810-21 | 142811 | Robert Price | 09/2018 |
3792 | 32287^26494+26494^32287 | 142811 | Hans Havermann | 06/2021 |
3793 | 37162^6965+6965^37162 | 142811 | Hans Havermann | 06/2021 |
3794 | (34*10^142805-601)/9 | 142806 | Robert Price | 07/2022 |
3795 | 37456^6493+6493^37456 | 142799 | Hans Havermann | 05/2021 |
3796 | 35141^11572+11572^35141 | 142793 | Hans Havermann | 05/2021 |
3797 | 32231^26908+26908^32231 | 142780 | Hans Havermann | 05/2021 |
3798 | (3*2^474166+1)/7 | 142738 | Lelio R Paula | 08/2015 |
3799 | 2^474053+2897 | 142705 | Lelio R Paula | 08/2012 |
3800 | (10^142699+359)/9 | 142699 | Serge Batalov | 12/2014 |
3801 | 26073^32312-32312^26073 | 142696 | Frank Doornink | 03/2024 |
3802 | 898^48311-897^48311 | 142676 | Jean-Louis Charton | 12/2012 |
3803 | 2^473740-1856639 | 142610 | Enzo Doria | 09/2015 |
3804 | (25*10^142573-403)/9 | 142574 | Robert Price | 12/2020 |
3805 | 2^473617-114223 | 142573 | Enzo Doria | 12/2014 |
3806 | 36115^8856+8856^36115 | 142555 | Hans Havermann | 05/2021 |
3807 | fibonacci(682007)+4 | 142531 | Jon Grantham | 08/2023 |
3808 | 2^473257+1873217 | 142465 | Enzo Doria | 06/2016 |
3809 | (19*2^473242+1)/11 | 142461 | Lelio R Paula | 09/2015 |
3810 | 32750^22371+22371^32750 | 142453 | Hans Havermann | 06/2021 |
3811 | (61*10^142446-1)/3 | 142448 | Robert Price | 01/2020 |
3812 | (14*10^142440+61)/3 | 142441 | Robert Price | 12/2018 |
3813 | (10^142425+359)/9 | 142425 | Serge Batalov | 12/2014 |
3814 | 2^473101+773027 | 142418 | Enzo Doria | 05/2016 |
3815 | (13*2^472838-1)/3 | 142340 | Lelio R Paula | 09/2015 |
3816 | (17*2^472789-1)/187347 | 142320 | Lelio R Paula | 09/2015 |
3817 | 36915^7162+7162^36915 | 142309 | Hans Havermann | 05/2021 |
3818 | 2^472634-109511 | 142278 | Enzo Doria | 04/2014 |
3819 | 31870^28997+28997^31870 | 142216 | Hans Havermann | 06/2021 |
3820 | (48^84589+1)/49 | 142213 | Robert Price | 01/2014 |
3821 | 7*10^142189+87 | 142190 | Robert Price | 07/2019 |
3822 | 2^472258+7 | 142164 | Lelio R Paula | 08/2015 |
3823 | 40135^3484+3484^40135 | 142162 | Hans Havermann | 05/2021 |
3824 | 9*33^93598+26 | 142131 | Eric Chen | 12/2023 |
3825 | (23*10^142105+91)/3 | 142106 | Robert Price | 08/2019 |
3826 | tau(317^10330) | 142098 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
3827 | (11*2^471913-1)/21 | 142060 | Lelio R Paula | 09/2015 |
3828 | (16*10^142058+197)/3 | 142059 | Robert Price | 04/2019 |
3829 | 9*10^142037+91 | 142038 | Robert Price | 10/2020 |
3830 | (4*10^142034+17)/3 | 142035 | Tyler Busby | 01/2023 |
3831 | 2^471792+1880881 | 142024 | Enzo Doria | 11/2016 |
3832 | (509*10^142018+31)/9 | 142020 | Robert Price | 08/2022 |
3833 | (31*2^471580-1)/135 | 141960 | Lelio R Paula | 08/2015 |
3834 | (4*10^141926-79)/3 | 141927 | Robert Price | 02/2018 |
3835 | 2^471464-111546435 | 141925 | Paul Bourdelais | 10/2021 |
3836 | (904*19^110984-1)/3 | 141924 | Curtis Bright | 05/2015 |
3837 | (14*10^141853+37)/3 | 141854 | Robert Price | 12/2018 |
3838 | (41*10^141836-59)/9 | 141837 | Robert Price | 10/2018 |
3839 | 4*5^202913-9 | 141831 | Lelio R Paula | 04/2015 |
3840 | 2*7^167812-3 | 141818 | Lelio R Paula | 12/2014 |
3841 | 2^471043+35 | 141799 | Robert Price | 11/2015 |
3842 | (11*2^470956-1)/7945 | 141770 | Lelio R Paula | 08/2015 |
3843 | 43636^1773+1773^43636 | 141761 | Hans Havermann | 05/2021 |
3844 | (2*10^141751-17)/3 | 141751 | Serge Batalov | 11/2022 |
3845 | (53*10^141722-611)/9 | 141723 | Robert Price | 02/2022 |
3846 | (11*10^141718-131)/3 | 141719 | Robert Price | 09/2018 |
3847 | (61*10^141716+47)/9 | 141717 | Robert Price | 07/2022 |
3848 | 26057^32088-32088^26057 | 141699 | Frank Doornink | 03/2024 |
3849 | 2^470692+76771 | 141693 | Enzo Doria | 05/2016 |
3850 | 50160^667+667^50160 | 141659 | Hans Havermann | 05/2021 |
3851 | 31522^31181+31181^31522 | 141657 | Hans Havermann | 05/2021 |
3852 | 29487^31690-31690^29487 | 141643 | Frank Doornink | 06/2024 |
3853 | 33076^19135+19135^33076 | 141626 | Hans Havermann | 04/2021 |
3854 | 28237^31818-31818^28237 | 141617 | Frank Doornink | 06/2024 |
3855 | (91*10^141610+71)/9 | 141612 | Robert Price | 01/2022 |
3856 | (21*2^470391+1)/533 | 141601 | Lelio R Paula | 09/2015 |
3857 | (5*10^141594-23)/9 | 141594 | Serge Batalov | 11/2022 |
3858 | 31932^27155+27155^31932 | 141582 | Hans Havermann | 05/2021 |
3859 | 36449^7660+7660^36449 | 141577 | Hans Havermann | 05/2021 |
3860 | 2^470305-459373 | 141576 | Enzo Doria | 05/2015 |
3861 | 32195^24936+24936^32195 | 141556 | Hans Havermann | 05/2021 |
3862 | 2^470183+72623 | 141540 | Enzo Doria | 04/2016 |
3863 | 2^470173-16465 | 141537 | Enzo Doria | 04/2013 |
3864 | 37297^6234+6234^37297 | 141534 | Hans Havermann | 05/2021 |
3865 | (509*10^141479+13)/9 | 141481 | Robert Price | 05/2022 |
3866 | 44*10^141476+9 | 141478 | Robert Price | 10/2020 |
3867 | 2^469974-1841 | 141477 | Enzo Doria | 05/2014 |
3868 | (23*2^469939+1)/25 | 141466 | Lelio R Paula | 08/2015 |
3869 | 312*33^93158+23 | 141465 | Eric Chen | 12/2023 |
3870 | 2*10^141448+63 | 141449 | Robert Price | 05/2018 |
3871 | 2^469824+43 | 141432 | Lelio R Paula | 09/2017 |
3872 | 2*10^141407-27 | 141408 | Robert Price | 05/2018 |
3873 | (214*10^141385-1)/3 | 141387 | Robert Price | 01/2021 |
3874 | 2^469630-59711 | 141373 | Enzo Doria | 10/2015 |
3875 | 35277^10172+10172^35277 | 141370 | Hans Havermann | 04/2021 |
3876 | 33397^17100+17100^33397 | 141370 | Hans Havermann | 04/2021 |
3877 | (25*10^141366-331)/9 | 141367 | Robert Price | 08/2018 |
3878 | 36986^6639+6639^36986 | 141365 | Hans Havermann | 06/2021 |
3879 | 34572^12271+12271^34572 | 141361 | Hans Havermann | 06/2021 |
3880 | 37179^6338+6338^37179 | 141353 | Hans Havermann | 05/2021 |
3881 | (2^469564-3)/611 | 141351 | Lelio R Paula | 08/2015 |
3882 | 197^61601+2 | 141342 | Lelio R Paula | 08/2017 |
3883 | 33420^16951+16951^33420 | 141340 | Hans Havermann | 05/2021 |
3884 | 31623^29458+29458^31623 | 141330 | Hans Havermann | 05/2021 |
3885 | 48112^865+865^48112 | 141306 | Hans Havermann | 05/2021 |
3886 | 2^469372-112949 | 141296 | Enzo Doria | 07/2014 |
3887 | 5*10^141294-63 | 141295 | Robert Price | 04/2021 |
3888 | 3^296115+4 | 141283 | Tyler NeSmith | 01/2021 |
3889 | (64*10^141256+161)/9 | 141257 | Robert Price | 08/2022 |
3891 | 143^(2^16)+106^(2^16) | 141253 | Valeryi Kuryshev | 02/2011 |
3890 | 143^65536+106^65536 | 141253 | Serge Batalov | 03/2018 |
3892 | (11*10^141243-23)/3 | 141244 | Robert Price | 09/2021 |
3894 | 2^469198+782569 | 141243 | Enzo Doria | 10/2016 |
3893 | 38129^5062+5062^38129 | 141243 | Hans Havermann | 05/2021 |
3895 | 2^469076-2786939 | 141206 | Enzo Doria | 11/2015 |
3896 | 38630^4521+4521^38630 | 141202 | Hans Havermann | 05/2021 |
3897 | 31755^27836+27836^31755 | 141139 | Hans Havermann | 05/2021 |
3898 | 35554^9325+9325^35554 | 141137 | Hans Havermann | 05/2021 |
3899 | 2^468804+1874941 | 141125 | Enzo Doria | 06/2016 |
3900 | 2^468787+81353 | 141119 | Enzo Doria | 08/2016 |
3901 | 30204^31493-31493^30204 | 141091 | Frank Doornink | 06/2024 |
3902 | 2^468595-350407 | 141062 | Enzo Doria | 06/2015 |
3903 | 2^468564+87855 | 141052 | Lelio R Paula | 01/2016 |
3904 | 2^468551-21987 | 141048 | Enzo Doria | 07/2013 |
3905 | 2^468523-7 | 141040 | Lelio R Paula | 08/2015 |
3906 | (25*10^141019-13)/3 | 141020 | Robert Price | 09/2019 |
3907 | 2^468405+87855 | 141004 | Lelio R Paula | 01/2016 |
3908 | 39338^3831+3831^39338 | 140961 | Hans Havermann | 05/2021 |
3909 | 31458^30239+30239^31458 | 140950 | Hans Havermann | 05/2021 |
3910 | 8*10^140932+29 | 140933 | Robert Price | 11/2021 |
3911 | 33166^17691+17691^33166 | 140881 | Hans Havermann | 06/2021 |
3912 | 2^467978-113051 | 140876 | Enzo Doria | 07/2014 |
3913 | 2^467780-344429 | 140816 | Enzo Doria | 07/2015 |
3914 | 9*10^140802-89 | 140803 | Robert Price | 04/2020 |
3915 | 2^467605-1855603 | 140764 | Enzo Doria | 09/2015 |
3916 | (9^147503-5^147503)/4 | 140754 | Jon Grantham | 07/2023 |
3917 | 5*10^140744-7 | 140745 | Robert Price | 09/2015 |
3918 | (5^201359-1)/4 | 140744 | Paul Bourdelais | 12/2008 |
3919 | 2^467401-1850023 | 140702 | Enzo Doria | 08/2015 |
3920 | (14*10^140693+13)/9 | 140694 | Tyler Busby | 02/2023 |
3921 | (266*10^140681-17)/3 | 140683 | Robert Price | 07/2020 |
3922 | (2^467270+78557)/23247 | 140658 | Lelio R Paula | 07/2015 |
3923 | 32138^23781+23781^32138 | 140644 | Hans Havermann | 05/2021 |
3924 | 31654^27735+27735^31654 | 140640 | Hans Havermann | 05/2021 |
3925 | (29*2^467205+1)/2780517107 | 140635 | Lelio R Paula | 08/2015 |
3926 | 2^467166-1854941 | 140631 | Enzo Doria | 09/2015 |
3927 | (203*10^140615-11)/3 | 140617 | Robert Price | 12/2020 |
3928 | (85*10^140609+473)/9 | 140610 | Robert Price | 01/2020 |
3929 | 39231^3836+3836^39231 | 140600 | Hans Havermann | 06/2021 |
3930 | 5*3^294676+2^294676 | 140597 | Jon Grantham | 08/2023 |
3931 | 2^466866-1840571 | 140541 | Enzo Doria | 06/2015 |
3932 | 2^466829-459523 | 140530 | Enzo Doria | 05/2015 |
3933 | 2^466692-113213 | 140489 | Enzo Doria | 07/2014 |
3934 | 23*10^140464-3 | 140466 | Robert Price | 10/2021 |
3935 | (2*10^140461-17)/3 | 140461 | Serge Batalov | 11/2022 |
3936 | 31335^30364+30364^31335 | 140455 | Hans Havermann | 05/2021 |
3937 | 28511^31524-31524^28511 | 140440 | Frank Doornink | 06/2024 |
3938 | 32795^19126+19126^32795 | 140416 | Hans Havermann | 05/2021 |
3939 | (44*10^140410-503)/9 | 140411 | Robert Price | 12/2018 |
3940 | 28332^31535-31535^28332 | 140403 | Frank Doornink | 06/2024 |
3941 | 153^64265-2 | 140400 | Lelio R Paula | 11/2017 |
3942 | 30323^31322-31322^30323 | 140379 | Frank Doornink | 06/2024 |
3943 | (112*10^140357-1)/3 | 140359 | Serge Batalov | 12/2014 |
3944 | (29*10^140337-17)/3 | 140338 | Robert Price | 09/2019 |
3945 | 2^466181-112735 | 140335 | Enzo Doria | 07/2014 |
3946 | (16*10^140290-37)/3 | 140291 | Robert Price | 05/2021 |
3947 | (5*10^140281-119)/3 | 140282 | Robert Price | 03/2018 |
3948 | 34568^11415+11415^34568 | 140259 | Hans Havermann | 05/2021 |
3949 | (27*2^465872+1)/691 | 140241 | Lelio R Paula | 08/2015 |
3950 | 33632^14781+14781^33632 | 140236 | Hans Havermann | 05/2021 |
3951 | 31803^25670+25670^31803 | 140233 | Hans Havermann | 05/2021 |
3952 | 2^465803-114817 | 140221 | Enzo Doria | 05/2015 |
3953 | floor(Pi*10^140344)%10^140165 | 140165 | Serge Batalov | 08/2012 |
3954 | 2^465503-112735 | 140131 | Enzo Doria | 07/2014 |
3955 | (16*10^140091+167)/3 | 140092 | Robert Price | 06/2019 |
3956 | (8*10^140087-137)/3 | 140088 | Robert Price | 03/2022 |
3957 | 6^179964+179964^6-1 | 140040 | Robert Price | 04/2014 |
3958 | (89*10^140008-179)/9 | 140009 | Robert Price | 12/2019 |
3959 | (29*2^465077-1)/9 | 140003 | Lelio R Paula | 08/2015 |
3960 | 2^465072-344789 | 140001 | Enzo Doria | 07/2015 |
3961 | 34742^10683+10683^34742 | 139965 | Hans Havermann | 05/2021 |
3962 | 5*10^139945+81 | 139946 | Robert Price | 03/2019 |
3963 | 32648^19335+19335^32648 | 139941 | Hans Havermann | 05/2021 |
3964 | 2^464864-17 | 139939 | Lelio R Paula | 09/2017 |
3965 | 8*10^139920+51 | 139921 | Robert Price | 08/2019 |
3966 | (85*10^139913-1)/3 | 139915 | Robert Price | 02/2020 |
3967 | 31203^30436+30436^31203 | 139896 | Hans Havermann | 04/2021 |
3968 | 2^464642+22189 | 139872 | Enzo Doria | 09/2023 |
3969 | 26138^31663-31663^26138 | 139865 | Frank Doornink | 03/2024 |
3970 | (16^116139+619)/5 | 139845 | Anonymous | 08/2022 |
3971 | (2^464556+619)/5 | 139845 | Eric Chen | 10/2023 |
3972 | 4*10^139839-27 | 139840 | Robert Price | 08/2021 |
3973 | 33582^14573+14573^33582 | 139821 | Hans Havermann | 05/2021 |
3974 | (17^113621+1)/18 | 139804 | Paul Bourdelais | 09/2011 |
3976 | 2*10^139800-21 | 139801 | Robert Price | 09/2020 |
3975 | 32628^19261+19261^32628 | 139801 | Hans Havermann | 04/2021 |
3977 | (13*10^139782+191)/3 | 139783 | Robert Price | 11/2018 |
3978 | (64*10^139776+791)/9 | 139777 | Robert Price | 01/2022 |
3979 | (695*10^139772+7)/9 | 139774 | Robert Price | 12/2021 |
3980 | (19*2^464312-1)/3 | 139773 | Lelio R Paula | 08/2015 |
3981 | (74*10^139723+133)/9 | 139724 | Robert Price | 06/2019 |
3982 | 3*10^139722+13 | 139723 | Robert Price | 07/2018 |
3983 | 31577^26592+26592^31577 | 139721 | Hans Havermann | 05/2021 |
3984 | 77*10^139692+3 | 139694 | Robert Price | 06/2020 |
3985 | (31*2^463970+1)/5 | 139670 | Lelio R Paula | 08/2015 |
3986 | (18203^(2^15)+(18201)^(2^15))/2 | 139597 | Robert Price | 05/2018 |
3987 | 39640^3321+3321^39640 | 139584 | Hans Havermann | 05/2021 |
3988 | 36663^6410+6410^36663 | 139571 | Hans Havermann | 05/2021 |
3989 | 2^463633-2788423 | 139568 | Enzo Doria | 11/2015 |
3990 | 33659^13978+13978^33659 | 139532 | Hans Havermann | 05/2021 |
3991 | 31811^24318+24318^31811 | 139521 | Hans Havermann | 04/2021 |
3992 | 34149^12172+12172^34149 | 139512 | Hans Havermann | 04/2021 |
3993 | (29*10^139476+313)/9 | 139477 | Robert Price | 04/2021 |
3994 | 31721^24940+24940^31721 | 139474 | Hans Havermann | 05/2021 |
3995 | 32833^17698+17698^32833 | 139473 | Hans Havermann | 05/2021 |
3996 | 2^463271-109501 | 139459 | Enzo Doria | 04/2014 |
3997 | (5*10^139457+79)/3 | 139458 | Robert Price | 03/2018 |
3998 | 2^463237-99 | 139449 | Lelio R Paula | 09/2017 |
3999 | (49*10^139442+383)/9 | 139443 | Robert Price | 04/2019 |
4000 | 31155^29902+29902^31155 | 139441 | Hans Havermann | 05/2021 |