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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3751 | 2^486893-79 | 146570 | Yves Minet | 09/2017 |
| 3752 | 36818^9567+9567^36818 | 146565 | Hans Havermann | 12/2020 |
| 3753 | 2^486840+1879141 | 146554 | Enzo Doria | 08/2016 |
| 3754 | 2^486774-87 | 146534 | Lelio R Paula | 12/2017 |
| 3755 | 38655^6176+6176^38655 | 146530 | Hans Havermann | 11/2020 |
| 3756 | 8*10^146522-81 | 146523 | Robert Price | 02/2021 |
| 3757 | 32820^29059+29059^32820 | 146485 | Hans Havermann | 12/2020 |
| 3758 | 37261^8530+8530^37261 | 146472 | Hans Havermann | 12/2020 |
| 3759 | 66953^154+154^66953 | 146462 | Hans Havermann | 12/2020 |
| 3760 | 96^73877-95^73877 | 146445 | Robert Price | 10/2015 |
| 3761 | 8*10^146421+81 | 146422 | Robert Price | 08/2019 |
| 3762 | 33153^26090+26090^33153 | 146420 | Hans Havermann | 11/2020 |
| 3763 | 2^486275+23961 | 146384 | Enzo Doria | 10/2023 |
| 3764 | (52^85259+1)/53 | 146304 | Paul Bourdelais | 09/2017 |
| 3765 | 179^64935+2 | 146290 | Lelio R Paula | 10/2017 |
| 3766 | 32595^30758+30758^32595 | 146285 | Hans Havermann | 11/2020 |
| 3767 | 34972^15157+15157^34972 | 146205 | Hans Havermann | 12/2020 |
| 3768 | (16*10^146200+131)/3 | 146201 | Robert Price | 03/2022 |
| 3769 | (19*10^146181-49)/3 | 146182 | Robert Price | 05/2019 |
| 3770 | 2^485531-114621 | 146160 | Enzo Doria | 05/2015 |
| 3771 | 2^485473-933075 | 146142 | Paul Bourdelais | 06/2021 |
| 3772 | (2^485461-9)/4249 | 146135 | Lelio R Paula | 09/2015 |
| 3773 | (22*10^146130-193)/9 | 146131 | Robert Price | 07/2022 |
| 3774 | 2^485389+81887 | 146117 | Enzo Doria | 08/2016 |
| 3775 | 32554^30773+30773^32554 | 146108 | Hans Havermann | 11/2020 |
| 3776 | 28075^32844-32844^28075 | 146101 | Frank Doornink | 06/2024 |
| 3777 | (10^146063+71)/9 | 146063 | Serge Batalov | 07/2015 |
| 3778 | 2*10^146051-63 | 146052 | Robert Price | 01/2022 |
| 3779 | (2^485119+7)/2745 | 146032 | Lelio R Paula | 09/2015 |
| 3780 | (22*10^146029+257)/9 | 146030 | Robert Price | 06/2018 |
| 3781 | 7*10^145982-53 | 145983 | Robert Price | 06/2020 |
| 3782 | 2^484743+1872923 | 145923 | Enzo Doria | 05/2016 |
| 3783 | 33140^25287+25287^33140 | 145913 | Hans Havermann | 01/2021 |
| 3784 | 37875^7112+7112^37875 | 145895 | Hans Havermann | 01/2021 |
| 3785 | 30542^32529-32529^30542 | 145890 | Frank Doornink | 06/2024 |
| 3786 | 32862^27473+27473^32862 | 145872 | Hans Havermann | 01/2021 |
| 3787 | V(1046652)/2093303 | 145817 | Serge Batalov | 07/2024 |
| 3788 | 32836^27587+27587^32836 | 145815 | Hans Havermann | 01/2021 |
| 3789 | 2^484341+1879157 | 145802 | Enzo Doria | 08/2016 |
| 3790 | 2*10^145784-91 | 145785 | Robert Price | 04/2020 |
| 3791 | 2^484271-51 | 145781 | Lelio R Paula | 11/2017 |
| 3792 | (188*10^145750-11)/3 | 145752 | Robert Price | 02/2022 |
| 3793 | 70^78989-69^78989 | 145743 | Robert Price | 01/2014 |
| 3794 | 51^85334+2 | 145714 | Robert Price | 07/2015 |
| 3795 | 2^483886-1857101 | 145665 | Enzo Doria | 10/2015 |
| 3796 | 29312^32607-32607^29312 | 145657 | Frank Doornink | 06/2024 |
| 3797 | 33350^23307+23307^33350 | 145656 | Hans Havermann | 01/2021 |
| 3798 | (19*10^145585+131)/3 | 145586 | Robert Price | 06/2020 |
| 3799 | 31815^32332-32332^31815 | 145580 | Frank Doornink | 01/2024 |
| 3800 | 2^483563-1863457 | 145567 | Enzo Doria | 12/2015 |
| 3801 | 4*10^145563-69 | 145564 | Robert Price | 01/2022 |
| 3802 | 2^483516-1861409 | 145553 | Enzo Doria | 11/2015 |
| 3803 | 2^483384-115019 | 145514 | Enzo Doria | 06/2015 |
| 3804 | (259*10^145501-1)/3 | 145503 | Robert Price | 12/2020 |
| 3805 | (19*10^145499-61)/3 | 145500 | Robert Price | 05/2019 |
| 3806 | 2^483302-3221 | 145489 | Lelio R Paula | 12/2012 |
| 3807 | (23*10^145463+61)/3 | 145464 | Robert Price | 01/2022 |
| 3808 | 35523^12434+12434^35523 | 145453 | Hans Havermann | 01/2021 |
| 3809 | (29121^32761-1)/(29121^181-1) | 145444 | Ryan Propper | 11/2023 |
| 3810 | 2^483046+1874029 | 145412 | Enzo Doria | 06/2016 |
| 3811 | 2^482991-2789317 | 145395 | Enzo Doria | 12/2015 |
| 3812 | 2^482978-2789711 | 145391 | Enzo Doria | 12/2015 |
| 3813 | 2^482966-2789711 | 145388 | Enzo Doria | 12/2015 |
| 3814 | 2^482817-1858843 | 145343 | Enzo Doria | 10/2015 |
| 3815 | 2^482751-113635 | 145323 | Enzo Doria | 08/2014 |
| 3816 | 2^482705-459763 | 145309 | Enzo Doria | 05/2015 |
| 3817 | (4^241306+11)/3 | 145281 | Robert Price | 03/2017 |
| 3818 | (238*10^145276-1)/3 | 145278 | Robert Price | 04/2020 |
| 3819 | (19*2^482534+1)/7 | 145258 | Lelio R Paula | 09/2015 |
| 3820 | 53^84239-52^84239 | 145252 | Robert Price | 01/2013 |
| 3821 | U(1042497) | 145243 | Serge Batalov | 07/2024 |
| 3822 | 2^482386+212419 | 145213 | Enzo Doria | 08/2023 |
| 3823 | 47952^1067+1067^47952 | 145207 | Hans Havermann | 01/2021 |
| 3824 | (2^482333+5)/9287 | 145193 | Lelio R Paula | 09/2015 |
| 3825 | 2^482087+72623 | 145123 | Enzo Doria | 04/2016 |
| 3826 | 2^482016-286565 | 145102 | Enzo Doria | 07/2015 |
| 3827 | (19*10^145093+101)/3 | 145094 | Robert Price | 09/2019 |
| 3828 | 2^481956+121 | 145084 | Stefano Morozzi | 04/2021 |
| 3829 | 27535^32676-32676^27535 | 145078 | Frank Doornink | 06/2024 |
| 3830 | 2^481840+15 | 145049 | Robert Price | 09/2015 |
| 3831 | (23*10^145040+7)/3 | 145041 | Robert Price | 05/2023 |
| 3832 | 2^481801-481801 | 145037 | Henri Lifchitz | 03/2005 |
| 3833 | 2^481775+1869083 | 145029 | Enzo Doria | 05/2016 |
| 3834 | 29^99167+2 | 145022 | Ray Chandler | 08/2011 |
| 3835 | 2^481663+1875653 | 144996 | Enzo Doria | 07/2016 |
| 3836 | 8*10^144977+27 | 144978 | Robert Price | 09/2021 |
| 3837 | 29840^32393-32393^29840 | 144953 | Frank Doornink | 06/2024 |
| 3838 | 36486^9379+9379^36486 | 144929 | Hans Havermann | 12/2020 |
| 3839 | 31580^32209-32209^31580 | 144922 | Frank Doornink | 01/2024 |
| 3840 | 35111^13378+13378^35111 | 144882 | Hans Havermann | 01/2021 |
| 3841 | 2^481149-459073 | 144841 | Enzo Doria | 05/2015 |
| 3842 | 2^481113+181419 | 144830 | Boyan Hu | 04/2024 |
| 3843 | 34619^15246+15246^34619 | 144817 | Hans Havermann | 01/2021 |
| 3844 | 2^481045-113215 | 144809 | Enzo Doria | 07/2014 |
| 3845 | (64*10^144797+287)/9 | 144798 | Robert Price | 04/2019 |
| 3846 | 27320^32629-32629^27320 | 144758 | Frank Doornink | 06/2024 |
| 3847 | 2^480859-113695 | 144753 | Enzo Doria | 09/2014 |
| 3848 | (106*10^144744+17)/3 | 144746 | Robert Price | 04/2021 |
| 3849 | 7*10^144742-27 | 144743 | Robert Price | 11/2022 |
| 3850 | 2^480766-2787191 | 144725 | Enzo Doria | 11/2015 |
| 3851 | (21*27^101106-151)/26 | 144720 | Curtis Bright | 05/2015 |
| 3852 | 28915^32438-32438^28915 | 144710 | Frank Doornink | 06/2024 |
| 3853 | 2^480678+1874239 | 144699 | Enzo Doria | 06/2016 |
| 3854 | (8*10^144683+1)/9 | 144683 | Serge Batalov | 05/2010 |
| 3855 | L(692147) | 144651 | Henri Lifchitz | 10/2008 |
| 3856 | (76*10^144648+77)/9 | 144649 | Robert Price | 10/2019 |
| 3857 | 32672^26721+26721^32672 | 144635 | Hans Havermann | 01/2021 |
| 3858 | 31478^32153-32153^31478 | 144625 | Frank Doornink | 01/2024 |
| 3859 | 2^480417+35 | 144620 | Robert Price | 11/2015 |
| 3860 | 2^480296-59879 | 144584 | Enzo Doria | 10/2015 |
| 3861 | 33157^22878+22878^33157 | 144546 | Hans Havermann | 12/2020 |
| 3862 | 27520^32541-32541^27520 | 144471 | Frank Doornink | 06/2024 |
| 3863 | 45494^1497+1497^45494 | 144454 | Hans Havermann | 12/2020 |
| 3864 | 2^479844+3 | 144448 | Donovan Johnson | 06/2006 |
| 3865 | 33442^20803+20803^33442 | 144407 | Hans Havermann | 01/2021 |
| 3866 | (441*33^95095-3833)/32 | 144405 | Eric Chen | 12/2023 |
| 3867 | 31892^32061-32061^31892 | 144393 | Norbert Schneider | 01/2023 |
| 3868 | (27*2^479642+1)/733 | 144386 | Lelio R Paula | 08/2015 |
| 3869 | (56*10^144380+169)/9 | 144381 | Robert Price | 03/2022 |
| 3870 | 44917^1638+1638^44917 | 144378 | Hans Havermann | 12/2020 |
| 3871 | (21*2^479605-1)/11 | 144376 | Lelio R Paula | 09/2015 |
| 3872 | (56*10^144336+583)/9 | 144337 | Robert Price | 08/2021 |
| 3873 | 5*2^479430-3 | 144324 | Jon Grantham | 07/2023 |
| 3874 | 2^479348-2792219 | 144299 | Enzo Doria | 02/2016 |
| 3875 | 31134^32111-32111^31134 | 144283 | Frank Doornink | 01/2024 |
| 3876 | 3^302389-6242 | 144277 | Enzo Doria | 05/2014 |
| 3877 | 31665^32056-32056^31665 | 144271 | Frank Doornink | 01/2024 |
| 3878 | 33778^18641+18641^33778 | 144248 | Hans Havermann | 01/2021 |
| 3879 | 29083^32312-32312^29083 | 144230 | Frank Doornink | 06/2024 |
| 3880 | 2*10^144220-3 | 144221 | Robert Price | 07/2015 |
| 3881 | 25313^32750-32750^25313 | 144210 | Frank Doornink | 01/2024 |
| 3882 | 2^478904-109109 | 144165 | Enzo Doria | 04/2014 |
| 3883 | 43698^1987+1987^43698 | 144125 | Hans Havermann | 12/2020 |
| 3884 | 79^75948+75948 | 144121 | Kellen Shenton | 06/2023 |
| 3885 | 26941^32522-32522^26941 | 144086 | Frank Doornink | 06/2024 |
| 3886 | 36128^9723+9723^36128 | 144072 | Hans Havermann | 01/2021 |
| 3887 | 32817^24518+24518^32817 | 144050 | Hans Havermann | 12/2020 |
| 3888 | (772*10^144036-7)/9 | 144038 | Robert Price | 06/2022 |
| 3889 | 34295^15828+15828^34295 | 144020 | Hans Havermann | 01/2021 |
| 3890 | 2^478337-115333 | 143994 | Enzo Doria | 07/2015 |
| 3891 | (7*2^478330-1)/3 | 143993 | Lelio R Paula | 08/2015 |
| 3892 | 88^74047-87^74047 | 143984 | Robert Price | 05/2015 |
| 3893 | 33242^21441+21441^33242 | 143980 | Hans Havermann | 01/2021 |
| 3894 | (19*10^143963+467)/9 | 143964 | Robert Price | 02/2018 |
| 3895 | (71^77761+1)/72 | 143954 | Paul Bourdelais | 09/2017 |
| 3896 | 33490^19859+19859^33490 | 143939 | Hans Havermann | 01/2021 |
| 3897 | (853*10^143931-7)/9 | 143933 | Robert Price | 07/2021 |
| 3898 | 2^478088+27 | 143919 | Robert Price | 11/2015 |
| 3899 | (8*10^143898-137)/3 | 143899 | Robert Price | 03/2022 |
| 3900 | 7*10^143857-93 | 143858 | Robert Price | 08/2020 |
| 3901 | 3*10^143844+61 | 143845 | Robert Price | 09/2020 |
| 3902 | 41358^3005+3005^41358 | 143837 | Hans Havermann | 01/2021 |
| 3903 | 2^477475-22071 | 143735 | Enzo Doria | 07/2013 |
| 3904 | 2^477417-22123 | 143717 | Enzo Doria | 07/2013 |
| 3905 | 2^477359-3577 | 143700 | Yves Minet | 03/2017 |
| 3906 | 39435^4402+4402^39435 | 143688 | Hans Havermann | 01/2021 |
| 3907 | (14*10^143662-71)/3 | 143663 | Robert Price | 12/2018 |
| 3908 | 6^184614+5 | 143658 | Paul Bourdelais | 01/2021 |
| 3909 | 46371^1252+1252^46371 | 143640 | Hans Havermann | 12/2020 |
| 3910 | 34975^12748+12748^34975 | 143588 | Hans Havermann | 01/2021 |
| 3911 | 2^476936-396765 | 143573 | Enzo Doria | 07/2013 |
| 3912 | 2^476888-2791229 | 143558 | Enzo Doria | 01/2016 |
| 3913 | 2^476868-1859939 | 143552 | Enzo Doria | 11/2015 |
| 3914 | 40807^3294+3294^40807 | 143548 | Hans Havermann | 12/2020 |
| 3915 | 755^49878+49878^755 | 143547 | Norbert Schneider | 04/2019 |
| 3916 | (19^112247-4^112247)/15 | 143536 | Robert Price | 03/2021 |
| 3917 | 35561^10872+10872^35561 | 143536 | Hans Havermann | 06/2021 |
| 3918 | 37637^6492+6492^37637 | 143487 | Hans Havermann | 05/2021 |
| 3919 | 61567^214+214^61567 | 143477 | Hans Havermann | 05/2021 |
| 3920 | 25933^32504-32504^25933 | 143468 | Frank Doornink | 03/2024 |
| 3921 | 2^476558-113627 | 143459 | Enzo Doria | 08/2014 |
| 3922 | 2^476478-45 | 143435 | Lelio R Paula | 11/2017 |
| 3923 | 36380^8757+8757^36380 | 143423 | Hans Havermann | 06/2021 |
| 3924 | 32510^25707+25707^32510 | 143371 | Hans Havermann | 05/2021 |
| 3925 | 8*10^143361+17 | 143362 | Robert Price | 07/2021 |
| 3926 | (2^475854+9)/73 | 143245 | Lelio R Paula | 08/2015 |
| 3927 | 2^475813-113239 | 143234 | Enzo Doria | 07/2014 |
| 3928 | (19*10^143212+137)/3 | 143213 | Robert Price | 03/2022 |
| 3929 | 32218^27849+27849^32218 | 143203 | Hans Havermann | 04/2021 |
| 3930 | 580*33^94296+19 | 143193 | Eric Chen | 12/2023 |
| 3931 | 2^475624-114059 | 143178 | Enzo Doria | 11/2014 |
| 3932 | (11*2^475553-7)/15 | 143156 | Renaud Lifchitz | 03/2011 |
| 3933 | 2^475480-2786129 | 143134 | Enzo Doria | 10/2015 |
| 3934 | 33912^16621+16621^33912 | 143131 | Hans Havermann | 05/2021 |
| 3935 | (19*10^143129-43)/3 | 143130 | Robert Price | 05/2019 |
| 3936 | 31830^31373+31373^31830 | 143126 | Hans Havermann | 05/2021 |
| 3937 | 6*10^143105-53 | 143106 | Robert Price | 05/2021 |
| 3938 | (14*10^143097+73)/3 | 143098 | Robert Price | 12/2018 |
| 3939 | 2^475299-111937 | 143080 | Enzo Doria | 05/2014 |
| 3940 | 35488^10753+10753^35488 | 143071 | Hans Havermann | 04/2021 |
| 3941 | 29695^31986-31986^29695 | 143064 | Frank Doornink | 06/2024 |
| 3942 | 2^475160-2797859 | 143038 | Enzo Doria | 04/2016 |
| 3943 | (2^475069+3)/395 | 143008 | Lelio R Paula | 08/2015 |
| 3944 | 2^475027-461437 | 142998 | Enzo Doria | 07/2015 |
| 3945 | (2^474958+78557)/3 | 142977 | Lelio R Paula | 07/2015 |
| 3946 | (8*10^142932+43)/3 | 142933 | Robert Price | 06/2018 |
| 3947 | 35055^11942+11942^35055 | 142922 | Hans Havermann | 05/2021 |
| 3948 | 37650^6239+6239^37650 | 142887 | Hans Havermann | 05/2021 |
| 3949 | (54^82471-1)/53 | 142871 | Paul Bourdelais | 09/2017 |
| 3950 | 31205^31784-31784^31205 | 142845 | Frank Doornink | 01/2024 |
| 3951 | (11*2^474432-1)/95 | 142818 | Lelio R Paula | 09/2015 |
| 3952 | 2^474417-59923 | 142814 | Enzo Doria | 10/2015 |
| 3953 | 4*10^142810-21 | 142811 | Robert Price | 09/2018 |
| 3954 | 32287^26494+26494^32287 | 142811 | Hans Havermann | 06/2021 |
| 3955 | 37162^6965+6965^37162 | 142811 | Hans Havermann | 06/2021 |
| 3956 | (34*10^142805-601)/9 | 142806 | Robert Price | 07/2022 |
| 3957 | 37456^6493+6493^37456 | 142799 | Hans Havermann | 05/2021 |
| 3958 | 35141^11572+11572^35141 | 142793 | Hans Havermann | 05/2021 |
| 3959 | 32231^26908+26908^32231 | 142780 | Hans Havermann | 05/2021 |
| 3960 | (3*2^474166+1)/7 | 142738 | Lelio R Paula | 08/2015 |
| 3961 | 2^474053+2897 | 142705 | Lelio R Paula | 08/2012 |
| 3962 | (10^142699+359)/9 | 142699 | Serge Batalov | 12/2014 |
| 3963 | 26073^32312-32312^26073 | 142696 | Frank Doornink | 03/2024 |
| 3964 | 898^48311-897^48311 | 142676 | Jean-Louis Charton | 12/2012 |
| 3965 | 2^473740-1856639 | 142610 | Enzo Doria | 09/2015 |
| 3966 | (25*10^142573-403)/9 | 142574 | Robert Price | 12/2020 |
| 3967 | 2^473617-114223 | 142573 | Enzo Doria | 12/2014 |
| 3968 | 36115^8856+8856^36115 | 142555 | Hans Havermann | 05/2021 |
| 3969 | fibonacci(682007)+4 | 142531 | Jon Grantham | 08/2023 |
| 3970 | 2^473257+1873217 | 142465 | Enzo Doria | 06/2016 |
| 3971 | (19*2^473242+1)/11 | 142461 | Lelio R Paula | 09/2015 |
| 3972 | 32750^22371+22371^32750 | 142453 | Hans Havermann | 06/2021 |
| 3973 | (61*10^142446-1)/3 | 142448 | Robert Price | 01/2020 |
| 3974 | (14*10^142440+61)/3 | 142441 | Robert Price | 12/2018 |
| 3975 | (10^142425+359)/9 | 142425 | Serge Batalov | 12/2014 |
| 3976 | 2^473101+773027 | 142418 | Enzo Doria | 05/2016 |
| 3977 | (13*2^472838-1)/3 | 142340 | Lelio R Paula | 09/2015 |
| 3978 | (17*2^472789-1)/187347 | 142320 | Lelio R Paula | 09/2015 |
| 3979 | 36915^7162+7162^36915 | 142309 | Hans Havermann | 05/2021 |
| 3980 | 2^472634-109511 | 142278 | Enzo Doria | 04/2014 |
| 3981 | 31870^28997+28997^31870 | 142216 | Hans Havermann | 06/2021 |
| 3982 | (48^84589+1)/49 | 142213 | Robert Price | 01/2014 |
| 3983 | 7*10^142189+87 | 142190 | Robert Price | 07/2019 |
| 3984 | 2^472258+7 | 142164 | Lelio R Paula | 08/2015 |
| 3985 | 40135^3484+3484^40135 | 142162 | Hans Havermann | 05/2021 |
| 3986 | 9*33^93598+26 | 142131 | Eric Chen | 12/2023 |
| 3987 | (23*10^142105+91)/3 | 142106 | Robert Price | 08/2019 |
| 3988 | tau(317^10330) | 142098 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 3989 | (11*2^471913-1)/21 | 142060 | Lelio R Paula | 09/2015 |
| 3990 | (16*10^142058+197)/3 | 142059 | Robert Price | 04/2019 |
| 3991 | 9*10^142037+91 | 142038 | Robert Price | 10/2020 |
| 3992 | (4*10^142034+17)/3 | 142035 | Tyler Busby | 01/2023 |
| 3993 | 2^471792+1880881 | 142024 | Enzo Doria | 11/2016 |
| 3994 | (509*10^142018+31)/9 | 142020 | Robert Price | 08/2022 |
| 3995 | (31*2^471580-1)/135 | 141960 | Lelio R Paula | 08/2015 |
| 3996 | (4*10^141926-79)/3 | 141927 | Robert Price | 02/2018 |
| 3997 | 2^471464-111546435 | 141925 | Paul Bourdelais | 10/2021 |
| 3998 | (904*19^110984-1)/3 | 141924 | Curtis Bright | 05/2015 |
| 3999 | (14*10^141853+37)/3 | 141854 | Robert Price | 12/2018 |
| 4000 | (41*10^141836-59)/9 | 141837 | Robert Price | 10/2018 |
