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 ? |
| 2751 | (20^140053+1)/21 | 182212 | Paul Bourdelais | 04/2010 |
| 2752 | (14*10^182177-221)/9 | 182178 | Robert Price | 04/2018 |
| 2753 | 2^605174-112751 | 182176 | Enzo Doria | 06/2014 |
| 2754 | (905^61609-1)/904 | 182154 | Anonymous | 05/2024 |
| 2755 | 2^604761+1874507 | 182052 | Enzo Doria | 06/2016 |
| 2756 | 2^604705+1871957 | 182035 | Enzo Doria | 05/2016 |
| 2757 | (14*10^182000+229)/9 | 182001 | Robert Price | 03/2018 |
| 2758 | (10^181996+41)/3 | 181996 | Robert Price | 12/2017 |
| 2759 | (17*10^181979+91)/9 | 181980 | Robert Price | 02/2022 |
| 2760 | (10^181960+3)/7 | 181960 | Jinyuan Wang | 11/2024 |
| 2761 | (5*10^181950-101)/3 | 181951 | Robert Price | 04/2018 |
| 2762 | 2^603915+75233 | 181797 | Enzo Doria | 04/2016 |
| 2763 | 39470^39537+39537^39470 | 181723 | Norbert Schneider | 12/2022 |
| 2764 | (10^181710+7)/563747/2019847 | 181698 | Alfred Reich | 08/2021 |
| 2765 | 7*10^181594-57 | 181595 | Robert Price | 06/2020 |
| 2766 | 8*10^181580+29 | 181581 | Robert Price | 11/2021 |
| 2767 | (83*10^181544+61)/9 | 181545 | Serge Batalov | 01/2023 |
| 2768 | (2*10^181457+7)/9 | 181457 | Rytis Slatkevicius | 01/2023 |
| 2769 | 3*10^181445+23 | 181446 | Robert Price | 03/2022 |
| 2770 | (194*10^181369-11)/3 | 181371 | Robert Price | 09/2020 |
| 2771 | 11^174145-360 | 181354 | Enzo Doria | 10/2012 |
| 2772 | 2^602351-396765 | 181326 | Enzo Doria | 08/2013 |
| 2773 | 6*10^181306+17 | 181307 | Robert Price | 04/2019 |
| 2774 | (353^71143-1)/352 | 181254 | Anonymous | 04/2024 |
| 2775 | (286*10^181220-1)/3 | 181222 | Robert Price | 11/2020 |
| 2776 | 2^601957-113833 | 181208 | Enzo Doria | 09/2014 |
| 2777 | 66^99581-65^99581 | 181193 | Robert Price | 09/2013 |
| 2778 | 10^181182+383973 | 181183 | Patrick De Geest | 04/2016 |
| 2779 | 10^181182-21 | 181182 | Serge Batalov | 12/2014 |
| 2780 | (797*10^181171-41)/9 | 181173 | Robert Price | 04/2022 |
| 2781 | 2^601722+74209 | 181137 | Enzo Doria | 08/2023 |
| 2782 | (5*10^181127-29)/3 | 181128 | Robert Price | 03/2018 |
| 2783 | 2^601521-29143 | 181076 | Enzo Doria | 07/2015 |
| 2784 | 2^601442-2797811 | 181053 | Enzo Doria | 04/2016 |
| 2785 | 44*10^181029+3 | 181031 | Robert Price | 04/2020 |
| 2786 | 5*10^180992-9 | 180993 | Robert Price | 05/2015 |
| 2787 | 10^180979+79477 | 180980 | Patrick De Geest | 04/2016 |
| 2788 | 10^180979+107739 | 180980 | Patrick De Geest | 04/2016 |
| 2789 | 10^180979-11 | 180979 | Serge Batalov | 12/2014 |
| 2790 | 2^601023-113851 | 180926 | Enzo Doria | 10/2014 |
| 2791 | (23*10^180862-143)/3 | 180863 | Robert Price | 12/2019 |
| 2792 | 3*10^180852+29 | 180853 | Robert Price | 05/2018 |
| 2793 | (277*10^180782-7)/9 | 180784 | Robert Price | 02/2022 |
| 2794 | 2^600412+29851 | 180743 | Enzo Doria | 03/2024 |
| 2795 | (8*10^180725-629)/9 | 180725 | Robert Price | 01/2022 |
| 2796 | (79*10^180710-1)/3 | 180712 | Robert Price | 02/2020 |
| 2797 | 2^600300-1852559 | 180709 | Enzo Doria | 08/2015 |
| 2798 | (2*10^180706-77)/3 | 180706 | Robert Price | 02/2021 |
| 2799 | (156^82393-1)/155 | 180696 | Anonymous | 06/2024 |
| 2800 | (10^180689+71)/9 | 180689 | Serge Batalov | 07/2015 |
| 2801 | 2^600209+76487 | 180681 | Enzo Doria | 05/2016 |
| 2802 | 2^599999+378461 | 180618 | Norman Luhn | 09/2023 |
| 2803 | (8*10^180536-269)/9 | 180536 | Robert Price | 09/2021 |
| 2804 | 2^599702-369885 | 180529 | Enzo Doria | 11/2013 |
| 2805 | Tau(643^11688) | 180524 | Nik Lygeros / Olivier Rozier | 05/2015 |
| 2806 | (2951*29^123418-3)/4 | 180490 | Curtis Bright | 05/2015 |
| 2807 | (29*10^180432-17)/3 | 180433 | Robert Price | 09/2019 |
| 2808 | 4*10^180360+93 | 180361 | Robert Price | 08/2018 |
| 2809 | 2^599035+219323 | 180328 | Enzo Doria | 03/2024 |
| 2810 | 2^598942+80779 | 180300 | Enzo Doria | 07/2016 |
| 2811 | (38*10^180296+403)/9 | 180297 | Robert Price | 10/2018 |
| 2812 | (85*10^180241+77)/9 | 180242 | Robert Price | 07/2022 |
| 2813 | 2^598591-1844797 | 180194 | Enzo Doria | 06/2015 |
| 2814 | (100^90089+1)/101 | 180176 | Paul Bourdelais | 08/2017 |
| 2815 | 2^598301+28517 | 180107 | Enzo Doria | 01/2024 |
| 2816 | (29*10^180072+691)/9 | 180073 | Robert Price | 08/2021 |
| 2817 | (59*10^180038+157)/9 | 180039 | Robert Price | 12/2021 |
| 2818 | 95*10^180019-9 | 180021 | Robert Price | 01/2022 |
| 2819 | 6*10^179970+91 | 179971 | Robert Price | 05/2019 |
| 2820 | (4*10^179963-79)/3 | 179964 | Robert Price | 02/2018 |
| 2821 | (403*10^179944-43)/9 | 179946 | Robert Price | 06/2021 |
| 2822 | Gamma-Prime(179849) | 179849 | Eric W. Weisstein | 06/2011 |
| 2823 | 2^597424-1859729 | 179843 | Enzo Doria | 11/2015 |
| 2824 | Phi(180683,10) | 179760 | Maksym Voznyy | 09/2015 |
| 2825 | (10^180683-1)*9/(10^643-1)/(10^281-1) | 179760 | Robert Price | 07/2016 |
| 2826 | (3^376657-2^376657)/22301107657 | 179701 | Mike Oakes | 04/2017 |
| 2827 | (29*10^179697+223)/9 | 179698 | Robert Price | 09/2018 |
| 2828 | U(1289697) | 179687 | Serge Batalov | 07/2024 |
| 2830 | 2^596884+73 | 179680 | Stefano Morozzi | 04/2021 |
| 2829 | (11*10^179679+13)/3 | 179680 | Robert Price | 03/2022 |
| 2831 | (68*10^179656+7)/3 | 179658 | Robert Price | 01/2020 |
| 2832 | (10^179643+173)/3 | 179643 | Robert Price | 05/2021 |
| 2833 | 2^596690-461261 | 179622 | Enzo Doria | 07/2015 |
| 2834 | 2^596684-113939 | 179620 | Enzo Doria | 10/2014 |
| 2835 | 2^596642+39 | 179608 | Jon Grantham | 08/2023 |
| 2836 | 2*10^179602+63 | 179603 | Robert Price | 05/2018 |
| 2837 | 32262^39815-39815^32262 | 179514 | Frank Doornink | 02/2024 |
| 2838 | (25*10^179488-403)/9 | 179489 | Robert Price | 01/2021 |
| 2839 | 7*10^179460+99 | 179461 | Robert Price | 05/2021 |
| 2840 | 2^596127+74333 | 179453 | Enzo Doria | 07/2023 |
| 2841 | 3^375887-112696 | 179344 | Enzo Doria | 07/2014 |
| 2842 | 4*10^179265-71 | 179266 | Robert Price | 12/2018 |
| 2843 | 2*10^179193+83 | 179194 | Robert Price | 12/2021 |
| 2844 | 2^595144-1850429 | 179157 | Enzo Doria | 08/2015 |
| 2845 | 2^595122-5 | 179150 | Stefano Morozzi | 07/2022 |
| 2846 | 3*10^179138+89 | 179139 | Robert Price | 10/2018 |
| 2847 | (52*10^179062-133)/9 | 179063 | Robert Price | 09/2021 |
| 2848 | 2^594531+82253 | 178972 | Enzo Doria | 09/2016 |
| 2849 | (664*10^178939-61)/9 | 178941 | Robert Price | 09/2021 |
| 2850 | 2^594260-2787899 | 178891 | Enzo Doria | 11/2015 |
| 2851 | (14*10^178822+67)/9 | 178823 | Robert Price | 05/2022 |
| 2852 | (29*10^178732-119)/9 | 178733 | Robert Price | 12/2021 |
| 2853 | 2^593631+101381 | 178701 | Jorge Menendez | 04/2018 |
| 2854 | 10^178695+136719 | 178696 | Patrick De Geest | 05/2016 |
| 2855 | 10^178695-71 | 178695 | Serge Batalov | 12/2014 |
| 2856 | (2*10^178649-161)/3 | 178649 | Robert Price | 12/2020 |
| 2857 | (691^62903-1)/690 | 178609 | Michael Stocker | 05/2020 |
| 2858 | (2^148330+1)^4-2 | 178608 | Cletus Emmanuel | 12/2003 |
| 2859 | 2^593242+28309 | 178584 | Enzo Doria | 01/2024 |
| 2860 | 2^593222-14145 | 178578 | Jorge Menendez | 10/2017 |
| 2861 | 7*10^178566+33 | 178567 | Robert Price | 06/2020 |
| 2862 | 2^593178+1867219 | 178565 | Enzo Doria | 03/2016 |
| 2863 | 2^593152+22441 | 178557 | Enzo Doria | 09/2023 |
| 2864 | (38*10^178456+151)/9 | 178457 | Robert Price | 03/2022 |
| 2865 | (302*10^178369+13)/9 | 178371 | Robert Price | 02/2020 |
| 2866 | (26*10^178296-113)/3 | 178297 | Robert Price | 06/2020 |
| 2867 | (18^142031-1)/17 | 178287 | Paul Bourdelais | 03/2010 |
| 2868 | (13*10^178233+137)/3 | 178234 | Robert Price | 06/2021 |
| 2869 | (5*10^178206+91)/3 | 178207 | Robert Price | 04/2018 |
| 2870 | 2^591872-291929 | 178172 | Enzo Doria | 07/2015 |
| 2871 | 2^591682-286871 | 178115 | Enzo Doria | 07/2015 |
| 2872 | (7^210761-5^210761)/2 | 178114 | Jon Grantham | 08/2023 |
| 2873 | 4*10^178091+9 | 178092 | Robert Price | 05/2015 |
| 2874 | 2^591435+335931 | 178040 | Enzo Doria | 09/2024 |
| 2875 | 410747#+478483 | 178007 | Makoto Morimoto | 02/2016 |
| 2876 | 3*10^177872+73 | 177873 | Robert Price | 08/2018 |
| 2877 | 2^590762-396765 | 177838 | Enzo Doria | 08/2013 |
| 2878 | (136*10^177754-1)/9 | 177756 | Serge Batalov | 12/2014 |
| 2879 | ReverseConsecutiveIntegerPrime(37765) | 177719 | Eric W. Weisstein | 04/2010 |
| 2880 | Smr(37765) | 177719 | Eric W. Weisstein | 12/2021 |
| 2881 | 598^128^209+209^128^598 | 177594 | Henri Lifchitz | 03/2025 |
| 2882 | (266*10^177577-11)/3 | 177579 | Robert Price | 04/2020 |
| 2883 | (11*10^177466-113)/3 | 177467 | Robert Price | 10/2018 |
| 2884 | 3*10^177373-97 | 177374 | Robert Price | 07/2018 |
| 2885 | 2^589204+1881151 | 177369 | Enzo Doria | 11/2016 |
| 2886 | 2^589132-69479 | 177347 | Enzo Doria | 01/2016 |
| 2887 | (101*10^177302-17)/3 | 177304 | Robert Price | 02/2020 |
| 2888 | 2^588912-113519 | 177281 | Enzo Doria | 08/2014 |
| 2889 | (682*10^177266-7)/9 | 177268 | Robert Price | 08/2021 |
| 2890 | 15^150706+2 | 177245 | Robert Price | 06/2015 |
| 2891 | 2^588403+335931 | 177127 | Enzo Doria | 09/2024 |
| 2892 | (31208^39601-1)/(31208^199-1) | 177084 | Ryan Propper | 11/2023 |
| 2893 | 2^588194-1861001 | 177065 | Enzo Doria | 11/2015 |
| 2894 | 5*10^177016-37 | 177017 | Robert Price | 11/2021 |
| 2895 | fibonacci(846926)-4 | 176997 | Jon Grantham | 08/2023 |
| 2896 | (23*10^176964-47)/3 | 176965 | Robert Price | 09/2019 |
| 2897 | 20530^41031+41031^20530 | 176942 | Norbert Schneider | 07/2022 |
| 2898 | (19*10^176932+521)/9 | 176933 | Robert Price | 05/2018 |
| 2899 | (8*10^176908+43)/3 | 176909 | Robert Price | 06/2018 |
| 2900 | (85*10^176900+203)/9 | 176901 | Robert Price | 09/2020 |
| 2901 | 2^587560-113699 | 176874 | Enzo Doria | 09/2014 |
| 2902 | 20596^40995+40995^20596 | 176844 | Norbert Schneider | 07/2022 |
| 2903 | (101*10^176815-17)/3 | 176817 | Robert Price | 02/2020 |
| 2904 | (25*10^176715-37)/3 | 176716 | Robert Price | 10/2019 |
| 2905 | 5^252763-12862 | 176674 | Enzo Doria | 05/2014 |
| 2906 | 38442^38531+38531^38442 | 176658 | Norbert Schneider | 09/2022 |
| 2907 | 2^586829+23961 | 176654 | Enzo Doria | 10/2023 |
| 2908 | 2^586804+81721 | 176646 | Enzo Doria | 08/2016 |
| 2909 | (10^176584+77)/3 | 176584 | Robert Price | 01/2018 |
| 2910 | 2^586570+1874419 | 176576 | Enzo Doria | 06/2016 |
| 2911 | (157*10^176482-1)/3 | 176484 | Robert Price | 01/2022 |
| 2912 | 5*2^586202+3 | 176466 | Jon Grantham | 07/2023 |
| 2913 | 27122^39799-39799^27122 | 176442 | Frank Doornink | 01/2024 |
| 2914 | 2^585994-3311 | 176402 | Yves Minet | 12/2014 |
| 2915 | 8*10^176383-81 | 176384 | Robert Price | 02/2021 |
| 2916 | (23*10^176357+61)/3 | 176358 | Robert Price | 01/2022 |
| 2917 | 2^585832-112799 | 176354 | Enzo Doria | 07/2014 |
| 2918 | fibonacci(843383)+4 | 176257 | Jon Grantham | 08/2023 |
| 2919 | (29*10^176240+49)/3 | 176241 | Robert Price | 09/2021 |
| 2920 | (2^585387-11)/3 | 176219 | Stefano Morozzi | 08/2022 |
| 2921 | 2^585336-461039 | 176204 | Enzo Doria | 06/2015 |
| 2922 | (25*10^176164+143)/3 | 176165 | Robert Price | 08/2020 |
| 2923 | 2^585095-1848127 | 176132 | Enzo Doria | 08/2015 |
| 2924 | (5*10^176101-311)/9 | 176101 | Robert Price | 12/2021 |
| 2925 | 6*10^176092+77 | 176093 | Robert Price | 06/2020 |
| 2926 | 2^584950-115451 | 176088 | Enzo Doria | 07/2015 |
| 2927 | (646*10^176044+11)/9 | 176046 | Robert Price | 10/2021 |
| 2928 | (7^208283-5^208283)/2 | 176020 | Jon Grantham | 08/2023 |
| 2929 | 2^584671-3697 | 176004 | Yves Minet | 03/2017 |
| 2930 | (13*10^175965-37)/3 | 175966 | Robert Price | 01/2019 |
| 2931 | 31728^39089-39089^31728 | 175957 | Frank Doornink | 01/2024 |
| 2932 | 2*10^175860-87 | 175861 | Robert Price | 04/2018 |
| 2933 | 27009^39670-39670^27009 | 175798 | Frank Doornink | 01/2024 |
| 2934 | (86*10^175774-221)/9 | 175775 | Robert Price | 09/2019 |
| 2935 | 2^583614+216037 | 175686 | Enzo Doria | 11/2023 |
| 2936 | 9*10^175654+47 | 175655 | Robert Price | 01/2022 |
| 2937 | 25430^39869-39869^25430 | 175637 | Frank Doornink | 01/2024 |
| 2938 | 10^175608+2971 | 175609 | Mike Oakes | 05/2010 |
| 2939 | 10^175608-55829 | 175608 | Patrick De Geest | 09/2013 |
| 2940 | 2^583051+1879793 | 175516 | Enzo Doria | 09/2016 |
| 2941 | (76*10^175514+491)/9 | 175515 | Robert Price | 10/2021 |
| 2943 | 2^582860-23829 | 175459 | Enzo Doria | 08/2013 |
| 2942 | (200^76253-1)/199 | 175459 | Anonymous | 06/2024 |
| 2944 | (8*10^175428-53)/9 | 175428 | Serge Batalov | 11/2022 |
| 2945 | (28*10^175417-67)/3 | 175418 | Robert Price | 10/2020 |
| 2946 | 2^582670-23913 | 175402 | Enzo Doria | 08/2013 |
| 2947 | 2^582573-29563 | 175372 | Enzo Doria | 08/2015 |
| 2948 | 2^582435-1862767 | 175331 | Enzo Doria | 12/2015 |
| 2949 | 10^175295-40000001 | 175295 | Robert Price | 07/2022 |
| 2950 | 31093^39018-39018^31093 | 175295 | Frank Doornink | 01/2024 |
| 2951 | (11*10^175250-149)/3 | 175251 | Robert Price | 09/2018 |
| 2952 | (29*10^175236+31)/3 | 175237 | Robert Price | 04/2021 |
| 2953 | 2^582072-1848599 | 175222 | Enzo Doria | 08/2015 |
| 2954 | (404267#+465)/(3^4*5^2*31) | 175208 | Makoto Morimoto | 06/2019 |
| 2955 | Phi(262767,10)/259613797 | 175168 | Makoto Kamada | 12/2022 |
| 2956 | (2^581871-15)/7 | 175160 | Stefano Morozzi | 08/2022 |
| 2957 | (5*10^175117-311)/9 | 175117 | Robert Price | 12/2021 |
| 2958 | 31193^38966-38966^31193 | 175116 | Frank Doornink | 01/2024 |
| 2959 | 2^581695+225893 | 175108 | Enzo Doria | 08/2024 |
| 2960 | 10^175093-89 | 175093 | Riley Fisher | 10/2023 |
| 2961 | (220221^32768+1)/2 | 175075 | Serge Batalov | 03/2018 |
| 2962 | 2^581560+1874911 | 175068 | Enzo Doria | 06/2016 |
| 2963 | (25*10^174987-97)/9 | 174988 | Robert Price | 01/2022 |
| 2964 | (75^93307-1)/74 | 174955 | Paul Bourdelais | 09/2017 |
| 2965 | 26446^39555-39555^26446 | 174927 | Frank Doornink | 03/2024 |
| 2966 | 31522^38883-38883^31522 | 174920 | Frank Doornink | 01/2024 |
| 2967 | (27398^39601-1)/(27398^199-1) | 174855 | Ryan Propper | 11/2023 |
| 2968 | (861^59557-1)/860 | 174798 | Jinyuan Wang | 11/2023 |
| 2969 | 31492^38859-38859^31492 | 174796 | Frank Doornink | 01/2024 |
| 2970 | (47*10^174790+493)/9 | 174791 | Robert Price | 03/2019 |
| 2971 | 2^580528-114035 | 174757 | Enzo Doria | 11/2014 |
| 2972 | (19*10^174754+737)/9 | 174755 | Robert Price | 07/2018 |
| 2973 | V(1045270)/4181081/12543241/81333115129561 | 174730 | Serge Batalov | 07/2024 |
| 2974 | (35*10^174704-377)/9 | 174705 | Robert Price | 07/2018 |
| 2976 | (49*10^174681+293)/9 | 174682 | Robert Price | 03/2021 |
| 2975 | 6*10^174681+11 | 174682 | Robert Price | 07/2022 |
| 2977 | 3*10^174665-97 | 174666 | Robert Price | 07/2018 |
| 2978 | 2^580046-459161 | 174612 | Enzo Doria | 05/2015 |
| 2979 | 2^579992-39779 | 174595 | Enzo Doria | 09/2015 |
| 2980 | 25613^39582-39582^25613 | 174496 | Frank Doornink | 02/2024 |
| 2981 | (29*10^174481-149)/3 | 174482 | Robert Price | 08/2022 |
| 2982 | (4*10^174423+101)/3 | 174424 | Robert Price | 11/2021 |
| 2983 | (2^579371-17)/3 | 174408 | Stefano Morozzi | 08/2022 |
| 2984 | (2*10^174301-71)/3 | 174301 | Robert Price | 12/2017 |
| 2985 | 14^152048+3 | 174267 | Paul Bourdelais | 12/2020 |
| 2986 | (2^578696+1)/257 | 174203 | Lelio R Paula | 09/2015 |
| 2987 | 2^578656-1851809 | 174193 | Enzo Doria | 08/2015 |
| 2988 | 2^578583-113917 | 174171 | Enzo Doria | 10/2014 |
| 2989 | 2^578434-83 | 174126 | Yves Minet | 07/2017 |
| 2990 | 15^148048-2 | 174118 | Robert Price | 06/2015 |
| 2991 | 5*10^174101+81 | 174102 | Robert Price | 03/2019 |
| 2992 | 2^578346+2794249 | 174100 | Enzo Doria | 03/2016 |
| 2993 | 10^173947+1372429 | 173948 | Patrick De Geest | 08/2021 |
| 2995 | 10^173947-500000001 | 173947 | Robert Price | 12/2020 |
| 2994 | 10^173947-286391 | 173947 | Patrick De Geest | 08/2021 |
| 2996 | 5*10^173904-13 | 173905 | Robert Price | 01/2019 |
| 2997 | (8*10^173862-59)/3 | 173863 | Robert Price | 08/2021 |
| 2998 | (71*10^173854-287)/9 | 173855 | Robert Price | 09/2019 |
| 2999 | (43*10^173826+101)/9 | 173827 | Robert Price | 11/2018 |
| 3000 | 2*10^173809-87 | 173810 | Robert Price | 04/2018 |
