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 ? |
| 2751 | 2^675027+106733 | 203204 | Stefano Morozzi | 01/2025 |
| 2752 | 2^675026-67377 | 203204 | Stefano Morozzi | 01/2025 |
| 2753 | 2^675021+13335 | 203202 | Stefano Morozzi | 01/2025 |
| 2754 | 2^675020-180497 | 203202 | Stefano Morozzi | 01/2025 |
| 2755 | 2^675016+174777 | 203201 | Stefano Morozzi | 01/2025 |
| 2756 | 2^675017+128379 | 203201 | Stefano Morozzi | 01/2025 |
| 2757 | 2^675017+171249 | 203201 | Stefano Morozzi | 01/2025 |
| 2758 | 2^675018+86517 | 203201 | Stefano Morozzi | 01/2025 |
| 2759 | 2^675019+125891 | 203201 | Stefano Morozzi | 01/2025 |
| 2760 | 2^675019+163251 | 203201 | Stefano Morozzi | 01/2025 |
| 2761 | 2^675016-170847 | 203201 | Stefano Morozzi | 01/2025 |
| 2762 | 2^675019-44755 | 203201 | Stefano Morozzi | 01/2025 |
| 2763 | 2^675015+120225 | 203200 | Stefano Morozzi | 01/2025 |
| 2764 | 2^675013-69831 | 203200 | Stefano Morozzi | 01/2025 |
| 2765 | 2^675014-3897 | 203200 | Stefano Morozzi | 01/2025 |
| 2766 | 2^675006+75357 | 203198 | Stefano Morozzi | 01/2025 |
| 2767 | 2^675008+112231 | 203198 | Stefano Morozzi | 01/2025 |
| 2768 | 2^675007-123309 | 203198 | Stefano Morozzi | 01/2025 |
| 2769 | 2^675003+52529 | 203197 | Stefano Morozzi | 01/2025 |
| 2770 | 2^675002+50595 | 203196 | Stefano Morozzi | 01/2025 |
| 2771 | 2^674627-25161 | 203083 | Enzo Doria | 09/2013 |
| 2772 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
| 2773 | (182*10^203048+1)/3 | 203050 | Robert Price | 09/2023 |
| 2774 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
| 2775 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
| 2776 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
| 2777 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
| 2778 | 5^289926-289926^5 | 202650 | Henri Lifchitz | 07/2024 |
| 2779 | (2^673184-7)/3 | 202649 | Stefano Morozzi | 08/2022 |
| 2780 | (467617#+14534)/(2^2*13*43) | 202603 | Makoto Morimoto | 06/2019 |
| 2781 | (155^92479-1)/154 | 202558 | Anonymous | 06/2024 |
| 2782 | 2^672773+219407 | 202525 | Enzo Doria | 03/2024 |
| 2783 | 1374^64531-64531^1374 | 202498 | Henri Lifchitz | 10/2024 |
| 2784 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
| 2785 | (7*10^202267+179)/3 | 202268 | Robert Price | 02/2023 |
| 2786 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
| 2787 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
| 2788 | (2*10^202059+7)/9 | 202059 | Rytis Slatkevicius | 01/2023 |
| 2789 | 98*10^202021-9 | 202023 | Robert Price | 05/2023 |
| 2790 | Phi(265967,7) | 202013 | Henri Lifchitz | 02/2026 |
| 2791 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
| 2792 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |
| 2793 | 10^201801-93 | 201801 | Robert Price | 02/2023 |
| 2794 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
| 2795 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
| 2796 | 2^670133+89 | 201731 | Stefano Morozzi | 05/2021 |
| 2797 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
| 2798 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
| 2799 | (299*10^201547-17)/3 | 201549 | Robert Price | 02/2023 |
| 2800 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
| 2801 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
| 2802 | (198^87623-1)/197 | 201239 | Anonymous | 06/2024 |
| 2803 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
| 2804 | 7*10^201140-87 | 201141 | Robert Price | 03/2023 |
| 2805 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
| 2806 | 10194^50161-50161^10194 | 201063 | Norbert Schneider | 09/2020 |
| 2807 | 2^667894+1875589 | 201057 | Enzo Doria | 06/2016 |
| 2808 | Phi(253483,-7) | 201019 | Henri Lifchitz | 02/2026 |
| 2809 | 2^667569-1836559 | 200959 | Enzo Doria | 05/2015 |
| 2810 | (172*10^200746-1)/9 | 200748 | Serge Batalov | 12/2014 |
| 2811 | (166^90407-1)/165 | 200712 | Anonymous | 06/2024 |
| 2812 | 2^666430+782569 | 200616 | Enzo Doria | 10/2016 |
| 2813 | Phi(81682,-81682) | 200612 | Henri Lifchitz | 12/2025 |
| 2814 | (13*10^200610-43)/3 | 200611 | Robert Price | 08/2023 |
| 2815 | Phi(221863,-9) | 200552 | Henri Lifchitz | 12/2025 |
| 2816 | (8*10^200408-11)/3 | 200409 | Robert Price | 07/2023 |
| 2817 | p(38635)#-p(38635+1) | 200356 | Henri Lifchitz | 11/2024 |
| 2818 | (19*10^200260+101)/3 | 200261 | Robert Price | 06/2023 |
| 2819 | 43183^43183+4^4 | 200167 | Serge Batalov | 04/2024 |
| 2820 | (86^103471+1)/87 | 200163 | Paul Bourdelais | 05/2018 |
| 2821 | (10^(2*100072+1)+36*10^100072-1)/9 | 200145 | Robert Price | 09/2023 |
| 2822 | 2^664778+34789 | 200119 | Enzo Doria | 07/2024 |
| 2823 | Phi(23488,19!) | 200101 | Henri Lifchitz | 12/2025 |
| 2824 | 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 | 200003 | Robert Price | 05/2017 |
| 2825 | 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 | 200003 | Robert Price | 01/2018 |
| 2826 | numbpart(32235776596) | 200002 | Serge Batalov | 04/2017 |
| 2827 | (10^200001+149)/3 | 200001 | Serge Batalov | 12/2014 |
| 2828 | 10^200000+571791 | 200001 | Patrick De Geest | 08/2019 |
| 2829 | (3^419180-621444)/3 | 200000 | Stefano Morozzi | 06/2019 |
| 2830 | (3^419180-1941384)/3 | 200000 | Stefano Morozzi | 08/2019 |
| 2831 | 10^200000-45557 | 200000 | Patrick De Geest | 08/2019 |
| 2833 | (10^200000-1)/9-10^58838 | 200000 | Akihiko Yoshida | 04/2020 |
| 2832 | 2593604092947240127723272^8192+2593604092947240127722755^8192 | 200000 | Youcef Lemsafer | 01/2023 |
| 2834 | (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 | 199999 | Youcef Lemsafer | 01/2023 |
| 2835 | (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 | 199994 | Youcef Lemsafer | 01/2023 |
| 2836 | (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 | 199989 | Youcef Lemsafer | 01/2023 |
| 2837 | (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 | 199986 | Youcef Lemsafer | 01/2023 |
| 2838 | 92*10^199980-9 | 199982 | Robert Price | 12/2021 |
| 2839 | (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 | 199977 | Youcef Lemsafer | 01/2023 |
| 2840 | (85*10^199951-139)/9 | 199952 | Robert Price | 08/2021 |
| 2841 | (10^199926+7)/29/373/2339 | 199919 | Alfred Reich | 08/2021 |
| 2842 | 2^663838+25819 | 199836 | Enzo Doria | 11/2023 |
| 2843 | 23*10^199833-9 | 199835 | Robert Price | 10/2021 |
| 2844 | fibonacci(956176)-4 | 199829 | Jon Grantham | 08/2023 |
| 2845 | (299*10^199801-17)/3 | 199803 | Robert Price | 04/2020 |
| 2846 | 6*10^199788+77 | 199789 | Robert Price | 06/2020 |
| 2847 | (2^663604+1)/270750449 | 199757 | Anonymous | 10/2024 |
| 2848 | (23*10^199615+37)/3 | 199616 | Robert Price | 02/2022 |
| 2849 | (17*10^199607-167)/3 | 199608 | Robert Price | 05/2022 |
| 2850 | 2^663020-933075 | 199589 | Paul Bourdelais | 06/2021 |
| 2851 | 2^663007+29963 | 199585 | Enzo Doria | 03/2024 |
| 2852 | 3*2^662703-5 | 199494 | Jon Grantham | 07/2023 |
| 2853 | (14*10^199447+73)/3 | 199448 | Robert Price | 12/2018 |
| 2854 | (2^662424-15)/7 | 199409 | Stefano Morozzi | 08/2022 |
| 2855 | 2^662194+22189 | 199341 | Enzo Doria | 09/2023 |
| 2856 | 2^662103-29287 | 199313 | Enzo Doria | 08/2015 |
| 2857 | (2*10^199283+457)/9 | 199283 | Robert Price | 01/2018 |
| 2858 | (10^199248-19)/9 | 199248 | Robert Price | 01/2018 |
| 2859 | (83*10^199213+529)/9 | 199214 | Robert Price | 12/2021 |
| 2860 | (194*10^199146-17)/3 | 199148 | Robert Price | 09/2020 |
| 2861 | (151*10^199003-1)/3 | 199005 | Robert Price | 03/2020 |
| 2862 | 9*10^198946-73 | 198947 | Robert Price | 01/2021 |
| 2863 | 45*10^198931-7 | 198933 | Robert Price | 07/2020 |
| 2864 | 2^660482-2891 | 198825 | Yves Minet | 05/2016 |
| 2865 | 2^659594+37729 | 198558 | Enzo Doria | 10/2024 |
| 2866 | 2^659589-21 | 198557 | Stefano Morozzi | 07/2022 |
| 2867 | 2^659583+1879223 | 198555 | Enzo Doria | 08/2016 |
| 2868 | (53*10^198529+1)/9 | 198530 | Serge Batalov | 07/2010 |
| 2869 | (17^161333-1)/913790128 | 198504 | Paul Vanderveen | 05/2025 |
| 2870 | (5^329624)%(4^329624) | 198454 | Henri Lifchitz | 07/2025 |
| 2871 | (49*10^198403+311)/9 | 198404 | Robert Price | 06/2019 |
| 2872 | 96*10^198376-7 | 198378 | Robert Price | 03/2021 |
| 2873 | (10^198375+7)/59/1201/87589 | 198366 | Alfred Reich | 08/2021 |
| 2874 | 2^658828-29819 | 198327 | Enzo Doria | 08/2015 |
| 2875 | 2^658776-2791229 | 198312 | Enzo Doria | 01/2016 |
| 2876 | (35*10^198294-377)/9 | 198295 | Robert Price | 07/2018 |
| 2877 | (4*10^198268+137)/3 | 198269 | Robert Price | 03/2018 |
| 2878 | 2^658544-1854029 | 198242 | Enzo Doria | 09/2015 |
| 2879 | (62*10^198229-233)/9 | 198230 | Robert Price | 02/2022 |
| 2880 | (26*10^198200-41)/3 | 198201 | Robert Price | 02/2022 |
| 2881 | (157^90239-1)/156 | 198154 | Alexander Zhirkov | 06/2016 |
| 2882 | 2^657815+26213 | 198023 | Enzo Doria | 12/2023 |
| 2883 | 2*10^197959-37 | 197960 | Robert Price | 11/2021 |
| 2884 | (29*10^197941-41)/3 | 197942 | Tyler Busby | 03/2024 |
| 2885 | (232*10^197897+17)/3 | 197899 | Robert Price | 04/2021 |
| 2886 | (4*10^197778+173)/3 | 197779 | Robert Price | 02/2018 |
| 2887 | 2^656964+6561 | 197766 | Henri Lifchitz | 01/2025 |
| 2888 | 2^656763+211373 | 197706 | Enzo Doria | 08/2023 |
| 2889 | 78*10^197702-7 | 197704 | Robert Price | 10/2020 |
| 2890 | (17*10^197640-23)/3 | 197641 | Robert Price | 03/2021 |
| 2891 | (29*10^197629-77)/3 | 197630 | Robert Price | 02/2020 |
| 2892 | 2^656462+1874419 | 197615 | Enzo Doria | 06/2016 |
| 2893 | (89^101363+1)/90 | 197595 | Paul Bourdelais | 11/2017 |
| 2894 | 2^656172+229051 | 197528 | Enzo Doria | 11/2024 |
| 2895 | 2^655893-344563 | 197444 | Enzo Doria | 07/2015 |
| 2896 | 2^655875+71333 | 197439 | Enzo Doria | 04/2016 |
| 2897 | 2^655845-9 | 197430 | Robert Price | 01/2017 |
| 2898 | (299*10^197426+1)/3 | 197428 | Robert Price | 04/2020 |
| 2899 | 2^655682-1849121 | 197380 | Enzo Doria | 08/2015 |
| 2900 | 4*10^197268-89 | 197269 | Robert Price | 11/2018 |
| 2901 | (11*10^197198-89)/3 | 197199 | Robert Price | 05/2021 |
| 2902 | 2^655045-49603 | 197189 | Enzo Doria | 10/2015 |
| 2903 | 2^655000-2784089 | 197175 | Enzo Doria | 10/2015 |
| 2904 | (18^157051-1)/17 | 197141 | Paul Bourdelais | 03/2010 |
| 2905 | (4*10^197061+41)/9 | 197061 | Serge Batalov | 11/2022 |
| 2906 | (154*10^197005+17)/9 | 197007 | Robert Price | 06/2022 |
| 2907 | 2^654400-39719 | 196995 | Enzo Doria | 09/2015 |
| 2908 | (5^281807-2^281807)/3 | 196975 | Jon Grantham | 08/2023 |
| 2909 | (14*10^196965-221)/9 | 196966 | Robert Price | 04/2018 |
| 2910 | (7^233069-1)/52258731186 | 196956 | Paul Vanderveen | 05/2025 |
| 2911 | 2^654216-459995 | 196939 | Enzo Doria | 06/2015 |
| 2912 | (17*10^196921+31)/3 | 196922 | Robert Price | 01/2019 |
| 2913 | (14*10^196885-89)/3 | 196886 | Robert Price | 05/2020 |
| 2914 | 3*10^196881-59 | 196882 | Robert Price | 09/2018 |
| 2915 | 2^653851+82295 | 196829 | Enzo Doria | 09/2016 |
| 2916 | (38*10^196792+691)/9 | 196793 | Robert Price | 10/2018 |
| 2917 | (65*10^196768+493)/9 | 196769 | Robert Price | 08/2021 |
| 2919 | 2^653636-29429 | 196765 | Enzo Doria | 08/2015 |
| 2918 | 2^653638-11 | 196765 | Stefano Morozzi | 07/2022 |
| 2920 | 2^653601-69673 | 196754 | Enzo Doria | 02/2016 |
| 2921 | (44*10^196684+1)/9 | 196685 | Serge Batalov | 07/2010 |
| 2922 | 2^652786-1852571 | 196509 | Enzo Doria | 08/2015 |
| 2923 | 2^652752-1325 | 196498 | Yves Minet | 07/2015 |
| 2924 | 2^652470-1859141 | 196414 | Enzo Doria | 10/2015 |
| 2925 | 2^652346+29329 | 196376 | Enzo Doria | 02/2024 |
| 2926 | 2^652307+1877483 | 196364 | Enzo Doria | 08/2016 |
| 2927 | 2^652293-115273 | 196360 | Enzo Doria | 06/2015 |
| 2928 | (47*10^196281+403)/9 | 196282 | Robert Price | 03/2019 |
| 2929 | 2^652025+218027 | 196280 | Enzo Doria | 01/2024 |
| 2930 | 2^652004+23961 | 196273 | Enzo Doria | 10/2023 |
| 2931 | (7*10^196125-31)/3 | 196126 | Robert Price | 12/2021 |
| 2932 | 33^129128+129128^33 | 196083 | Norbert Schneider | 06/2022 |
| 2933 | 6*10^196070+73 | 196071 | Robert Price | 04/2019 |
| 2934 | 2^651218-1868201 | 196037 | Enzo Doria | 04/2016 |
| 2935 | 2^651047-49687 | 195985 | Enzo Doria | 10/2015 |
| 2936 | 10^195968-700001 | 195968 | Robert Price | 08/2021 |
| 2937 | fibonacci(937485)+3 | 195923 | Jon Grantham | 08/2023 |
| 2938 | (29*10^195875-197)/3 | 195876 | Robert Price | 08/2021 |
| 2939 | (25*10^195808-97)/9 | 195809 | Robert Price | 01/2022 |
| 2940 | 2^650285-2785333 | 195756 | Enzo Doria | 10/2015 |
| 2941 | (10^195732+7)/18089/49605893 | 195721 | Alfred Reich | 08/2021 |
| 2942 | (29*10^195648-41)/3 | 195649 | Tyler Busby | 03/2024 |
| 2943 | (69^106397-1)/68 | 195647 | Paul Bourdelais | 10/2017 |
| 2944 | 2^649811+1877573 | 195613 | Enzo Doria | 08/2016 |
| 2945 | 2^649662-170531 | 195568 | Hans Havermann | 10/2018 |
| 2946 | 2^649586+182839 | 195545 | Enzo Doria | 11/2016 |
| 2947 | 2^649537-1867363 | 195531 | Enzo Doria | 04/2016 |
| 2948 | 2^649536-1861499 | 195530 | Enzo Doria | 12/2015 |
| 2949 | 2^649493+25907 | 195517 | Enzo Doria | 11/2023 |
| 2950 | (103*10^195478-1)/3 | 195480 | Serge Batalov | 12/2014 |
| 2951 | 2^649102-59351 | 195400 | Enzo Doria | 10/2015 |
| 2952 | (2*10^195399+529)/9 | 195399 | Robert Price | 01/2018 |
| 2953 | (202*10^195383-13)/9 | 195385 | Robert Price | 01/2020 |
| 2954 | 2^648988+1178971 | 195365 | Enzo Doria | 06/2016 |
| 2955 | 2^648975-114319 | 195361 | Enzo Doria | 02/2015 |
| 2956 | (11*10^195350-137)/9 | 195351 | Robert Price | 01/2018 |
| 2957 | 2^648619-24835 | 195254 | Enzo Doria | 09/2013 |
| 2958 | 5*10^195250-21 | 195251 | Robert Price | 12/2021 |
| 2959 | (14*10^195234-83)/3 | 195235 | Robert Price | 12/2018 |
| 2960 | 5*10^195221+81 | 195222 | Robert Price | 03/2019 |
| 2961 | 10^195143-5001 | 195143 | Robert Price | 12/2021 |
| 2962 | 2^648190-24737 | 195125 | Enzo Doria | 09/2013 |
| 2963 | (57^111119+1)/58 | 195110 | Paul Bourdelais | 10/2017 |
| 2964 | (29*10^195098-197)/3 | 195099 | Robert Price | 08/2021 |
| 2965 | 10^195060+89701 | 195061 | Patrick De Geest | 02/2021 |
| 2967 | 10^195060-40000000001 | 195060 | Robert Price | 09/2020 |
| 2966 | 10^195060-110337 | 195060 | Patrick De Geest | 02/2021 |
| 2968 | 56*10^195032-3 | 195034 | Robert Price | 03/2020 |
| 2969 | 11^187185-90 | 194934 | Enzo Doria | 09/2012 |
| 2970 | 2^647545-25 | 194931 | Boyan Hu | 12/2024 |
| 2971 | 2^647468+220141 | 194908 | Enzo Doria | 03/2024 |
| 2972 | (83^101533-1)/91545628589416644493342 | 194827 | Paul Vanderveen | 06/2025 |
| 2973 | (86*10^194818-437)/9 | 194819 | Robert Price | 03/2021 |
| 2974 | 7^230492-230492^7 | 194789 | Henri Lifchitz | 07/2024 |
| 2975 | 2^647068+77281 | 194787 | Enzo Doria | 05/2016 |
| 2976 | 2*10^194716-93 | 194717 | Robert Price | 12/2021 |
| 2977 | 15^165559-14^165559 | 194713 | Jean-Louis Charton | 03/2011 |
| 2978 | F(931517) | 194676 | Henri Lifchitz | 09/2008 |
| 2979 | 4*10^194668+49 | 194669 | Robert Price | 01/2019 |
| 2980 | 408^74564+407 | 194662 | Alfred Reich | 04/2026 |
| 2981 | 2^646589+1179407 | 194643 | Enzo Doria | 06/2016 |
| 2982 | 2^646289-114621 | 194553 | Enzo Doria | 05/2015 |
| 2983 | 2^646236-39659 | 194537 | Enzo Doria | 09/2015 |
| 2984 | (16*10^194536+53)/3 | 194537 | Robert Price | 03/2019 |
| 2985 | 2^646161-59833 | 194514 | Enzo Doria | 11/2015 |
| 2986 | (17*10^194502+31)/3 | 194503 | Robert Price | 01/2019 |
| 2987 | (19*10^194428+287)/9 | 194429 | Robert Price | 10/2021 |
| 2988 | 2*10^194413+3 | 194414 | Robert Price | 07/2015 |
| 2989 | 2^645360-1848599 | 194273 | Enzo Doria | 08/2015 |
| 2990 | 22470^44641+44641^22470 | 194260 | Norbert Schneider | 08/2023 |
| 2991 | (112*10^194150-1)/3 | 194152 | Serge Batalov | 12/2014 |
| 2992 | Phi(293127,10) | 194041 | Makoto Kamada | 12/2023 |
| 2993 | 2*10^193981-43 | 193982 | Robert Price | 04/2018 |
| 2994 | 2^644382+75169 | 193979 | Enzo Doria | 04/2016 |
| 2995 | 2^644304-1861409 | 193955 | Enzo Doria | 11/2015 |
| 2996 | (29*10^193950-23)/3 | 193951 | Robert Price | 03/2022 |
| 2997 | 5*10^193907-9 | 193908 | Robert Price | 05/2015 |
| 2998 | 2^644043+1876703 | 193877 | Enzo Doria | 07/2016 |
| 2999 | 2*10^193841-63 | 193842 | Robert Price | 01/2022 |
| 3000 | 2^643735+1879733 | 193784 | Enzo Doria | 09/2016 |
