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 ? |
| 2751 | 7*10^170348+33 | 170349 | Robert Price | 06/2020 |
| 2752 | 2^565799+216011 | 170323 | Enzo Doria | 12/2023 |
| 2753 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
| 2754 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
| 2755 | 3*2^565024-5 | 170090 | Jon Grantham | 07/2023 |
| 2756 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
| 2757 | (7*10^169944+23)/3 | 169945 | Robert Price | 06/2020 |
| 2758 | (37*10^169943+251)/9 | 169944 | Robert Price | 09/2021 |
| 2759 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
| 2760 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
| 2761 | (2^563903-13)/5 | 169752 | Stefano Morozzi | 08/2022 |
| 2762 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
| 2763 | 2^563583+89 | 169656 | Stefano Morozzi | 04/2021 |
| 2764 | 2^563311+215813 | 169574 | Enzo Doria | 11/2023 |
| 2765 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
| 2766 | (194*10^169461-17)/3 | 169463 | Robert Price | 09/2020 |
| 2767 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
| 2768 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
| 2769 | (109*10^169337+11)/3 | 169339 | Robert Price | 06/2022 |
| 2770 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
| 2771 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
| 2772 | (17*10^169283+19)/9 | 169284 | Robert Price | 03/2021 |
| 2773 | 390151#-2322911 | 169082 | Hayden Chesnut | 07/2024 |
| 2774 | 10^169074-5000000001 | 169074 | Robert Price | 09/2022 |
| 2775 | 8*10^169071+59 | 169072 | Robert Price | 11/2021 |
| 2776 | (10^169044+173)/3 | 169044 | Robert Price | 05/2021 |
| 2777 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
| 2778 | (64*10^168935+143)/9 | 168936 | Robert Price | 05/2021 |
| 2779 | (22*10^168906+47)/3 | 168907 | Robert Price | 06/2021 |
| 2780 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
| 2781 | (77*10^168803-149)/9 | 168804 | Robert Price | 03/2022 |
| 2782 | 4*10^168788-47 | 168789 | Robert Price | 10/2021 |
| 2783 | (154*10^168781+17)/9 | 168783 | Robert Price | 06/2022 |
| 2784 | (418*10^168751-31)/9 | 168753 | Robert Price | 05/2022 |
| 2785 | (29*10^168711+691)/9 | 168712 | Robert Price | 08/2021 |
| 2786 | 2^560405-39943 | 168699 | Enzo Doria | 09/2015 |
| 2787 | (397*10^168634+17)/9 | 168636 | Robert Price | 03/2022 |
| 2788 | 89*10^168614-7 | 168616 | Robert Price | 04/2020 |
| 2789 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
| 2790 | (94*10^168541+11)/3 | 168543 | Robert Price | 04/2020 |
| 2791 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
| 2792 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
| 2793 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
| 2794 | 2024^50920+3 | 168353 | Martin Hopf | 01/2024 |
| 2795 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
| 2796 | 2^558830+25009 | 168225 | Enzo Doria | 11/2023 |
| 2797 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
| 2798 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
| 2799 | (74*10^168170+529)/9 | 168171 | Robert Price | 02/2022 |
| 2800 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
| 2801 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
| 2802 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
| 2803 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
| 2804 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
| 2805 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
| 2806 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
| 2807 | (8*10^167965-11)/3 | 167966 | Robert Price | 07/2023 |
| 2808 | 2^557916+216151 | 167950 | Enzo Doria | 12/2023 |
| 2809 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
| 2810 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |
| 2811 | 36^107827-107827 | 167812 | Kellen Shenton | 06/2023 |
| 2812 | 32027^37242-37242^32027 | 167795 | Frank Doornink | 01/2024 |
| 2813 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
| 2814 | 2^557322+217519 | 167771 | Enzo Doria | 01/2024 |
| 2815 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
| 2816 | 6*10^167662-13 | 167663 | Robert Price | 07/2022 |
| 2817 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
| 2818 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
| 2819 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
| 2820 | (88*10^167522-637)/9 | 167523 | Robert Price | 11/2020 |
| 2821 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
| 2822 | 7*10^167437-93 | 167438 | Robert Price | 08/2020 |
| 2823 | 25455^37978-37978^25455 | 167323 | Frank Doornink | 01/2024 |
| 2824 | 11^160663+6 | 167314 | Paul Bourdelais | 02/2021 |
| 2825 | (7*10^167308-493)/9 | 167308 | Robert Price | 04/2021 |
| 2826 | 2^555759+74333 | 167301 | Enzo Doria | 07/2023 |
| 2827 | 26084^37871-37871^26084 | 167253 | Frank Doornink | 03/2024 |
| 2828 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
| 2829 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
| 2830 | 9*10^166996+59 | 166997 | Robert Price | 01/2020 |
| 2831 | (68*10^166976-329)/9 | 166977 | Robert Price | 03/2021 |
| 2832 | (64*10^166901+683)/9 | 166902 | Robert Price | 06/2022 |
| 2833 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
| 2834 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
| 2835 | (185*10^166837+7)/3 | 166839 | Robert Price | 03/2020 |
| 2836 | (14*10^166813+139)/9 | 166814 | Robert Price | 11/2021 |
| 2837 | 26084^37767-37767^26084 | 166794 | Frank Doornink | 03/2024 |
| 2838 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
| 2839 | 31861^37028-37028^31861 | 166747 | Frank Doornink | 01/2024 |
| 2840 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
| 2841 | 2*10^166646+69 | 166647 | Robert Price | 06/2020 |
| 2842 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
| 2843 | (188*10^166611+7)/3 | 166613 | Robert Price | 03/2020 |
| 2844 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
| 2845 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
| 2846 | 25218^37819-37819^25218 | 166469 | Frank Doornink | 12/2023 |
| 2847 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
| 2848 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
| 2849 | 25214^37799-37799^25214 | 166378 | Frank Doornink | 11/2023 |
| 2850 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
| 2851 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
| 2852 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
| 2853 | (19*10^166325+137)/3 | 166326 | Robert Price | 03/2022 |
| 2854 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
| 2855 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
| 2856 | (85*10^166297-1)/3 | 166299 | Robert Price | 02/2020 |
| 2857 | (19*10^166280-7)/3 | 166281 | Robert Price | 12/2023 |
| 2858 | 25533^37726-37726^25533 | 166263 | Frank Doornink | 02/2024 |
| 2859 | 8*10^166227+87 | 166228 | Robert Price | 10/2019 |
| 2860 | 2^552137+1879397 | 166210 | Enzo Doria | 09/2016 |
| 2861 | (103*10^166126+11)/3 | 166128 | Robert Price | 01/2021 |
| 2862 | (22*10^166077+179)/3 | 166078 | Robert Price | 02/2022 |
| 2863 | (23^121949-1)/22 | 166061 | Paul Bourdelais | 10/2017 |
| 2864 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
| 2865 | 2^551535-23821 | 166029 | Enzo Doria | 08/2013 |
| 2866 | 2^551507-23557 | 166021 | Enzo Doria | 08/2013 |
| 2867 | 32030^36841-36841^32030 | 165990 | Frank Doornink | 01/2024 |
| 2868 | 10^165947-7000000001 | 165947 | Robert Price | 12/2021 |
| 2869 | 4*10^165938-47 | 165939 | Robert Price | 10/2021 |
| 2870 | 7*10^165916-3 | 165917 | Robert Price | 08/2015 |
| 2871 | (29*10^165796+67)/3 | 165797 | Robert Price | 12/2019 |
| 2872 | 81^86837-80^86837 | 165728 | Robert Price | 01/2015 |
| 2873 | (71*10^165716-17)/9 | 165717 | Serge Batalov | 01/2023 |
| 2874 | fibonacci(792909)+3 | 165708 | Jon Grantham | 08/2023 |
| 2875 | (71*10^165663-539)/9 | 165664 | Robert Price | 07/2019 |
| 2876 | 25682^37567-37567^25682 | 165657 | Frank Doornink | 02/2024 |
| 2877 | 2^550270-69551 | 165648 | Enzo Doria | 12/2015 |
| 2878 | 2^550250+29329 | 165642 | Enzo Doria | 03/2024 |
| 2879 | (202*10^165569-13)/9 | 165571 | Robert Price | 01/2020 |
| 2880 | 2^550000-23625 | 165567 | Enzo Doria | 08/2013 |
| 2881 | 31688^36783-36783^31688 | 165557 | Frank Doornink | 01/2024 |
| 2882 | 2^549675-1852057 | 165469 | Enzo Doria | 08/2015 |
| 2883 | 2^549663+212543 | 165466 | Enzo Doria | 08/2023 |
| 2884 | (529*10^165394-7)/9 | 165396 | Robert Price | 08/2021 |
| 2885 | 26253^37424-37424^26253 | 165384 | Frank Doornink | 03/2024 |
| 2886 | -tau(103^14938) | 165374 | Nik Lygeros / Olivier Rozier | 10/2013 |
| 2887 | (28*10^165358-1)/9 | 165359 | Serge Batalov | 10/2014 |
| 2888 | 2^549278+1879669 | 165350 | Enzo Doria | 09/2016 |
| 2889 | (7*10^165350-439)/9 | 165350 | Robert Price | 02/2018 |
| 2890 | 2^549252-351269 | 165342 | Enzo Doria | 06/2015 |
| 2891 | 67*10^165327-9 | 165329 | Robert Price | 03/2021 |
| 2892 | (14*10^165282+73)/3 | 165283 | Robert Price | 12/2018 |
| 2893 | (8*10^165283-629)/9 | 165283 | Robert Price | 01/2022 |
| 2894 | 2^549049+2797607 | 165281 | Enzo Doria | 04/2016 |
| 2895 | (218*10^165258+7)/9 | 165260 | Robert Price | 06/2022 |
| 2896 | (7*10^165239+107)/3 | 165240 | Robert Price | 02/2018 |
| 2897 | 2^548880+23961 | 165230 | Enzo Doria | 10/2023 |
| 2898 | 5*2^548778+3 | 165200 | Jon Grantham | 07/2023 |
| 2899 | (44^100511-1)/43 | 165184 | Paul Bourdelais | 11/2017 |
| 2900 | (7*10^165134+107)/3 | 165135 | Robert Price | 02/2018 |
| 2901 | (301*10^165082+23)/9 | 165084 | Robert Price | 06/2021 |
| 2902 | (23*10^165060-83)/3 | 165061 | Robert Price | 08/2019 |
| 2903 | 7*10^165023-27 | 165024 | Robert Price | 11/2022 |
| 2904 | (76*10^164984+77)/9 | 164985 | Robert Price | 10/2019 |
| 2905 | 31058^36715-36715^31058 | 164931 | Frank Doornink | 01/2024 |
| 2906 | (4*10^164929-211)/9 | 164929 | Robert Price | 03/2022 |
| 2907 | 10^164878-500001 | 164878 | Robert Price | 03/2022 |
| 2908 | 9*10^164791-89 | 164792 | Robert Price | 04/2020 |
| 2909 | 2^547178-1856501 | 164717 | Enzo Doria | 10/2015 |
| 2910 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
| 2911 | (26*10^164643-167)/3 | 164644 | Robert Price | 10/2019 |
| 2912 | (10^164643+83)/3 | 164643 | Robert Price | 08/2021 |
| 2913 | 2^546398-59201 | 164483 | Enzo Doria | 10/2015 |
| 2914 | 2^546332-114893 | 164463 | Enzo Doria | 05/2015 |
| 2915 | 32003^36504-36504^32003 | 164458 | Frank Doornink | 01/2024 |
| 2916 | (65*10^164427+277)/9 | 164428 | Robert Price | 08/2021 |
| 2917 | 2^545958+1876189 | 164350 | Enzo Doria | 07/2016 |
| 2918 | 2^545878-49841 | 164326 | Enzo Doria | 10/2015 |
| 2919 | (10^164284+77)/3 | 164284 | Robert Price | 01/2018 |
| 2920 | 2^545668-4019 | 164263 | Yves Minet | 04/2017 |
| 2921 | 10^164216+780639 | 164217 | Patrick De Geest | 08/2021 |
| 2923 | 10^164216-50000000001 | 164216 | Robert Price | 12/2020 |
| 2922 | 10^164216-891051 | 164216 | Patrick De Geest | 08/2021 |
| 2924 | (13*53^238539*617^9)/10^247183 | 164151 | Hans Havermann | 07/2017 |
| 2925 | (16*10^164122+197)/3 | 164123 | Robert Price | 04/2019 |
| 2926 | 2^545185+76757 | 164118 | Enzo Doria | 05/2016 |
| 2927 | 2^545076-114329 | 164085 | Enzo Doria | 01/2015 |
| 2928 | (2*10^164043-143)/3 | 164043 | Robert Price | 03/2018 |
| 2929 | (33085^36481-1)/(33085^191-1) | 164018 | Ryan Propper | 11/2023 |
| 2930 | (29^112153+1)/30 | 164011 | Lelio R Paula | 03/2017 |
| 2931 | 2^544757+1874777 | 163989 | Enzo Doria | 06/2016 |
| 2932 | 2^544723+211193 | 163978 | Enzo Doria | 08/2023 |
| 2933 | 2^544444-457199 | 163894 | Enzo Doria | 01/2015 |
| 2934 | (32804^36481-1)/(32804^191-1) | 163883 | Ryan Propper | 11/2023 |
| 2935 | 2^544264-343529 | 163840 | Enzo Doria | 07/2015 |
| 2936 | 7*10^163780+9 | 163781 | Robert Price | 09/2015 |
| 2937 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
| 2938 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
| 2939 | (2013^49729-1)/(2013^223-1) | 163561 | Ryan Propper | 11/2023 |
| 2940 | (23*10^163523+301)/9 | 163524 | Robert Price | 06/2021 |
| 2941 | (68*10^163521-329)/9 | 163522 | Robert Price | 03/2021 |
| 2942 | 35820^35899+35899^35820 | 163489 | Norbert Schneider | 11/2021 |
| 2943 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
| 2944 | 2^542502+24799 | 163310 | Enzo Doria | 10/2023 |
| 2945 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
| 2946 | 2^542258+216949 | 163236 | Enzo Doria | 12/2023 |
| 2947 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
| 2948 | fibonacci(780566)-4 | 163129 | Jon Grantham | 08/2023 |
| 2949 | (682*10^163106-7)/9 | 163108 | Robert Price | 08/2021 |
| 2950 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
| 2951 | (29*10^163056+313)/9 | 163057 | Robert Price | 04/2021 |
| 2952 | 2^541476+214743 | 163001 | Enzo Doria | 11/2023 |
| 2953 | 13^142159+14^142159-2 | 162933 | Harsh Aggarwal | 05/2024 |
| 2954 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
| 2955 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
| 2956 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
| 2957 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
| 2958 | (203*10^162689+1)/3 | 162691 | Robert Price | 03/2020 |
| 2959 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
| 2960 | 2^540180+26791 | 162611 | Enzo Doria | 12/2023 |
| 2961 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
| 2962 | 2^539807-114081 | 162499 | Enzo Doria | 12/2014 |
| 2963 | 414^62093+62093^414 | 162498 | Norbert Schneider | 03/2022 |
| 2964 | 2^539654-114893 | 162453 | Enzo Doria | 05/2015 |
| 2965 | 9*10^162449-71 | 162450 | Robert Price | 11/2020 |
| 2966 | 2^539617-1851583 | 162441 | Enzo Doria | 08/2015 |
| 2967 | (509*10^162422+31)/9 | 162424 | Robert Price | 08/2022 |
| 2968 | (91*10^162410+11)/3 | 162412 | Robert Price | 02/2020 |
| 2969 | 2^539346+81049 | 162360 | Enzo Doria | 07/2016 |
| 2970 | 2^539220-115499 | 162322 | Enzo Doria | 07/2015 |
| 2971 | 2^539217-113713 | 162321 | Enzo Doria | 09/2014 |
| 2972 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
| 2973 | 4*10^162263-39 | 162264 | Robert Price | 09/2020 |
| 2974 | 31243^36098-36098^31243 | 162252 | Frank Doornink | 01/2024 |
| 2975 | 31987^36000-36000^31987 | 162180 | Frank Doornink | 01/2024 |
| 2976 | (115*10^162153-1)/3 | 162155 | Serge Batalov | 12/2014 |
| 2977 | (10^162138+11)/3 | 162138 | Serge Batalov | 07/2015 |
| 2978 | (61*10^162100-403)/9 | 162101 | Robert Price | 10/2021 |
| 2979 | 2^538473-112723 | 162097 | Enzo Doria | 06/2014 |
| 2980 | 2^538157+79337 | 162002 | Enzo Doria | 06/2016 |
| 2981 | 2^538136-114749 | 161996 | Enzo Doria | 05/2015 |
| 2982 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
| 2983 | (9*29^110727-1199)/14 | 161927 | Curtis Bright | 05/2015 |
| 2984 | ((2^179294-1)^3+2)/11 | 161918 | Serge Batalov | 03/2023 |
| 2985 | 31198^36027-36027^31198 | 161910 | Frank Doornink | 01/2024 |
| 2986 | 2^537815-22737 | 161899 | Enzo Doria | 07/2013 |
| 2987 | 2^537804-39839 | 161896 | Enzo Doria | 09/2015 |
| 2988 | (754*10^161816-7)/9 | 161818 | Robert Price | 05/2020 |
| 2989 | 2^537461+29867 | 161792 | Enzo Doria | 03/2024 |
| 2990 | 2^537458-59201 | 161791 | Enzo Doria | 10/2015 |
| 2991 | 2*10^161766+51 | 161767 | Robert Price | 05/2018 |
| 2992 | (7*10^161760+131)/3 | 161761 | Robert Price | 06/2020 |
| 2993 | 2^537209-49849 | 161717 | Enzo Doria | 10/2015 |
| 2994 | (58*10^161691+329)/9 | 161692 | Robert Price | 05/2019 |
| 2995 | 23*10^161668-3 | 161670 | Robert Price | 10/2021 |
| 2996 | 2^536937+1879397 | 161635 | Enzo Doria | 09/2016 |
| 2997 | 3*2^536868-5 | 161614 | Jon Grantham | 07/2023 |
| 2998 | 34*10^161593-9 | 161595 | Robert Price | 06/2020 |
| 2999 | (31*10^161582-1)/3 | 161584 | Robert Price | 02/2020 |
| 3000 | 24494^36813+36813^24494 | 161575 | Norbert Schneider | 11/2023 |
