## PRP Records

### Probable Primes Top 10000

#### (295461 PRPs in the top)

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) !!!

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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 2751 2^563583+89 169656 Stefano Morozzi 04/2021 2752 2^563311+215813 169574 Enzo Doria 11/2023 2753 (4*10^169559+83)/3 169560 Robert Price 02/2018 2754 (194*10^169461-17)/3 169463 Robert Price 09/2020 2755 2^562749+2793047 169405 Enzo Doria 02/2016 2756 (154*10^169337-1)/9 169339 Serge Batalov 12/2014 2757 (109*10^169337+11)/3 169339 Robert Price 06/2022 2758 (56*10^169311+691)/9 169312 Robert Price 05/2019 2759 2^562369-29503 169290 Enzo Doria 08/2015 2760 (17*10^169283+19)/9 169284 Robert Price 03/2021 2761 390151#-2322911 169082 Hayden Chesnut 07/2024 2762 10^169074-5000000001 169074 Robert Price 09/2022 2763 8*10^169071+59 169072 Robert Price 11/2021 2764 (10^169044+173)/3 169044 Robert Price 05/2021 2765 (22*10^169019+383)/9 169020 Robert Price 05/2018 2766 (64*10^168935+143)/9 168936 Robert Price 05/2021 2767 (22*10^168906+47)/3 168907 Robert Price 06/2021 2768 5*10^168807+87 168808 Robert Price 02/2019 2769 (77*10^168803-149)/9 168804 Robert Price 03/2022 2770 4*10^168788-47 168789 Robert Price 10/2021 2771 (154*10^168781+17)/9 168783 Robert Price 06/2022 2772 (418*10^168751-31)/9 168753 Robert Price 05/2022 2773 (29*10^168711+691)/9 168712 Robert Price 08/2021 2774 2^560405-39943 168699 Enzo Doria 09/2015 2775 (397*10^168634+17)/9 168636 Robert Price 03/2022 2776 89*10^168614-7 168616 Robert Price 04/2020 2777 (23*10^168608-83)/3 168609 Robert Price 08/2019 2778 (94*10^168541+11)/3 168543 Robert Price 04/2020 2779 2^559686-350471 168483 Enzo Doria 06/2015 2780 2^559672-1855889 168479 Enzo Doria 09/2015 2781 (5*10^168379-473)/9 168379 Robert Price 01/2018 2782 2024^50920+3 168353 Martin Hopf 01/2024 2783 2^559000-59939 168276 Enzo Doria 11/2015 2784 2^558830+25009 168225 Enzo Doria 11/2023 2785 (16*10^168181+41)/3 168182 Robert Price 03/2019 2786 (19*10^168173+77)/3 168174 Robert Price 05/2019 2787 (74*10^168170+529)/9 168171 Robert Price 02/2022 2788 2^558640-114149 168168 Enzo Doria 12/2014 2789 2^558498-1849277 168125 Enzo Doria 08/2015 2790 2^558476-1850249 168119 Enzo Doria 08/2015 2791 (7*10^168067+71)/3 168068 Robert Price 05/2018 2792 2^558150-1852211 168020 Enzo Doria 08/2015 2793 2^558125-113661 168013 Enzo Doria 09/2014 2794 393^64747-392^64747 167980 Jean-Louis Charton 08/2012 2795 (8*10^167965-11)/3 167966 Robert Price 07/2023 2796 2^557916+216151 167950 Enzo Doria 12/2023 2797 (13*10^167911+179)/3 167912 Robert Price 11/2018 2798 (26*10^167861-167)/3 167862 Robert Price 10/2019 2799 36^107827-107827 167812 Kellen Shenton 06/2023 2800 32027^37242-37242^32027 167795 Frank Doornink 01/2024 2801 39^105456+2 167788 Robert Price 04/2015 2802 2^557322+217519 167771 Enzo Doria 01/2024 2803 (28^115877-1)/27 167691 Paul Bourdelais 12/2017 2804 6*10^167662-13 167663 Robert Price 07/2022 2805 10^167639+121911 167640 Patrick De Geest 07/2018 2806 10^167639-8001 167639 Robert Price 03/2018 2807 2^556504-462059 167525 Enzo Doria 07/2015 2808 (88*10^167522-637)/9 167523 Robert Price 11/2020 2809 5*10^167510+9 167511 Robert Price 08/2015 2810 7*10^167437-93 167438 Robert Price 08/2020 2811 25455^37978-37978^25455 167323 Frank Doornink 01/2024 2812 11^160663+6 167314 Paul Bourdelais 02/2021 2813 (7*10^167308-493)/9 167308 Robert Price 04/2021 2814 2^555759+74333 167301 Enzo Doria 07/2023 2815 26084^37871-37871^26084 167253 Frank Doornink 03/2024 2816 2^555343+1874333 167175 Enzo Doria 06/2016 2817 2^555210-461261 167135 Enzo Doria 07/2015 2818 9*10^166996+59 166997 Robert Price 01/2020 2819 (68*10^166976-329)/9 166977 Robert Price 03/2021 2820 (64*10^166901+683)/9 166902 Robert Price 06/2022 2821 2^554372+1880527 166883 Enzo Doria 11/2016 2822 2^554299+72173 166861 Enzo Doria 04/2016 2823 (185*10^166837+7)/3 166839 Robert Price 03/2020 2824 (14*10^166813+139)/9 166814 Robert Price 11/2021 2825 26084^37767-37767^26084 166794 Frank Doornink 03/2024 2826 2^554037-2797063 166782 Enzo Doria 03/2016 2827 31861^37028-37028^31861 166747 Frank Doornink 01/2024 2828 (49*10^166721-139)/9 166722 Robert Price 03/2019 2829 2*10^166646+69 166647 Robert Price 06/2020 2830 2^553484-29819 166616 Enzo Doria 08/2015 2831 (188*10^166611+7)/3 166613 Robert Price 03/2020 2832 2^553383-2784217 166585 Enzo Doria 10/2015 2833 2^553069+76427 166491 Enzo Doria 05/2016 2834 25218^37819-37819^25218 166469 Frank Doornink 12/2023 2835 2*10^166458+51 166459 Robert Price 05/2018 2836 589^60089-588^60089 166454 Jean-Louis Charton 09/2012 2837 25214^37799-37799^25214 166378 Frank Doornink 11/2023 2838 11^159756-2424 166369 Mike Oakes 06/2010 2839 2^552649-361275 166364 Enzo Doria 05/2014 2840 2^552628-113669 166358 Enzo Doria 09/2014 2841 (19*10^166325+137)/3 166326 Robert Price 03/2022 2842 10^166324+550603 166325 Patrick De Geest 07/2018 2843 10^166324-801 166324 Robert Price 02/2018 2844 (85*10^166297-1)/3 166299 Robert Price 02/2020 2845 (19*10^166280-7)/3 166281 Robert Price 12/2023 2846 25533^37726-37726^25533 166263 Frank Doornink 02/2024 2847 8*10^166227+87 166228 Robert Price 10/2019 2848 2^552137+1879397 166210 Enzo Doria 09/2016 2849 (103*10^166126+11)/3 166128 Robert Price 01/2021 2850 (22*10^166077+179)/3 166078 Robert Price 02/2022 2851 (23^121949-1)/22 166061 Paul Bourdelais 10/2017 2852 2^551542+19249 166031 Payam Samidoost 08/2002 2853 2^551535-23821 166029 Enzo Doria 08/2013 2854 2^551507-23557 166021 Enzo Doria 08/2013 2855 32030^36841-36841^32030 165990 Frank Doornink 01/2024 2856 10^165947-7000000001 165947 Robert Price 12/2021 2857 4*10^165938-47 165939 Robert Price 10/2021 2858 7*10^165916-3 165917 Robert Price 08/2015 2859 (29*10^165796+67)/3 165797 Robert Price 12/2019 2860 81^86837-80^86837 165728 Robert Price 01/2015 2861 (71*10^165716-17)/9 165717 Serge Batalov 01/2023 2862 fibonacci(792909)+3 165708 Jon Grantham 08/2023 2863 (71*10^165663-539)/9 165664 Robert Price 07/2019 2864 25682^37567-37567^25682 165657 Frank Doornink 02/2024 2865 2^550270-69551 165648 Enzo Doria 12/2015 2866 2^550250+29329 165642 Enzo Doria 03/2024 2867 (202*10^165569-13)/9 165571 Robert Price 01/2020 2868 2^550000-23625 165567 Enzo Doria 08/2013 2869 31688^36783-36783^31688 165557 Frank Doornink 01/2024 2870 2^549675-1852057 165469 Enzo Doria 08/2015 2871 2^549663+212543 165466 Enzo Doria 08/2023 2872 (529*10^165394-7)/9 165396 Robert Price 08/2021 2873 26253^37424-37424^26253 165384 Frank Doornink 03/2024 2874 -tau(103^14938) 165374 Nik Lygeros / Olivier Rozier 10/2013 2875 (28*10^165358-1)/9 165359 Serge Batalov 10/2014 2876 2^549278+1879669 165350 Enzo Doria 09/2016 2877 (7*10^165350-439)/9 165350 Robert Price 02/2018 2878 2^549252-351269 165342 Enzo Doria 06/2015 2879 67*10^165327-9 165329 Robert Price 03/2021 2880 (14*10^165282+73)/3 165283 Robert Price 12/2018 2881 (8*10^165283-629)/9 165283 Robert Price 01/2022 2882 2^549049+2797607 165281 Enzo Doria 04/2016 2883 (218*10^165258+7)/9 165260 Robert Price 06/2022 2884 (7*10^165239+107)/3 165240 Robert Price 02/2018 2885 2^548880+23961 165230 Enzo Doria 10/2023 2886 5*2^548778+3 165200 Jon Grantham 07/2023 2887 (44^100511-1)/43 165184 Paul Bourdelais 11/2017 2888 (7*10^165134+107)/3 165135 Robert Price 02/2018 2889 (301*10^165082+23)/9 165084 Robert Price 06/2021 2890 (23*10^165060-83)/3 165061 Robert Price 08/2019 2891 7*10^165023-27 165024 Robert Price 11/2022 2892 (76*10^164984+77)/9 164985 Robert Price 10/2019 2893 31058^36715-36715^31058 164931 Frank Doornink 01/2024 2894 (4*10^164929-211)/9 164929 Robert Price 03/2022 2895 10^164878-500001 164878 Robert Price 03/2022 2896 9*10^164791-89 164792 Robert Price 04/2020 2897 2^547178-1856501 164717 Enzo Doria 10/2015 2898 11^158160-60 164707 Enzo Doria 07/2012 2899 (26*10^164643-167)/3 164644 Robert Price 10/2019 2900 (10^164643+83)/3 164643 Robert Price 08/2021 2901 2^546398-59201 164483 Enzo Doria 10/2015 2902 2^546332-114893 164463 Enzo Doria 05/2015 2903 32003^36504-36504^32003 164458 Frank Doornink 01/2024 2904 (65*10^164427+277)/9 164428 Robert Price 08/2021 2905 2^545958+1876189 164350 Enzo Doria 07/2016 2906 2^545878-49841 164326 Enzo Doria 10/2015 2907 (10^164284+77)/3 164284 Robert Price 01/2018 2908 2^545668-4019 164263 Yves Minet 04/2017 2909 10^164216+780639 164217 Patrick De Geest 08/2021 2911 10^164216-50000000001 164216 Robert Price 12/2020 2910 10^164216-891051 164216 Patrick De Geest 08/2021 2912 (13*53^238539*617^9)/10^247183 164151 Hans Havermann 07/2017 2913 (16*10^164122+197)/3 164123 Robert Price 04/2019 2914 2^545185+76757 164118 Enzo Doria 05/2016 2915 2^545076-114329 164085 Enzo Doria 01/2015 2916 (2*10^164043-143)/3 164043 Robert Price 03/2018 2917 (33085^36481-1)/(33085^191-1) 164018 Ryan Propper 11/2023 2918 (29^112153+1)/30 164011 Lelio R Paula 03/2017 2919 2^544757+1874777 163989 Enzo Doria 06/2016 2920 2^544723+211193 163978 Enzo Doria 08/2023 2921 2^544444-457199 163894 Enzo Doria 01/2015 2922 (32804^36481-1)/(32804^191-1) 163883 Ryan Propper 11/2023 2923 2^544264-343529 163840 Enzo Doria 07/2015 2924 7*10^163780+9 163781 Robert Price 09/2015 2925 2^543989+2793047 163758 Enzo Doria 02/2016 2926 (28*10^163709+113)/3 163710 Robert Price 03/2020 2927 (2013^49729-1)/(2013^223-1) 163561 Ryan Propper 11/2023 2928 (23*10^163523+301)/9 163524 Robert Price 06/2021 2929 (68*10^163521-329)/9 163522 Robert Price 03/2021 2930 35820^35899+35899^35820 163489 Norbert Schneider 11/2021 2931 2^542870-69551 163421 Enzo Doria 12/2015 2932 2^542502+24799 163310 Enzo Doria 10/2023 2933 2^542395+72533 163278 Enzo Doria 04/2016 2934 2^542258+216949 163236 Enzo Doria 12/2023 2935 2^542072-3683 163180 Yves Minet 03/2017 2936 fibonacci(780566)-4 163129 Jon Grantham 08/2023 2937 (682*10^163106-7)/9 163108 Robert Price 08/2021 2938 2^541779-1867357 163092 Enzo Doria 04/2016 2939 (29*10^163056+313)/9 163057 Robert Price 04/2021 2940 2^541476+214743 163001 Enzo Doria 11/2023 2941 13^142159+14^142159-2 162933 Harsh Aggarwal 05/2024 2942 8*10^162924+9 162925 Robert Price 12/2015 2943 2^540905+81557 162829 Enzo Doria 08/2016 2944 2^540628-2939 162746 Yves Minet 09/2014 2945 919^54919-918^54919 162743 Jean-Louis Charton 01/2013 2946 (203*10^162689+1)/3 162691 Robert Price 03/2020 2947 3*10^162620-59 162621 Robert Price 09/2018 2948 2^540180+26791 162611 Enzo Doria 12/2023 2949 3^340694-112960 162553 Enzo Doria 07/2014 2950 2^539807-114081 162499 Enzo Doria 12/2014 2951 414^62093+62093^414 162498 Norbert Schneider 03/2022 2952 2^539654-114893 162453 Enzo Doria 05/2015 2953 9*10^162449-71 162450 Robert Price 11/2020 2954 2^539617-1851583 162441 Enzo Doria 08/2015 2955 (509*10^162422+31)/9 162424 Robert Price 08/2022 2956 (91*10^162410+11)/3 162412 Robert Price 02/2020 2957 2^539346+81049 162360 Enzo Doria 07/2016 2958 2^539220-115499 162322 Enzo Doria 07/2015 2959 2^539217-113713 162321 Enzo Doria 09/2014 2960 9^170099-8^170099 162316 Jean-Louis Charton 05/2005 2961 4*10^162263-39 162264 Robert Price 09/2020 2962 31243^36098-36098^31243 162252 Frank Doornink 01/2024 2963 31987^36000-36000^31987 162180 Frank Doornink 01/2024 2964 (115*10^162153-1)/3 162155 Serge Batalov 12/2014 2965 (10^162138+11)/3 162138 Serge Batalov 07/2015 2966 (61*10^162100-403)/9 162101 Robert Price 10/2021 2967 2^538473-112723 162097 Enzo Doria 06/2014 2968 2^538157+79337 162002 Enzo Doria 06/2016 2969 2^538136-114749 161996 Enzo Doria 05/2015 2970 2^538104+1531 161986 Lelio R Paula 01/2013 2971 (9*29^110727-1199)/14 161927 Curtis Bright 05/2015 2972 ((2^179294-1)^3+2)/11 161918 Serge Batalov 03/2023 2973 31198^36027-36027^31198 161910 Frank Doornink 01/2024 2974 2^537815-22737 161899 Enzo Doria 07/2013 2975 2^537804-39839 161896 Enzo Doria 09/2015 2976 (754*10^161816-7)/9 161818 Robert Price 05/2020 2977 2^537461+29867 161792 Enzo Doria 03/2024 2978 2^537458-59201 161791 Enzo Doria 10/2015 2979 2*10^161766+51 161767 Robert Price 05/2018 2980 (7*10^161760+131)/3 161761 Robert Price 06/2020 2981 2^537209-49849 161717 Enzo Doria 10/2015 2982 (58*10^161691+329)/9 161692 Robert Price 05/2019 2983 23*10^161668-3 161670 Robert Price 10/2021 2984 2^536937+1879397 161635 Enzo Doria 09/2016 2985 3*2^536868-5 161614 Jon Grantham 07/2023 2986 34*10^161593-9 161595 Robert Price 06/2020 2987 (31*10^161582-1)/3 161584 Robert Price 02/2020 2988 24494^36813+36813^24494 161575 Norbert Schneider 11/2023 2989 2^536569-22881 161524 Enzo Doria 07/2013 2990 (46*10^161505+593)/9 161506 Robert Price 04/2022 2991 10^161253+573493 161254 Patrick De Geest 07/2018 2992 10^161253-8001 161253 Robert Price 03/2018 2993 97*10^161247-3 161249 Robert Price 05/2020 2994 7*10^161192-9 161193 Robert Price 10/2015 2995 2^535415-19 161176 Stefano Morozzi 07/2022 2996 2^535269-113803 161133 Enzo Doria 09/2014 2997 2^535205-23295 161113 Enzo Doria 08/2013 2998 (49*10^161105+437)/9 161106 Robert Price 09/2021 2999 (89^82609+1)/90 161036 Paul Bourdelais 10/2017 3000 2^534429-19 160880 Stefano Morozzi 07/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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