## PRP Records

### Probable Primes Top 10000

#### (294613 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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See the Latest PRPs
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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 (10^164643+83)/3 164643 Robert Price 08/2021 2752 2^546398-59201 164483 Enzo Doria 10/2015 2753 2^546332-114893 164463 Enzo Doria 05/2015 2754 32003^36504-36504^32003 164458 Frank Doornink 01/2024 2755 (65*10^164427+277)/9 164428 Robert Price 08/2021 2756 2^545958+1876189 164350 Enzo Doria 07/2016 2757 2^545878-49841 164326 Enzo Doria 10/2015 2758 (10^164284+77)/3 164284 Robert Price 01/2018 2759 2^545668-4019 164263 Yves Minet 04/2017 2760 10^164216+780639 164217 Patrick De Geest 08/2021 2762 10^164216-50000000001 164216 Robert Price 12/2020 2761 10^164216-891051 164216 Patrick De Geest 08/2021 2763 (13*53^238539*617^9)/10^247183 164151 Hans Havermann 07/2017 2764 (16*10^164122+197)/3 164123 Robert Price 04/2019 2765 2^545185+76757 164118 Enzo Doria 05/2016 2766 2^545076-114329 164085 Enzo Doria 01/2015 2767 (2*10^164043-143)/3 164043 Robert Price 03/2018 2768 (33085^36481-1)/(33085^191-1) 164018 Ryan Propper 11/2023 2769 (29^112153+1)/30 164011 Lelio R Paula 03/2017 2770 2^544757+1874777 163989 Enzo Doria 06/2016 2771 2^544723+211193 163978 Enzo Doria 08/2023 2772 2^544444-457199 163894 Enzo Doria 01/2015 2773 (32804^36481-1)/(32804^191-1) 163883 Ryan Propper 11/2023 2774 2^544264-343529 163840 Enzo Doria 07/2015 2775 7*10^163780+9 163781 Robert Price 09/2015 2776 2^543989+2793047 163758 Enzo Doria 02/2016 2777 (28*10^163709+113)/3 163710 Robert Price 03/2020 2778 (2013^49729-1)/(2013^223-1) 163561 Ryan Propper 11/2023 2779 (23*10^163523+301)/9 163524 Robert Price 06/2021 2780 (68*10^163521-329)/9 163522 Robert Price 03/2021 2781 35820^35899+35899^35820 163489 Norbert Schneider 11/2021 2782 2^542870-69551 163421 Enzo Doria 12/2015 2783 2^542502+24799 163310 Enzo Doria 10/2023 2784 2^542395+72533 163278 Enzo Doria 04/2016 2785 2^542258+216949 163236 Enzo Doria 12/2023 2786 2^542072-3683 163180 Yves Minet 03/2017 2787 fibonacci(780566)-4 163129 Jon Grantham 08/2023 2788 (682*10^163106-7)/9 163108 Robert Price 08/2021 2789 2^541779-1867357 163092 Enzo Doria 04/2016 2790 (29*10^163056+313)/9 163057 Robert Price 04/2021 2791 2^541476+214743 163001 Enzo Doria 11/2023 2792 8*10^162924+9 162925 Robert Price 12/2015 2793 2^540905+81557 162829 Enzo Doria 08/2016 2794 2^540628-2939 162746 Yves Minet 09/2014 2795 919^54919-918^54919 162743 Jean-Louis Charton 01/2013 2796 (203*10^162689+1)/3 162691 Robert Price 03/2020 2797 3*10^162620-59 162621 Robert Price 09/2018 2798 2^540180+26791 162611 Enzo Doria 12/2023 2799 3^340694-112960 162553 Enzo Doria 07/2014 2800 2^539807-114081 162499 Enzo Doria 12/2014 2801 414^62093+62093^414 162498 Norbert Schneider 03/2022 2802 2^539654-114893 162453 Enzo Doria 05/2015 2803 9*10^162449-71 162450 Robert Price 11/2020 2804 2^539617-1851583 162441 Enzo Doria 08/2015 2805 (509*10^162422+31)/9 162424 Robert Price 08/2022 2806 (91*10^162410+11)/3 162412 Robert Price 02/2020 2807 2^539346+81049 162360 Enzo Doria 07/2016 2808 2^539220-115499 162322 Enzo Doria 07/2015 2809 2^539217-113713 162321 Enzo Doria 09/2014 2810 9^170099-8^170099 162316 Jean-Louis Charton 05/2005 2811 4*10^162263-39 162264 Robert Price 09/2020 2812 31243^36098-36098^31243 162252 Frank Doornink 01/2024 2813 31987^36000-36000^31987 162180 Frank Doornink 01/2024 2814 (115*10^162153-1)/3 162155 Serge Batalov 12/2014 2815 (10^162138+11)/3 162138 Serge Batalov 07/2015 2816 (61*10^162100-403)/9 162101 Robert Price 10/2021 2817 2^538473-112723 162097 Enzo Doria 06/2014 2818 2^538157+79337 162002 Enzo Doria 06/2016 2819 2^538136-114749 161996 Enzo Doria 05/2015 2820 2^538104+1531 161986 Lelio R Paula 01/2013 2821 (9*29^110727-1199)/14 161927 Curtis Bright 05/2015 2822 ((2^179294-1)^3+2)/11 161918 Serge Batalov 03/2023 2823 31198^36027-36027^31198 161910 Frank Doornink 01/2024 2824 2^537815-22737 161899 Enzo Doria 07/2013 2825 2^537804-39839 161896 Enzo Doria 09/2015 2826 (754*10^161816-7)/9 161818 Robert Price 05/2020 2827 2^537458-59201 161791 Enzo Doria 10/2015 2828 2*10^161766+51 161767 Robert Price 05/2018 2829 (7*10^161760+131)/3 161761 Robert Price 06/2020 2830 2^537209-49849 161717 Enzo Doria 10/2015 2831 (58*10^161691+329)/9 161692 Robert Price 05/2019 2832 23*10^161668-3 161670 Robert Price 10/2021 2833 2^536937+1879397 161635 Enzo Doria 09/2016 2834 3*2^536868-5 161614 Jon Grantham 07/2023 2835 34*10^161593-9 161595 Robert Price 06/2020 2836 (31*10^161582-1)/3 161584 Robert Price 02/2020 2837 24494^36813+36813^24494 161575 Norbert Schneider 11/2023 2838 2^536569-22881 161524 Enzo Doria 07/2013 2839 (46*10^161505+593)/9 161506 Robert Price 04/2022 2840 10^161253+573493 161254 Patrick De Geest 07/2018 2841 10^161253-8001 161253 Robert Price 03/2018 2842 97*10^161247-3 161249 Robert Price 05/2020 2843 7*10^161192-9 161193 Robert Price 10/2015 2844 2^535415-19 161176 Stefano Morozzi 07/2022 2845 2^535269-113803 161133 Enzo Doria 09/2014 2846 2^535205-23295 161113 Enzo Doria 08/2013 2847 (49*10^161105+437)/9 161106 Robert Price 09/2021 2848 (89^82609+1)/90 161036 Paul Bourdelais 10/2017 2849 2^534429-19 160880 Stefano Morozzi 07/2022 2850 2^534359-23229 160859 Enzo Doria 08/2013 2851 10^160836-1001 160836 Robert Price 10/2022 2852 457^60454+60454^457 160803 Norbert Schneider 07/2021 2853 8*10^160782+53 160783 Robert Price 08/2020 2854 67^88037-66^88037 160763 Robert Price 10/2013 2855 (88*10^160761-637)/9 160762 Robert Price 11/2020 2856 2^533948-1852559 160735 Enzo Doria 08/2015 2857 2^533665-23335 160650 Enzo Doria 08/2013 2858 2^533600+217981 160630 Enzo Doria 01/2024 2859 (19*10^160619+77)/3 160620 Robert Price 05/2019 2860 2^533350-5 160555 Stefano Morozzi 07/2022 2861 (38*10^160508+151)/9 160509 Robert Price 03/2022 2862 3^336353-2^336353 160482 Mike Oakes 10/2007 2863 2*10^160339-63 160340 Robert Price 01/2022 2864 24419^36532+36532^24419 160293 Norbert Schneider 10/2023 2865 (91*10^160249+11)/3 160251 Robert Price 02/2020 2866 (772*10^160239-7)/9 160241 Robert Price 06/2022 2867 (2*10^160226+187)/9 160226 Robert Price 06/2022 2868 2^532253+1868417 160225 Enzo Doria 04/2016 2869 2^532108-291989 160181 Enzo Doria 07/2015 2870 (28*10^160171-79)/3 160172 Robert Price 02/2021 2871 (26*10^160166-131)/3 160167 Robert Price 10/2019 2872 55*10^160145+9 160147 Robert Price 03/2022 2873 (17*10^160143+67)/3 160144 Robert Price 01/2019 2874 (394^61637-1)/393 159977 Jinyuan Wang 04/2023 2875 (19*10^159921-49)/3 159922 Robert Price 05/2019 2876 2^531110-1853771 159881 Enzo Doria 09/2015 2877 (275^65536+53^65536)/2 159864 Kellen Shenton 11/2020 2878 2^530992-1845299 159845 Enzo Doria 07/2015 2879 2^530810+25 159790 Stefano Morozzi 04/2021 2880 25590^36241-36241^25590 159753 Frank Doornink 02/2024 2881 (136*10^159736-1)/9 159738 Serge Batalov 12/2014 2882 2^530417-113833 159672 Enzo Doria 09/2014 2883 2^530406-69701 159669 Enzo Doria 02/2016 2884 5*10^159656+41 159657 Robert Price 03/2019 2885 8*10^159614+29 159615 Robert Price 11/2021 2886 7^188858-188858^7 159604 Norbert Schneider 05/2018 2887 28^110278+27 159590 Alfred Reich 02/2024 2888 7*10^159553-27 159554 Robert Price 11/2022 2889 3^334409-5*2^334409 159554 Jon Grantham 08/2023 2890 (24^115597-1)/23 159547 Paul Bourdelais 09/2017 2891 25472^36209-36209^25472 159540 Frank Doornink 01/2024 2892 (17*10^159438-377)/9 159439 Robert Price 03/2018 2893 (203*10^159381+1)/3 159383 Robert Price 03/2020 2894 32282^35343-35343^32282 159361 Frank Doornink 02/2024 2895 2^529215+219383 159310 Enzo Doria 02/2024 2896 89*10^159258-9 159260 Robert Price 05/2020 2897 2^528944-461315 159229 Enzo Doria 07/2015 2898 (13*10^159147+161)/3 159148 Robert Price 11/2018 2899 2^528620-113879 159131 Enzo Doria 10/2014 2900 32125^35306-35306^32125 159119 Frank Doornink 02/2024 2901 (47*10^159083+259)/9 159084 Robert Price 03/2022 2902 (861^54181-1)/860 159019 Jinyuan Wang 11/2023 2903 2^528000-23307 158944 Enzo Doria 08/2013 2904 (29*10^158909+61)/9 158910 Robert Price 08/2018 2905 2^527817+1876817 158889 Enzo Doria 07/2016 2906 2^527774-49451 158876 Enzo Doria 10/2015 2907 2^527745-291553 158868 Enzo Doria 07/2015 2908 (91*10^158862+11)/3 158864 Robert Price 02/2020 2909 2^527644-1856999 158837 Enzo Doria 10/2015 2910 (37200^37199-37198^37199)/(2^37199) 158822 Henri Lifchitz 06/2013 2911 (17*10^158819+7)/3 158820 Robert Price 06/2023 2912 2^527573-1863253 158816 Enzo Doria 12/2015 2913 2^527553-23401 158810 Enzo Doria 08/2013 2914 (49*10^158783+437)/9 158784 Robert Price 09/2021 2915 10^158755+310207 158756 Patrick De Geest 08/2021 2916 10^158755-50001 158755 Robert Price 08/2020 2917 (61*10^158748-619)/9 158749 Robert Price 03/2022 2918 11^152420-210 158730 Enzo Doria 09/2012 2919 (13*10^158694+401)/9 158695 Robert Price 01/2018 2920 2^527052-69059 158659 Enzo Doria 11/2015 2921 2^526849-113233 158598 Enzo Doria 07/2014 2922 24286^36161+36161^24286 158579 Norbert Schneider 08/2023 2923 (2^526763-lucasV(1,2,526763)+1)/2 158572 Mike Oakes 11/2016 2924 (299*10^158544-17)/3 158546 Robert Price 04/2020 2925 2^526658-3551 158540 Yves Minet 03/2017 2926 7*10^158465-11 158466 Robert Price 06/2019 2927 (7^187507-3^187507)/4 158462 Jon Grantham 08/2023 2928 2^526375-23115 158455 Enzo Doria 08/2013 2929 (77*10^158407-293)/9 158408 Robert Price 09/2019 2930 31209^35242-35242^31209 158388 Frank Doornink 01/2024 2931 32071^35144-35144^32071 158363 Frank Doornink 01/2024 2932 2^526028-112793 158351 Enzo Doria 07/2014 2933 (229*10^158339-1)/3 158341 Robert Price 07/2020 2934 32042^35123-35123^32042 158255 Frank Doornink 01/2024 2935 2^525690-9221 158249 Lelio R Paula 01/2013 2936 2*10^158242-7 158243 Robert Price 10/2015 2937 2^525667-525667^2 158242 Henri Lifchitz 12/2017 2938 (56*10^158230+187)/9 158231 Robert Price 10/2021 2939 10^158209-7000000001 158209 Robert Price 12/2021 2940 31050^35207-35207^31050 158153 Frank Doornink 01/2024 2941 2^525186-1857431 158097 Enzo Doria 10/2015 2942 31527^35108-35108^31527 157940 Frank Doornink 01/2024 2943 2^524515-23245 157895 Enzo Doria 08/2013 2944 2^524499-109087 157890 Enzo Doria 04/2014 2945 2^524384-219533 157856 Enzo Doria 03/2024 2947 2^18067*(2^506221+1)-1 157827 Makoto Morimoto 05/2014 2948 2^524288+189093 157827 Makoto Morimoto 01/2016 2946 2^524288-164073 157827 Matthias Baur 03/2020 2949 (2^(2^19)-9333)/(19*23*463*1213*31973) 157814 Makoto Morimoto 09/2017 2950 (10^157792+359)/9 157792 Serge Batalov 12/2014 2951 2^524154+25 157787 Stefano Morozzi 04/2021 2952 2^523924+1876591 157717 Enzo Doria 07/2016 2953 (17*10^157705+67)/3 157706 Robert Price 01/2019 2954 (46^94841+1)/47 157696 Robert Price 01/2014 2955 2^523774+77839 157672 Enzo Doria 05/2016 2956 2^523587+2799143 157616 Enzo Doria 04/2016 2957 2^523371+1872113 157551 Enzo Doria 05/2016 2958 8*10^157477+27 157478 Robert Price 09/2021 2959 32268^34909-34909^32268 157397 Frank Doornink 02/2024 2960 (8*10^157368+49)/3 157369 Robert Price 05/2020 2961 (82*10^157319+449)/9 157320 Robert Price 11/2019 2962 2^522535-351457 157299 Enzo Doria 07/2015 2963 25401^35704-35704^25401 157271 Frank Doornink 01/2024 2964 2^522226+2799079 157206 Enzo Doria 04/2016 2965 (134*10^157191-11)/3 157193 Robert Price 01/2022 2966 2^522134-1849451 157178 Enzo Doria 08/2015 2967 9*10^157152+71 157153 Robert Price 08/2020 2968 4*10^157150+93 157151 Robert Price 08/2018 2969 31227^34952-34952^31227 157093 Frank Doornink 01/2024 2970 (32^104347+5^104347)/37 157057 Anonymous 12/2023 2971 fibonacci(751442)-2 157042 Jon Grantham 08/2023 2972 2^521401-29593 156958 Enzo Doria 08/2015 2973 7*10^156956+87 156957 Robert Price 07/2019 2974 2^521348-23397 156942 Enzo Doria 08/2013 2975 10^156902+34509 156903 Patrick De Geest 08/2021 2977 10^156902-80000001 156902 Robert Price 04/2021 2976 10^156902-69789 156902 Patrick De Geest 08/2021 2978 (98^78797+1)/99 156901 Paul Bourdelais 12/2017 2979 65^86522+64 156857 Lelio R Paula 04/2016 2980 8^173687-7^173687 156855 Jean-Louis Charton 09/2004 2981 2^520977-1858183 156830 Enzo Doria 10/2015 2982 (8*10^156718-101)/3 156719 Robert Price 08/2018 2983 (10^156640+7)/53 156639 Alfred Reich 07/2021 2984 2^520314-1849481 156631 Enzo Doria 08/2015 2985 (16*10^156563-637)/9 156564 Robert Price 09/2022 2986 (13*10^156522+89)/3 156523 Robert Price 09/2018 2988 (2^(6*86654+1)-5)/3 156513 Kevin Acres 12/2013 2987 (2^519925-5)/3 156513 Stefano Morozzi 08/2022 2989 (4*10^156501+119)/3 156502 Robert Price 12/2021 2990 (83*10^156476-101)/9 156477 Robert Price 08/2021 2991 3*10^156435-97 156436 Robert Price 07/2018 2992 (8*10^156371-77)/3 156372 Robert Price 07/2018 2993 53^90679-52^90679 156356 Robert Price 01/2013 2994 31267^34782-34782^31267 156349 Frank Doornink 01/2024 2995 (418*10^156309-31)/9 156311 Robert Price 05/2022 2996 2^519106-59141 156267 Enzo Doria 10/2015 2997 2^519053+6077 156251 Enzo Doria 02/2016 2998 31199^34764-34764^31199 156235 Frank Doornink 01/2024 2999 2^518968-1860989 156225 Enzo Doria 11/2015 3000 (25*10^156221-7)/9 156222 Robert Price 05/2018

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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