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 | 2^629036+1874011 | 189359 | Enzo Doria | 06/2016 |
| 2752 | 2^628930+80779 | 189327 | Enzo Doria | 07/2016 |
| 2753 | (134*10^189309-11)/3 | 189311 | Robert Price | 01/2022 |
| 2754 | 9*10^189306-11 | 189307 | Mischa Rodermond | 04/2023 |
| 2755 | 3^396740-396740^3 | 189294 | Henri Lifchitz | 07/2024 |
| 2756 | 2^628582+1179439 | 189223 | Enzo Doria | 06/2016 |
| 2757 | (44*10^188999-503)/9 | 189000 | Robert Price | 12/2018 |
| 2758 | (16*10^188823+167)/3 | 188824 | Robert Price | 06/2019 |
| 2759 | (10^188796+7)/4967/71933 | 188788 | Alfred Reich | 08/2021 |
| 2760 | 2^627037-2785843 | 188757 | Enzo Doria | 10/2015 |
| 2761 | (10^188566+7)/311640753181661 | 188552 | Alfred Reich | 04/2022 |
| 2762 | (16*10^188457+161)/3 | 188458 | Robert Price | 02/2019 |
| 2763 | L(901657) | 188436 | Renaud Lifchitz | 11/2008 |
| 2764 | (19*10^188375+137)/3 | 188376 | Robert Price | 03/2022 |
| 2765 | 2^625651+74213 | 188340 | Enzo Doria | 04/2016 |
| 2766 | 2^625584-460919 | 188320 | Enzo Doria | 06/2015 |
| 2767 | (8*10^188308-71)/9 | 188308 | Serge Batalov | 11/2022 |
| 2768 | 5^269399-3^269399-1 | 188302 | Jon Grantham | 08/2023 |
| 2769 | (14*10^188218+139)/9 | 188219 | Robert Price | 11/2021 |
| 2770 | 40760^40821-40821^40760 | 188195 | Norbert Schneider | 07/2024 |
| 2771 | (10^188164+359)/9 | 188164 | Serge Batalov | 12/2014 |
| 2772 | 2^624481-113611 | 187988 | Enzo Doria | 08/2014 |
| 2773 | (2^624389+125582)/2 | 187960 | Stefano Morozzi | 09/2019 |
| 2774 | (2^624389+166982)/2 | 187960 | Stefano Morozzi | 09/2019 |
| 2775 | (2^624389+179886)/2 | 187960 | Stefano Morozzi | 09/2019 |
| 2776 | (2^624387+64466)/2 | 187959 | Stefano Morozzi | 09/2019 |
| 2777 | (2^624378+112990)/2 | 187957 | Stefano Morozzi | 09/2019 |
| 2778 | (2^624380+161986)/2 | 187957 | Stefano Morozzi | 09/2019 |
| 2780 | (2^624376+55762)/2 | 187956 | Stefano Morozzi | 09/2019 |
| 2779 | (2^624377+169506)/2 | 187956 | Stefano Morozzi | 09/2019 |
| 2781 | (2^624355+80178)/2 | 187950 | Stefano Morozzi | 09/2019 |
| 2782 | (2^624351+61350)/2 | 187949 | Stefano Morozzi | 09/2019 |
| 2783 | (2^624341+63462)/2 | 187946 | Stefano Morozzi | 09/2019 |
| 2784 | (2^624344+135990)/2 | 187946 | Stefano Morozzi | 09/2019 |
| 2785 | (2^624344+183898)/2 | 187946 | Stefano Morozzi | 09/2019 |
| 2787 | (2^624340+126982)/2 | 187945 | Stefano Morozzi | 09/2019 |
| 2786 | (2^624338+196110)/2 | 187945 | Stefano Morozzi | 09/2019 |
| 2788 | (2^624337+105162)/2 | 187944 | Stefano Morozzi | 09/2019 |
| 2789 | (2^624333+44594)/2 | 187943 | Stefano Morozzi | 09/2019 |
| 2790 | (2^624321+88742)/2 | 187940 | Stefano Morozzi | 09/2019 |
| 2791 | (2^624324+135178)/2 | 187940 | Stefano Morozzi | 09/2019 |
| 2792 | (2^624317+14186)/2 | 187938 | Stefano Morozzi | 09/2019 |
| 2793 | (2^624313+24450)/2 | 187937 | Stefano Morozzi | 09/2019 |
| 2794 | (2^624309+184590)/2 | 187936 | Stefano Morozzi | 09/2019 |
| 2796 | (2^624307+152658)/2 | 187935 | Stefano Morozzi | 09/2019 |
| 2795 | (2^624307+185978)/2 | 187935 | Stefano Morozzi | 09/2019 |
| 2797 | (2^624303+40814)/2 | 187934 | Stefano Morozzi | 09/2019 |
| 2798 | (2^624304+99238)/2 | 187934 | Stefano Morozzi | 09/2019 |
| 2799 | 2^624077-112723 | 187866 | Enzo Doria | 07/2014 |
| 2800 | 2^624008+1874941 | 187846 | Enzo Doria | 06/2016 |
| 2801 | 2^623870+78679 | 187804 | Enzo Doria | 05/2016 |
| 2802 | 2^623714-114035 | 187757 | Enzo Doria | 11/2014 |
| 2803 | 2^623651-1834251 | 187738 | Enzo Doria | 07/2015 |
| 2804 | (7*10^187645+53)/3 | 187646 | Robert Price | 05/2018 |
| 2805 | 21650^43269+43269^21650 | 187591 | Norbert Schneider | 02/2023 |
| 2806 | 2^623146+1879609 | 187586 | Enzo Doria | 09/2016 |
| 2807 | (401*10^187512+13)/9 | 187514 | Robert Price | 09/2021 |
| 2808 | (5*10^187471+91)/3 | 187472 | Robert Price | 04/2018 |
| 2809 | 2^622500+81931 | 187392 | Enzo Doria | 08/2016 |
| 2810 | (13*10^187382-157)/9 | 187383 | Robert Price | 05/2021 |
| 2811 | 2^622300-1861739 | 187331 | Enzo Doria | 12/2015 |
| 2812 | (22*10^187317-91)/3 | 187318 | Robert Price | 02/2022 |
| 2813 | (38*10^187281+349)/9 | 187282 | Robert Price | 10/2018 |
| 2814 | 2^622052+76771 | 187257 | Enzo Doria | 05/2016 |
| 2815 | 2^622005-24091 | 187243 | Enzo Doria | 08/2013 |
| 2816 | 7*10^187205-57 | 187206 | Robert Price | 06/2020 |
| 2817 | 2^621879-351787 | 187205 | Enzo Doria | 07/2015 |
| 2818 | (5*10^187168-53)/3 | 187169 | Robert Price | 09/2020 |
| 2819 | (23*10^187164-143)/3 | 187165 | Robert Price | 12/2019 |
| 2820 | 2^621700+79411 | 187151 | Enzo Doria | 06/2016 |
| 2821 | 2^621597+39 | 187120 | Jon Grantham | 08/2023 |
| 2822 | (7*10^187101+131)/3 | 187102 | Robert Price | 06/2020 |
| 2823 | (2*10^187062-71)/3 | 187062 | Robert Price | 12/2017 |
| 2824 | V(1118570) | 187013 | Serge Batalov | 07/2024 |
| 2825 | 2^620929-113203 | 186919 | Enzo Doria | 07/2014 |
| 2826 | 10^186842+168223 | 186843 | Patrick De Geest | 07/2018 |
| 2827 | 10^186842-8001 | 186842 | Robert Price | 03/2018 |
| 2828 | V(1117640)/13411681/26823361/575709775681/989889277441 | 186814 | Serge Batalov | 07/2024 |
| 2829 | 2^620347-1777 | 186744 | Lelio R Paula | 07/2013 |
| 2830 | (11*10^186659+133)/9 | 186660 | Robert Price | 04/2022 |
| 2831 | 11^179143-4170 | 186559 | Enzo Doria | 12/2012 |
| 2832 | (13^186535)%(10^186535) | 186535 | Henri Lifchitz | 05/2025 |
| 2833 | (5^266863+1)/6 | 186529 | Paul Bourdelais | 07/2010 |
| 2834 | 2*10^186517+33 | 186518 | Robert Price | 11/2021 |
| 2835 | 2^619297-2792353 | 186427 | Enzo Doria | 02/2016 |
| 2836 | (49*10^186409+383)/9 | 186410 | Robert Price | 04/2019 |
| 2837 | 2^618940-460139 | 186320 | Enzo Doria | 06/2015 |
| 2838 | 2^618046+74179 | 186051 | Enzo Doria | 04/2016 |
| 2839 | 3*10^186019+11 | 186020 | Robert Price | 07/2018 |
| 2840 | (16*10^185978-19)/3 | 185979 | Robert Price | 02/2019 |
| 2841 | (22*10^185950-7)/3 | 185951 | Robert Price | 12/2022 |
| 2842 | 2*10^185930-3 | 185931 | Robert Price | 07/2015 |
| 2843 | (82^97151+1)/83 | 185928 | Paul Bourdelais | 10/2017 |
| 2844 | 4*10^185905+91 | 185906 | Robert Price | 08/2018 |
| 2845 | (34*10^185902-601)/9 | 185903 | Robert Price | 07/2022 |
| 2846 | (19*10^185873+131)/3 | 185874 | Robert Price | 06/2020 |
| 2847 | (37*10^185811+377)/9 | 185812 | Robert Price | 11/2018 |
| 2848 | 2^617250+9385 | 185811 | Lelio R Paula | 07/2013 |
| 2849 | 2^617130+9 | 185775 | Stefano Morozzi | 05/2021 |
| 2850 | 39^116749+2 | 185756 | Robert Price | 04/2015 |
| 2851 | 2^616924-39719 | 185713 | Enzo Doria | 09/2015 |
| 2852 | 2^616712+1867621 | 185649 | Enzo Doria | 04/2016 |
| 2853 | (3^388897+2^388897)/5 | 185551 | Jean-Louis Charton | 09/2011 |
| 2854 | 8*10^185529-67 | 185530 | Robert Price | 08/2019 |
| 2855 | (5*10^185520-11)/3 | 185521 | Tyler Busby | 02/2023 |
| 2856 | 5*2^616124+3 | 185473 | Jon Grantham | 07/2023 |
| 2857 | 2^615916+26791 | 185410 | Enzo Doria | 12/2023 |
| 2858 | 4*10^185355+9 | 185356 | Robert Price | 05/2015 |
| 2859 | (16*10^185347+89)/3 | 185348 | Robert Price | 03/2021 |
| 2860 | 40247^40247-56^56 | 185327 | Henri Lifchitz | 08/2024 |
| 2861 | 2^615622+76639 | 185321 | Enzo Doria | 05/2016 |
| 2862 | 2^615591+1879223 | 185312 | Enzo Doria | 08/2016 |
| 2863 | 2^615587+217013 | 185311 | Enzo Doria | 12/2023 |
| 2864 | 2^615503+1876643 | 185285 | Enzo Doria | 07/2016 |
| 2865 | 5^265007-4^265007 | 185232 | Jean-Louis Charton | 02/2013 |
| 2866 | (4*10^185221-91)/3 | 185222 | Robert Price | 03/2018 |
| 2867 | (7*10^185221+131)/3 | 185222 | Robert Price | 06/2020 |
| 2868 | (62*10^185216-413)/9 | 185217 | Robert Price | 09/2021 |
| 2869 | (232*10^185180+17)/3 | 185182 | Robert Price | 04/2021 |
| 2870 | 56*10^185139-3 | 185141 | Robert Price | 03/2020 |
| 2871 | (28*10^185105+47)/3 | 185106 | Robert Price | 02/2021 |
| 2872 | 2^614783-2790097 | 185069 | Enzo Doria | 12/2015 |
| 2873 | 2^614745-29323 | 185057 | Enzo Doria | 07/2015 |
| 2874 | (((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840 | 185052 | Serge Batalov | 07/2013 |
| 2875 | (49*10^184993-67)/9 | 184994 | Robert Price | 03/2019 |
| 2876 | (5*10^184954-191)/3 | 184955 | Robert Price | 05/2021 |
| 2877 | (14*10^184950+211)/9 | 184951 | Robert Price | 04/2018 |
| 2878 | 2^614360+215221 | 184941 | Enzo Doria | 11/2023 |
| 2879 | 2^614315+81353 | 184928 | Enzo Doria | 08/2016 |
| 2880 | 2^614294-1849961 | 184921 | Enzo Doria | 08/2015 |
| 2881 | 2^614266+1877809 | 184913 | Enzo Doria | 08/2016 |
| 2882 | (185*10^184878-11)/3 | 184880 | Robert Price | 10/2020 |
| 2883 | 91*10^184867-9 | 184869 | Robert Price | 06/2021 |
| 2884 | 39803^40170-40170^39803 | 184779 | Norbert Schneider | 05/2024 |
| 2885 | (14789^44521-1)/(14789^211-1) | 184770 | Ryan Propper | 11/2023 |
| 2886 | (85*10^184768+77)/9 | 184769 | Robert Price | 07/2022 |
| 2887 | 2^613715-1860727 | 184747 | Enzo Doria | 11/2015 |
| 2888 | (4*10^184730+89)/3 | 184731 | Robert Price | 08/2021 |
| 2889 | 2*10^184723+41 | 184724 | Robert Price | 05/2018 |
| 2890 | (49*10^184703+293)/9 | 184704 | Robert Price | 03/2021 |
| 2891 | 2^613487-349987 | 184678 | Enzo Doria | 07/2015 |
| 2892 | (95^93377+1)/96 | 184672 | Paul Bourdelais | 11/2017 |
| 2893 | 14^161089-161089^14 | 184629 | Serge Batalov | 05/2016 |
| 2894 | 40008^40109-40109^40008 | 184588 | Norbert Schneider | 05/2024 |
| 2895 | 2^613033-114621 | 184542 | Enzo Doria | 05/2015 |
| 2896 | 3*2^612759+5 | 184460 | Jon Grantham | 07/2023 |
| 2897 | 2^612587+213413 | 184408 | Enzo Doria | 09/2023 |
| 2898 | (9^193247+1)/10 | 184404 | Paul Bourdelais | 02/2010 |
| 2899 | 2^612424+212341 | 184358 | Enzo Doria | 08/2023 |
| 2900 | 2^612341-1604809 | 184334 | Enzo Doria | 05/2015 |
| 2901 | (11*10^184308-161)/3 | 184309 | Robert Price | 11/2021 |
| 2902 | (2^611999-1)/18464214225958267477777390354183 | 184199 | Dario Alpern | 06/2017 |
| 2903 | (14*10^184150+37)/3 | 184151 | Robert Price | 12/2018 |
| 2904 | 2^611731-4837 | 184150 | Yves Minet | 08/2018 |
| 2905 | 3*10^184124-7 | 184125 | Robert Price | 08/2015 |
| 2906 | 2^611644+29371 | 184124 | Enzo Doria | 02/2024 |
| 2907 | 9*10^184122-11 | 184123 | Mischa Rodermond | 04/2023 |
| 2908 | 2^611628-24537 | 184119 | Enzo Doria | 08/2013 |
| 2909 | 3*10^184110+13 | 184111 | Robert Price | 07/2018 |
| 2910 | (14280^44521-1)/(14280^211-1) | 184097 | Ryan Propper | 11/2023 |
| 2911 | (194*10^184093+1)/3 | 184095 | Robert Price | 01/2022 |
| 2912 | 2^611460+71881 | 184068 | Enzo Doria | 04/2016 |
| 2913 | 4*10^184004-63 | 184005 | Robert Price | 10/2018 |
| 2914 | 2^611111+84083 | 183963 | Boyan Hu | 05/2024 |
| 2915 | 2^610982-1867301 | 183924 | Enzo Doria | 03/2016 |
| 2916 | (10^183917+1)/11/9952852373 | 183906 | Alfred Reich | 02/2024 |
| 2917 | 3*10^183872-49 | 183873 | Robert Price | 07/2018 |
| 2918 | 2^610597+1178897 | 183809 | Enzo Doria | 05/2016 |
| 2919 | (8*10^183773-269)/9 | 183773 | Robert Price | 09/2021 |
| 2920 | (65*10^183768-29)/9 | 183769 | Robert Price | 01/2021 |
| 2921 | (17*10^183764+31)/3 | 183765 | Robert Price | 01/2019 |
| 2922 | (28*10^183760-1)/9 | 183761 | Serge Batalov | 10/2014 |
| 2923 | 2^610401+1277 | 183750 | Lelio R Paula | 07/2013 |
| 2924 | 2^610356-1849019 | 183736 | Enzo Doria | 08/2015 |
| 2925 | (63^102103+1)/64 | 183717 | Paul Bourdelais | 10/2017 |
| 2926 | 23*10^183710-7 | 183712 | Robert Price | 02/2020 |
| 2927 | (2^610289+1)/(3*528882550291) | 183704 | Gord Palameta | 08/2018 |
| 2928 | (4*10^183659+149)/9 | 183659 | Robert Price | 04/2018 |
| 2929 | (4*10^183657+41)/9 | 183657 | Serge Batalov | 11/2022 |
| 2930 | (11^176327-1)/31738870 | 183619 | Paul Vanderveen | 05/2025 |
| 2931 | 7*10^183596+39 | 183597 | Robert Price | 01/2023 |
| 2932 | 2^609846-1834251 | 183582 | Enzo Doria | 07/2015 |
| 2933 | 10^183546+1547323 | 183547 | Patrick De Geest | 02/2021 |
| 2935 | 10^183546-800000001 | 183546 | Robert Price | 09/2020 |
| 2934 | 10^183546-584297 | 183546 | Patrick De Geest | 02/2021 |
| 2936 | 7*10^183511+39 | 183512 | Robert Price | 01/2023 |
| 2937 | (23*10^183477-71)/3 | 183478 | Robert Price | 07/2020 |
| 2938 | 11^176176-240 | 183469 | Enzo Doria | 11/2012 |
| 2939 | (41^113749+1)/42 | 183451 | Paul Bourdelais | 11/2017 |
| 2940 | 6*10^183429+53 | 183430 | Robert Price | 05/2020 |
| 2941 | (28*10^183403+191)/3 | 183404 | Robert Price | 02/2020 |
| 2942 | U(1096855) | 183383 | Serge Batalov | 07/2024 |
| 2943 | (5^262337-1)/363486427756606700767551233751524443601036 | 183325 | Paul Vanderveen | 05/2025 |
| 2944 | (101^91463+1)/102 | 183320 | Paul Bourdelais | 11/2017 |
| 2945 | 2^608965-113989 | 183317 | Enzo Doria | 10/2014 |
| 2946 | A005165(43592) | 183312 | Serge Batalov | 07/2017 |
| 2947 | (61*10^183294+119)/9 | 183295 | Robert Price | 05/2019 |
| 2948 | 2^608814-461261 | 183272 | Enzo Doria | 06/2015 |
| 2949 | (163*10^183227-1)/9 | 183229 | Serge Batalov | 12/2014 |
| 2950 | 2^608541-608541^2 | 183190 | Henri Lifchitz | 02/2018 |
| 2951 | 2^608293+143807 | 183115 | Enzo Doria | 10/2016 |
| 2952 | 2^608164-462419 | 183076 | Enzo Doria | 08/2015 |
| 2953 | 2^607950-1862303 | 183012 | Enzo Doria | 12/2015 |
| 2954 | 5*3^383376+2^383376 | 182918 | Jon Grantham | 08/2023 |
| 2955 | (46*10^182896+683)/9 | 182897 | Robert Price | 03/2019 |
| 2956 | (2*10^182787+73)/3 | 182787 | Robert Price | 09/2020 |
| 2957 | 2^607101+1871987 | 182756 | Enzo Doria | 05/2016 |
| 2958 | 2^606869-69175 | 182686 | Enzo Doria | 11/2015 |
| 2959 | 8*10^182671+71 | 182672 | Robert Price | 05/2022 |
| 2960 | (23*10^182666-71)/3 | 182667 | Robert Price | 07/2020 |
| 2961 | 3*10^182614-11 | 182615 | Robert Price | 07/2018 |
| 2962 | 2^606560-357 | 182593 | Enzo Doria | 05/2014 |
| 2963 | 66*10^182420+7 | 182422 | Robert Price | 07/2020 |
| 2964 | 2^605687+1866983 | 182330 | Enzo Doria | 03/2016 |
| 2965 | 2^605655-114445 | 182321 | Enzo Doria | 02/2015 |
| 2966 | 94*10^182291-3 | 182293 | Robert Price | 05/2020 |
| 2967 | (20^140053+1)/21 | 182212 | Paul Bourdelais | 04/2010 |
| 2968 | (14*10^182177-221)/9 | 182178 | Robert Price | 04/2018 |
| 2969 | 2^605174-112751 | 182176 | Enzo Doria | 06/2014 |
| 2970 | (905^61609-1)/904 | 182154 | Anonymous | 05/2024 |
| 2971 | 2^604761+1874507 | 182052 | Enzo Doria | 06/2016 |
| 2972 | 2^604705+1871957 | 182035 | Enzo Doria | 05/2016 |
| 2973 | (14*10^182000+229)/9 | 182001 | Robert Price | 03/2018 |
| 2974 | (10^181996+41)/3 | 181996 | Robert Price | 12/2017 |
| 2975 | (17*10^181979+91)/9 | 181980 | Robert Price | 02/2022 |
| 2976 | (10^181960+3)/7 | 181960 | Jinyuan Wang | 11/2024 |
| 2977 | (5*10^181950-101)/3 | 181951 | Robert Price | 04/2018 |
| 2978 | 2^603915+75233 | 181797 | Enzo Doria | 04/2016 |
| 2979 | 39470^39537+39537^39470 | 181723 | Norbert Schneider | 12/2022 |
| 2980 | (10^181710+7)/563747/2019847 | 181698 | Alfred Reich | 08/2021 |
| 2981 | 7*10^181594-57 | 181595 | Robert Price | 06/2020 |
| 2982 | 8*10^181580+29 | 181581 | Robert Price | 11/2021 |
| 2983 | (83*10^181544+61)/9 | 181545 | Serge Batalov | 01/2023 |
| 2984 | (2*10^181457+7)/9 | 181457 | Rytis Slatkevicius | 01/2023 |
| 2985 | 3*10^181445+23 | 181446 | Robert Price | 03/2022 |
| 2986 | (194*10^181369-11)/3 | 181371 | Robert Price | 09/2020 |
| 2987 | 11^174145-360 | 181354 | Enzo Doria | 10/2012 |
| 2988 | 2^602351-396765 | 181326 | Enzo Doria | 08/2013 |
| 2989 | 6*10^181306+17 | 181307 | Robert Price | 04/2019 |
| 2990 | (353^71143-1)/352 | 181254 | Anonymous | 04/2024 |
| 2991 | (286*10^181220-1)/3 | 181222 | Robert Price | 11/2020 |
| 2992 | 2^601957-113833 | 181208 | Enzo Doria | 09/2014 |
| 2993 | 66^99581-65^99581 | 181193 | Robert Price | 09/2013 |
| 2994 | 10^181182+383973 | 181183 | Patrick De Geest | 04/2016 |
| 2995 | 10^181182-21 | 181182 | Serge Batalov | 12/2014 |
| 2996 | (797*10^181171-41)/9 | 181173 | Robert Price | 04/2022 |
| 2997 | 2^601722+74209 | 181137 | Enzo Doria | 08/2023 |
| 2998 | (5*10^181127-29)/3 | 181128 | Robert Price | 03/2018 |
| 2999 | 2^601521-29143 | 181076 | Enzo Doria | 07/2015 |
| 3000 | 2^601442-2797811 | 181053 | Enzo Doria | 04/2016 |
