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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
2751 | (289511#+292834)/(2^3*146417) | 125444 | Makoto Morimoto | 10/2017 |
2752 | (11*2^416691+1)/43 | 125436 | Lelio R Paula | 05/2014 |
2753 | (289511#+1896)/(2*3^3*79*780193*9911849) | 125434 | Makoto Morimoto | 06/2019 |
2754 | 2^416641-2*416641+1 | 125422 | Robert Price | 05/2018 |
2755 | (21*2^416566-1)/17 | 125399 | Lelio R Paula | 05/2014 |
2756 | 2^416530+1870429 | 125389 | Enzo Doria | 05/2016 |
2757 | (56*10^125385+691)/9 | 125386 | Robert Price | 05/2019 |
2758 | 2^416490+1875109 | 125376 | Enzo Doria | 09/2016 |
2759 | 2^416416-114929 | 125354 | Enzo Doria | 05/2015 |
2760 | (77*10^125330-293)/9 | 125331 | Robert Price | 09/2019 |
2761 | (172*10^125292-1)/9 | 125294 | Serge Batalov | 12/2014 |
2762 | 2^416134+1865899 | 125269 | Enzo Doria | 03/2016 |
2763 | 153^57337-152 | 125264 | Norbert Schneider | 12/2018 |
2764 | (9*2^415992+1)/13560845 | 125220 | Lelio R Paula | 05/2014 |
2765 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
2766 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
2767 | (38*10^125166+349)/9 | 125167 | Robert Price | 10/2018 |
2768 | 2^415765-112603 | 125158 | Enzo Doria | 06/2014 |
2769 | 8*10^125088-13 | 125089 | Robert Price | 08/2019 |
2770 | (25*10^125076-13)/3 | 125077 | Robert Price | 09/2019 |
2771 | (29*10^125021-113)/3 | 125022 | Robert Price | 10/2019 |
2772 | 2^415290-113591 | 125015 | Enzo Doria | 08/2014 |
2773 | 2^415276-460919 | 125011 | Enzo Doria | 06/2015 |
2774 | 2^415259+77243 | 125006 | Enzo Doria | 05/2016 |
2775 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
2776 | 2^414874+79 | 124890 | Lelio R Paula | 01/2015 |
2777 | (2^414765+7)/1389 | 124854 | Lelio R Paula | 05/2014 |
2778 | 2^414618+79459 | 124813 | Enzo Doria | 06/2016 |
2779 | (61*10^124809-1)/3 | 124811 | Robert Price | 01/2020 |
2780 | 2^414432-1846709 | 124757 | Enzo Doria | 07/2015 |
2781 | 2*10^124751-51 | 124752 | Robert Price | 04/2018 |
2782 | (56*10^124735+367)/9 | 124736 | Robert Price | 06/2019 |
2783 | (13*2^414274-1)/153 | 124708 | Lelio R Paula | 05/2014 |
2784 | 56*10^124656-3 | 124658 | Robert Price | 03/2020 |
2785 | (7*10^124648+197)/3 | 124649 | Robert Price | 07/2018 |
2787 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
2786 | 2^414032+1872331 | 124637 | Enzo Doria | 05/2016 |
2788 | 14120^30009-30009^14120 | 124533 | Norbert Schneider | 02/2015 |
2789 | (85*10^124485-49)/9 | 124486 | Robert Price | 12/2020 |
2790 | 64^68909-63^68909 | 124463 | Robert Price | 07/2013 |
2791 | 2^413387+76253 | 124442 | Enzo Doria | 04/2016 |
2792 | 2^413352+524287 | 124432 | Paul Underwood | 09/2018 |
2793 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
2794 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
2795 | (27*2^413207-1)/108335 | 124385 | Lelio R Paula | 05/2014 |
2796 | (41*10^124335-383)/9 | 124336 | Robert Price | 11/2018 |
2797 | (304*10^124329-43)/9 | 124331 | Robert Price | 02/2020 |
2798 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
2799 | 10^124248-1000001 | 124248 | Robert Price | 08/2020 |
2800 | 45^75145-2 | 124231 | Lelio R Paula | 08/2015 |
2801 | 2^412645-112213 | 124219 | Enzo Doria | 06/2014 |
2802 | 2^412248+74611 | 124100 | Enzo Doria | 04/2016 |
2803 | (22*10^124096-13)/9 | 124097 | Robert Price | 06/2018 |
2804 | 2^412192-3329 | 124083 | Yves Minet | 12/2014 |
2805 | (25*2^412191-1)/23 | 124082 | Lelio R Paula | 05/2014 |
2806 | (25*10^124076-67)/3 | 124077 | Robert Price | 06/2019 |
2807 | F(593689) | 124074 | Henri Lifchitz | 01/2005 |
2808 | (11*2^412161+1)/19 | 124073 | Lelio R Paula | 05/2014 |
2809 | (266*10^124022-11)/3 | 124024 | Robert Price | 04/2020 |
2810 | 2^411884-113279 | 123990 | Enzo Doria | 07/2014 |
2811 | (2^411832+1)/257 | 123972 | Lelio R Paula | 05/2014 |
2812 | (2^411833+2)/514 | 123972 | Stefano Morozzi | 03/2020 |
2813 | (26*10^123970-89)/9 | 123971 | Robert Price | 06/2018 |
2814 | 2^411790-1853531 | 123962 | Enzo Doria | 08/2015 |
2815 | (5^177337+1)/6 | 123953 | Paul Bourdelais | 11/2008 |
2816 | 2^411711-113257 | 123938 | Enzo Doria | 07/2014 |
2817 | (23*2^411675-1)/3 | 123928 | Lelio R Paula | 05/2014 |
2818 | (11*10^123899-179)/3 | 123900 | Robert Price | 09/2018 |
2819 | 2^411325-351103 | 123822 | Enzo Doria | 06/2015 |
2820 | 2^411052+1872481 | 123739 | Enzo Doria | 05/2016 |
2821 | 2^410997+39 | 123723 | Lelio R Paula | 05/2014 |
2822 | (649^43987-1)/648 | 123700 | Michael Stocker | 05/2020 |
2823 | (148*10^123688-1)/3 | 123690 | Robert Price | 03/2020 |
2824 | 8*10^123657+87 | 123658 | Robert Price | 10/2019 |
2825 | 155^56438+154 | 123618 | Norbert Schneider | 01/2019 |
2826 | 2^410596-39 | 123602 | Lelio R Paula | 05/2014 |
2827 | 2^410540-115079 | 123585 | Enzo Doria | 06/2015 |
2828 | (7*10^123563+107)/3 | 123564 | Robert Price | 02/2018 |
2829 | 9*10^123549+89 | 123550 | Robert Price | 11/2019 |
2830 | (197*10^123545+7)/3 | 123547 | Robert Price | 12/2020 |
2831 | (3*2^410392-1)/9229 | 123537 | Lelio R Paula | 05/2014 |
2832 | 2^410206-113081 | 123485 | Enzo Doria | 07/2014 |
2833 | (25*2^410192+1)/10397 | 123478 | Lelio R Paula | 04/2014 |
2834 | 2^409909-189 | 123395 | Enzo Doria | 05/2014 |
2835 | 2^409896-109043 | 123391 | Enzo Doria | 04/2014 |
2836 | 2^409890+75409 | 123390 | Enzo Doria | 04/2016 |
2837 | 133^58076-2 | 123345 | Lelio R Paula | 10/2017 |
2838 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
2839 | 2^409566-113501 | 123292 | Enzo Doria | 08/2014 |
2840 | 2^409533+77747 | 123282 | Enzo Doria | 05/2016 |
2841 | 2^409436-112799 | 123253 | Enzo Doria | 06/2014 |
2842 | 2^409225+1873787 | 123189 | Enzo Doria | 06/2016 |
2843 | 2^409174+73009 | 123174 | Enzo Doria | 04/2016 |
2844 | 2^409058-112685 | 123139 | Enzo Doria | 06/2014 |
2845 | (13*10^123137-61)/3 | 123138 | Robert Price | 11/2018 |
2846 | 4*10^123113+21 | 123114 | Robert Price | 12/2018 |
2847 | 2^408778+77689 | 123055 | Enzo Doria | 05/2016 |
2848 | 2^408690-75 | 123028 | Lelio R Paula | 11/2013 |
2849 | (29*10^122996+673)/9 | 122997 | Robert Price | 12/2018 |
2850 | 2^408574-2787341 | 122994 | Enzo Doria | 03/2016 |
2851 | 3*10^122977+37 | 122978 | Robert Price | 08/2018 |
2852 | Phi(157825,10) | 122961 | Maksym Voznyy | 06/2015 |
2853 | (68*10^122933-419)/9 | 122934 | Robert Price | 07/2019 |
2854 | (13*2^408283+1)/1665 | 122904 | Lelio R Paula | 05/2014 |
2855 | (266*10^122872-17)/3 | 122874 | Robert Price | 07/2020 |
2856 | (16*10^122871+77)/3 | 122872 | Robert Price | 03/2019 |
2857 | (11*2^408100-1)/35 | 122850 | Lelio R Paula | 04/2014 |
2858 | (19*10^122836-43)/3 | 122837 | Robert Price | 05/2019 |
2859 | (2^407821-lucasV(1,2,407821)+1)/2 | 122767 | Mike Oakes | 11/2016 |
2860 | (32*10^122733-77)/9 | 122734 | Robert Price | 06/2018 |
2861 | (21*2^407604-1)/215 | 122701 | Lelio R Paula | 04/2014 |
2862 | (22*10^122681+161)/3 | 122682 | Robert Price | 05/2019 |
2863 | (21*2^407433-1)/13 | 122650 | Lelio R Paula | 04/2014 |
2864 | (26*10^122625-131)/3 | 122626 | Robert Price | 10/2019 |
2865 | (73*10^122592-1)/9 | 122593 | Robert Price | 01/2015 |
2866 | (5*10^122592+91)/3 | 122593 | Robert Price | 04/2018 |
2867 | (85*10^122585-1)/3 | 122587 | Robert Price | 02/2020 |
2868 | 2^407179-112075 | 122574 | Enzo Doria | 06/2014 |
2869 | (21*2^407131+1)/207517523 | 122552 | Lelio R Paula | 04/2014 |
2870 | (66^67349+1)/67 | 122543 | Paul Bourdelais | 09/2017 |
2871 | 2^407008-1867919 | 122522 | Enzo Doria | 04/2016 |
2872 | 11^117642-300 | 122512 | Enzo Doria | 10/2012 |
2873 | (F(3*97700+1)^2+L(3*97700+1)^2)/2 | 122509 | Henri Lifchitz | 10/2017 |
2874 | 2^406949+72197 | 122504 | Enzo Doria | 04/2016 |
2875 | (19*10^122501+149)/3 | 122502 | Robert Price | 05/2019 |
2876 | 2^406826-65 | 122467 | Lelio R Paula | 11/2013 |
2877 | 2^406821-2797363 | 122466 | Enzo Doria | 04/2016 |
2878 | 2^406758-17 | 122447 | Lelio R Paula | 11/2013 |
2879 | (30^82883-1)/29 | 122427 | Robert Price | 12/2011 |
2880 | 27496^27577+27577^27496 | 122422 | Norbert Schneider | 12/2020 |
2881 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
2882 | 4*10^122377+19 | 122378 | Robert Price | 10/2018 |
2883 | Phi(246362,10) | 122365 | Makoto Kamada | 09/2019 |
2884 | 3*10^122345-97 | 122346 | Robert Price | 07/2018 |
2885 | 97^61575-2 | 122336 | Lelio R Paula | 12/2014 |
2886 | 208^52765+52765^208 | 122313 | Norbert Schneider | 11/2020 |
2887 | 2^406298+2799109 | 122308 | Enzo Doria | 04/2016 |
2888 | 7*10^122294+57 | 122295 | Robert Price | 06/2019 |
2889 | (27*2^406241-1)/10277 | 122289 | Lelio R Paula | 04/2014 |
2890 | 2^406229-1849993 | 122288 | Enzo Doria | 08/2015 |
2891 | 3*10^122274+7 | 122275 | Robert Price | 07/2015 |
2892 | 2^406117+1876577 | 122254 | Enzo Doria | 07/2016 |
2893 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
2894 | 2^405992-78557 | 122216 | Jorge Menendez | 03/2018 |
2895 | (8*10^122203+43)/3 | 122204 | Robert Price | 06/2018 |
2896 | (58*10^122170+329)/9 | 122171 | Robert Price | 05/2019 |
2897 | 2^405774+179149 | 122151 | Enzo Doria | 06/2016 |
2898 | 34*10^122082-9 | 122084 | Robert Price | 06/2020 |
2899 | 5*10^122082+41 | 122083 | Robert Price | 03/2019 |
2900 | 2^405514-3311 | 122072 | Yves Minet | 12/2014 |
2901 | 2^405514-115511 | 122072 | Enzo Doria | 07/2015 |
2902 | 23*10^122070-7 | 122072 | Robert Price | 02/2020 |
2903 | 2^405422-113261 | 122045 | Enzo Doria | 07/2014 |
2904 | 2^405173+71237 | 121970 | Enzo Doria | 04/2016 |
2905 | (2^405016+1)/257 | 121920 | Lelio R Paula | 04/2014 |
2906 | 2^404858+71329 | 121875 | Enzo Doria | 04/2016 |
2907 | 2^404813-114703 | 121861 | Enzo Doria | 04/2015 |
2908 | 2^404764+77791 | 121847 | Enzo Doria | 05/2016 |
2909 | 317^48694+48694^317 | 121787 | Norbert Schneider | 08/2015 |
2910 | 2^404536-115259 | 121778 | Enzo Doria | 06/2015 |
2911 | 2^404501-631 | 121767 | Yves Minet | 07/2012 |
2912 | 63^67620+2 | 121672 | Lelio R Paula | 08/2015 |
2913 | (16*10^121633+167)/3 | 121634 | Robert Price | 06/2019 |
2914 | (17*10^121621+1)/9 | 121622 | Serge Batalov | 05/2010 |
2915 | (15*2^403912+1)/271 | 121589 | Lelio R Paula | 05/2014 |
2916 | (10^121543-79)/3 | 121543 | Robert Price | 01/2018 |
2917 | 2^403676+76831 | 121519 | Enzo Doria | 05/2016 |
2918 | (7*10^121487+143)/3 | 121488 | Robert Price | 03/2018 |
2919 | 2^403363-113635 | 121425 | Enzo Doria | 08/2014 |
2920 | 2^403336-1861469 | 121417 | Enzo Doria | 03/2016 |
2921 | p(24442)#/2-64 | 121381 | Robert Price | 04/2017 |
2922 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
2923 | 2^403100-461267 | 121346 | Enzo Doria | 07/2015 |
2924 | 2^403093-112213 | 121344 | Enzo Doria | 06/2014 |
2925 | (316^48539+1)/317 | 121330 | Eric Chen | 10/2017 |
2926 | (23*10^121320-71)/3 | 121321 | Robert Price | 07/2020 |
2927 | 2^403004+1866361 | 121317 | Enzo Doria | 03/2016 |
2928 | 2^402953+89 | 121301 | Lelio R Paula | 10/2013 |
2929 | 2^402944-2788319 | 121299 | Enzo Doria | 03/2016 |
2930 | (44*10^121297-719)/9 | 121298 | Robert Price | 12/2018 |
2931 | (27*2^402865+1)/5 | 121276 | Lelio R Paula | 04/2014 |
2932 | 2^402828-113183 | 121264 | Enzo Doria | 07/2014 |
2933 | (17*10^121242+1)/9 | 121243 | Serge Batalov | 05/2010 |
2934 | (15*2^402757+1)/101 | 121242 | Lelio R Paula | 05/2014 |
2935 | 2^402715+1874223 | 121230 | Enzo Doria | 06/2016 |
2936 | (35*10^121229-593)/9 | 121230 | Robert Price | 07/2018 |
2937 | (91^61879+1)/92 | 121222 | Paul Bourdelais | 09/2017 |
2938 | 7*10^121144+9 | 121145 | Robert Price | 09/2015 |
2939 | 2^401725-113251 | 120932 | Enzo Doria | 07/2014 |
2940 | (15*2^401677-1)/19 | 120917 | Lelio R Paula | 05/2014 |
2941 | 2^401652+73711 | 120910 | Enzo Doria | 04/2016 |
2942 | (2^401632+3)/79 | 120902 | Lelio R Paula | 04/2014 |
2943 | 40450^973+973^40450 | 120870 | Hans Havermann | 01/2021 |
2944 | 10^120841+88417 | 120842 | Patrick De Geest | 04/2020 |
2945 | 10^120841-123456789 | 120841 | Robert Price | 02/2020 |
2946 | 10^120841-176853 | 120841 | Patrick De Geest | 04/2020 |
2947 | 2^401406-2791331 | 120836 | Enzo Doria | 03/2016 |
2948 | (28^83497+1)/29 | 120832 | Robert Price | 07/2013 |
2949 | (22*10^120828+161)/3 | 120829 | Robert Price | 05/2019 |
2950 | 2^401369+1867367 | 120825 | Enzo Doria | 03/2016 |
2951 | (10^120782+29)/3 | 120782 | Serge Batalov | 12/2014 |
2952 | 2^401215-1657 | 120778 | Yves Minet | 07/2014 |
2953 | 2^401159+53 | 120761 | Lelio R Paula | 10/2013 |
2954 | 27782^22179+22179^27782 | 120739 | Hans Havermann | 01/2021 |
2955 | 2^401031-113047 | 120723 | Enzo Doria | 07/2014 |
2956 | (71*10^120703-287)/9 | 120704 | Robert Price | 09/2019 |
2957 | (29*2^400909-1)/303 | 120685 | Lelio R Paula | 04/2014 |
2958 | (2^400846+538)/2 | 120667 | Stefano Morozzi | 09/2020 |
2959 | (2^400709+3546)/2 | 120626 | Stefano Morozzi | 09/2020 |
2960 | (2^400700+3126)/2 | 120623 | Stefano Morozzi | 09/2020 |
2961 | (2^400693+2634)/2 | 120621 | Stefano Morozzi | 09/2020 |
2962 | 2^400571-15 | 120584 | Lelio R Paula | 10/2013 |
2963 | (10^120574+359)/9 | 120574 | Serge Batalov | 12/2014 |
2964 | 2^400424-216413 | 120540 | Enzo Doria | 04/2013 |
2965 | (2^400346+1722)/2 | 120516 | Stefano Morozzi | 09/2020 |
2966 | (17*2^400200-1)/587 | 120471 | Lelio R Paula | 05/2014 |
2968 | 2^400166+1874899 | 120462 | Enzo Doria | 06/2016 |
2967 | (2^400165+1602)/2 | 120462 | Stefano Morozzi | 09/2020 |
2969 | (2^400084+1638)/2 | 120437 | Stefano Morozzi | 09/2020 |
2970 | (3*2^400045-1)/865 | 120424 | Lelio R Paula | 04/2014 |
2971 | 2^399966+73759 | 120402 | Enzo Doria | 04/2016 |
2972 | (112*10^120395-1)/3 | 120397 | Serge Batalov | 12/2014 |
2973 | 2^399918-95 | 120388 | Lelio R Paula | 04/2013 |
2974 | (28*10^120381-67)/3 | 120382 | Robert Price | 10/2020 |
2975 | (49*10^120380-139)/9 | 120381 | Robert Price | 03/2019 |
2976 | (2^399874+2194)/2 | 120374 | Stefano Morozzi | 09/2020 |
2977 | 2^399792-1849259 | 120350 | Enzo Doria | 08/2015 |
2978 | 9*10^120342-7 | 120343 | Robert Price | 09/2015 |
2979 | (2^399751+786)/2 | 120337 | Stefano Morozzi | 09/2020 |
2980 | (13*10^120306-37)/3 | 120307 | Robert Price | 01/2019 |
2981 | (2^399604+3070)/2 | 120293 | Stefano Morozzi | 09/2020 |
2982 | (2^399549+1062)/2 | 120276 | Stefano Morozzi | 09/2020 |
2983 | 2^399526-1861721 | 120270 | Enzo Doria | 11/2015 |
2984 | (10^(2*60126+1)+36*10^60126-1)/9 | 120253 | Robert Price | 10/2015 |
2985 | 2^399322-2798111 | 120208 | Enzo Doria | 04/2016 |
2986 | 72^64693-71^64693 | 120157 | Robert Price | 03/2014 |
2987 | 2^399111-28489 | 120145 | Enzo Doria | 08/2015 |
2989 | 2^398877+105 | 120074 | Donovan Johnson | 01/2006 |
2988 | (101*10^120072-87)/7 | 120074 | Hans Havermann | 02/2015 |
2990 | (88^61751+1)/89 | 120072 | Paul Bourdelais | 09/2017 |
2991 | 2^398710+57 | 120024 | Lelio R Paula | 04/2013 |
2992 | (2^398698+1138)/2 | 120020 | Stefano Morozzi | 09/2020 |
2993 | 2^398691-115057 | 120018 | Enzo Doria | 06/2015 |
2994 | L(574219) | 120005 | Renaud Lifchitz | 03/2004 |
2995 | 2^398571+60413 | 119982 | Yves Minet | 03/2011 |
2996 | p(24179)#/2-64 | 119949 | Robert Price | 04/2017 |
2997 | 2^398448+1872001 | 119945 | Enzo Doria | 05/2016 |
2998 | 634^42803+42803^634 | 119938 | Norbert Schneider | 07/2019 |
2999 | (68*10^119931-11)/3 | 119933 | Robert Price | 01/2020 |
3000 | 8*10^119930-3 | 119931 | Ray Chandler | 04/2011 |