## PRP Records

### Probable Primes Top 10000

#### (293510 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 ? 751 2^983620+60451 296100 Phil Moore 03/2008 752 2^982721-2683 295829 Yves Minet 02/2016 753 (23*10^295581+7)/3 295582 Robert Price 05/2023 754 2^981298-2788421 295401 Enzo Doria 12/2015 755 2^981163-2790967 295360 Enzo Doria 12/2015 756 2^981016-15 295316 Stefano Morozzi 07/2022 757 8*10^295160-13 295161 Robert Price 08/2023 758 2^979594+1865839 294888 Enzo Doria 02/2016 759 2*10^294527-91 294528 Robert Price 02/2023 760 10^294475+49 294476 Robert Price 02/2023 761 (11*10^294308+91)/3 294309 Robert Price 03/2023 762 2^976760+1885021 294035 Enzo Doria 02/2017 763 3*2^976518+5 293962 Jon Grantham 07/2023 764 2^974441+1878407 293336 Enzo Doria 08/2016 765 2^974180+1876831 293258 Enzo Doria 07/2016 766 2^974170+453319 293255 Enzo Doria 01/2017 767 2^972744-114419 292826 Enzo Doria 03/2015 768 11^281143+6 292781 Paul Bourdelais 03/2021 769 (4*10^292619-91)/3 292620 Robert Price 12/2022 770 CopelandErdos(292447) 292447 Mark Rodenkirch 12/2015 771 3*10^292344-97 292345 Robert Price 01/2023 772 2^970911+1873373 292274 Enzo Doria 07/2016 773 2^970670+383059 292201 Enzo Doria 12/2016 774 2^970141-100363 292042 Enzo Doria 02/2014 775 2^969945+1874717 291983 Enzo Doria 06/2016 776 2^969384+1880701 291814 Enzo Doria 10/2016 777 (13*10^291721-43)/3 291722 Robert Price 08/2023 778 (3^611333-2^611333)/(99035947*87109884549431) 291659 Mike Oakes 02/2017 779 3*2^963892+5 290161 Jon Grantham 07/2023 780 (151*10^289877-1)/3 289879 Robert Price 07/2023 781 2^962194+60139 289650 Enzo Doria 02/2016 782 2^959307-1861507 288781 Enzo Doria 11/2015 783 (17*10^288692+31)/3 288693 Robert Price 04/2023 784 14^251797-3 288592 Paul Bourdelais 12/2020 785 (2*10^288371-23)/3 288371 Robert Price 10/2022 786 (31*10^288238-1)/3 288240 Robert Price 02/2023 787 (7^341063-2^341063)/5 288231 Jon Grantham 08/2023 788 2^957372+283531 288198 Enzo Doria 02/2017 789 2^957192-1864049 288144 Enzo Doria 01/2016 790 2^956446+1875199 287919 Enzo Doria 06/2016 791 7*10^287854+39 287855 Robert Price 01/2023 792 (17^233689+1)/18 287542 Paul Bourdelais 09/2013 793 2^955178+1883587 287538 Enzo Doria 12/2016 794 2^954127-954127^2 287221 Henri Lifchitz 01/2021 795 2^954001+1875257 287183 Enzo Doria 07/2016 796 2*10^287175-49 287176 Robert Price 05/2023 797 (22*10^287085-19)/3 287086 Robert Price 07/2023 798 2^953488+22411 287029 Enzo Doria 09/2023 799 (23891^65536+1)/2 286932 Serge Batalov 03/2018 800 5*3^601336-2^601336 286911 Jon Grantham 08/2023 801 2^952268+1878601 286662 Enzo Doria 09/2016 802 2^950801+81557 286220 Enzo Doria 08/2016 803 22845^65536+22844^65536 285658 Kellen Shenton 03/2021 804 (11*2^948635-13)/15 285568 Renaud Lifchitz 11/2011 805 (54^164839+1)/55 285565 Paul Bourdelais 07/2019 806 2^948510+782569 285530 Enzo Doria 10/2016 807 2^948374-114137 285490 Enzo Doria 01/2015 808 2^947739+1872923 285298 Enzo Doria 06/2016 809 7*10^284751+9 284752 Robert Price 04/2023 810 2^944561-21 284342 Stefano Morozzi 07/2022 811 (4*10^284330-31)/9 284330 Serge Batalov 11/2022 812 (32*10^283826-23)/9 283827 Serge Batalov 01/2023 813 2^942533+82067 283731 Enzo Doria 09/2016 814 2^941469+39 283411 Jon Grantham 08/2023 815 (10^283342-31)/3 283342 Robert Price 03/2023 816 2^940950+1874989 283255 Enzo Doria 06/2016 817 2^940426-2786141 283097 Enzo Doria 11/2015 818 (2*10^282948-11)/9 282948 Serge Batalov 11/2022 819 2^939881-114115 282933 Enzo Doria 12/2014 820 (14*10^282673-143)/3 282674 Robert Price 05/2023 821 10^282493+632551 282494 Patrick De Geest 02/2017 823 10^282493-9^282493 282493 Jean-Louis Charton 03/2007 822 10^282493-132327 282493 Patrick De Geest 02/2017 824 3^591827-2^591827 282374 Mike Oakes 08/2009 825 Tau(509^18946) 282048 Nik Lygeros / Olivier Rozier 05/2015 826 2^936716-1835519 281980 Enzo Doria 04/2015 827 2^936588+79411 281942 Enzo Doria 06/2016 828 2^936047+1877423 281779 Enzo Doria 08/2016 829 2^935713+1869377 281678 Enzo Doria 05/2016 830 2^933082+1877059 280886 Enzo Doria 08/2016 831 (5*10^280710+1)/3 280711 Serge Batalov 10/2014 832 2^931976+25 280553 Stefano Morozzi 05/2021 833 (42^172663+1)/43 280274 Paul Bourdelais 07/2019 834 (10^279978+11)/3 279978 Serge Batalov 07/2015 835 2^929524-1864829 279815 Enzo Doria 01/2016 836 2^929329+22697 279756 Enzo Doria 09/2023 837 2^929152+60181 279703 Enzo Doria 02/2016 838 2^928621-2787883 279543 Enzo Doria 11/2015 839 (2^927763+lucasV(-1,2,927763)+1)/2 279285 Mike Oakes 04/2017 840 2^927429+1882277 279184 Enzo Doria 12/2016 841 2^926766-11 278985 Stefano Morozzi 07/2022 842 (71^150697-1)/70 278978 Paul Bourdelais 07/2019 843 (33^183661-1)/32 278891 Paul Bourdelais 12/2018 844 (166*10^278633-7)/3 278635 Robert Price 02/2023 845 (2^925391+lucasV(-1,2,925391)+1)/2 278571 Mike Oakes 03/2017 846 2^925330-1301 278553 Yves Minet 06/2015 847 (299*10^278546+1)/3 278548 Robert Price 01/2023 848 (21^210599+1)/22 278457 Paul Bourdelais 08/2013 849 (266*10^278325+1)/3 278327 Robert Price 01/2023 850 2^923261-69175 277930 Enzo Doria 11/2015 851 757^96487-756^96487 277796 Jean-Louis Charton 12/2012 852 2^922301+57 277641 Stefano Morozzi 05/2021 853 7*10^277478-39 277479 Robert Price 07/2023 854 ((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2 277369 Serge Batalov 07/2016 855 (5^396413-1)/4 277081 Paul Bourdelais 06/2010 856 2^920318+2792299 277044 Enzo Doria 02/2016 857 (16*10^276537-31)/3 276538 Robert Price 03/2023 858 2^918596-2786939 276525 Enzo Doria 11/2015 859 2^916639+60563 275936 Enzo Doria 04/2016 860 (2*10^275922+1)/3 275922 Serge Batalov 11/2022 861 2^916385-2786383 275860 Enzo Doria 11/2015 862 2^915928+82081 275722 Enzo Doria 09/2016 863 (4*10^275671+11)/3 275672 Tyler Busby 02/2023 864 2^915576-114137 275616 Enzo Doria 01/2015 865 2^914828+1876741 275391 Enzo Doria 07/2016 866 2^914757-2203 275370 Yves Minet 12/2015 867 7*10^275157-27 275158 Robert Price 11/2022 868 2^912744+20011 274764 Enzo Doria 06/2023 869 2^911900+1871245 274510 Enzo Doria 05/2016 870 (16*10^274251-91)/3 274252 Robert Price 11/2022 871 2^910999+9 274239 Stefano Morozzi 05/2021 872 (2^910869-7)/5 274199 Stefano Morozzi 08/2022 873 2^910490+283429 274085 Enzo Doria 01/2017 874 7*10^273983+39 273984 Robert Price 01/2023 875 2^909988-1862249 273934 Enzo Doria 12/2015 876 2^909297+1879157 273726 Enzo Doria 08/2016 877 2^909257-1864423 273714 Enzo Doria 01/2016 878 2^908739-7 273558 Stefano Morozzi 07/2022 879 2^908579-1861747 273510 Enzo Doria 12/2015 880 3*2^908005-5 273338 Jon Grantham 07/2023 881 2^907635-2791597 273226 Enzo Doria 01/2016 882 2^907059+211193 273052 Enzo Doria 08/2023 883 (53^158341+1)/54 273022 Paul Bourdelais 07/2019 884 2^906594-113201 272912 Enzo Doria 08/2014 885 9*10^272800+91 272801 Robert Price 05/2023 886 2*10^272710-49 272711 Robert Price 05/2023 887 2*10^272403-91 272404 Robert Price 02/2023 888 2^904773+1872167 272364 Enzo Doria 06/2016 889 6^349903+5 272278 Paul Bourdelais 02/2021 890 2^904149-1862473 272176 Enzo Doria 12/2015 891 (7*10^271757-61)/9 271757 Erik Branger 03/2012 892 2^902497+1880117 271679 Enzo Doria 09/2016 893 2^901858+77689 271487 Enzo Doria 06/2016 894 2^901372+1875301 271341 Enzo Doria 06/2016 895 (8*10^271039-77)/3 271040 Robert Price 04/2023 896 2^899999+1144031 270927 Norman Luhn 09/2023 897 2*10^270802-91 270803 Robert Price 02/2023 898 23*10^270799-7 270801 Robert Price 10/2022 899 2^899121-115033 270663 Enzo Doria 07/2015 900 2^898900+883021 270596 Enzo Doria 12/2016 901 2^898762-251511 270555 Enzo Doria 12/2013 902 2^898589+47 270503 Lelio R Paula 03/2016 903 187322*10^270343-187321 270349 Danilo Nitsche 09/2013 904 48358*10^270343-48357 270348 Danilo Nitsche 09/2013 905 (10^270343-1)/9 270343 Maksym Voznyy 07/2007 906 2^897867-3217 270285 Yves Minet 12/2016 907 2^897849-115273 270280 Enzo Doria 07/2015 908 2^896616-114179 269909 Enzo Doria 12/2014 909 (22*10^269517-19)/3 269518 Robert Price 07/2023 910 10^(2*134739+1)-7*10^134739-1 269479 Robert Price 07/2023 911 2^894928+583561 269401 Enzo Doria 04/2017 912 2^894673-39343 269324 Enzo Doria 08/2015 913 F(1285607) 268676 Henri Lifchitz 11/2008 914 2^892234+22189 268590 Enzo Doria 09/2023 915 2^892112+187663 268553 Enzo Doria 08/2016 916 (266*10^268407-17)/3 268409 Robert Price 02/2023 917 (10^268207+1)/11 268206 Paul Bourdelais 02/2010 918 2^890957-69583 268205 Enzo Doria 12/2015 919 32841!^2+32840!^2+...+2!^2+1!^2 268128 Serge Batalov 07/2017 920 2^890122-351401 267954 Enzo Doria 07/2015 921 (19^209359-1)/18 267718 Paul Bourdelais 08/2010 922 (85^138647+1)/86 267507 Paul Bourdelais 07/2019 923 (485^99523-1)/484 267291 Michael Stocker 05/2020 924 2^886324+77791 266811 Enzo Doria 06/2016 925 7*10^266731+87 266732 Robert Price 11/2022 926 2^884714+1880527 266326 Enzo Doria 10/2016 927 7*10^266024-47 266025 Robert Price 08/2023 928 11^255426+255426^11 265999 Serge Batalov 05/2014 929 2^883462-343421 265949 Enzo Doria 07/2015 930 2^883442+1875019 265943 Enzo Doria 06/2016 931 2^883333-291583 265910 Enzo Doria 07/2015 932 10^265566+3593037 265567 Paul Bourdelais 08/2023 933 (2*10^265321-17)/3 265321 Serge Batalov 11/2022 934 (16*10^265052-91)/3 265053 Robert Price 11/2022 935 2^880411+1882673 265031 Enzo Doria 12/2016 936 (14*10^264791-11)/3 264792 Robert Price 08/2022 937 2^879530-2788031 264765 Enzo Doria 12/2015 938 (2*10^264539+61)/9 264539 Serge Batalov 11/2022 939 2^878118+2793079 264340 Enzo Doria 02/2016 940 (2^878073-7)/5 264326 Stefano Morozzi 08/2022 941 (37^168527-1)/36 264283 Paul Bourdelais 08/2019 942 5^377865+3^377865-1 264117 Jon Grantham 08/2023 943 (19*10^263971+131)/3 263972 Robert Price 08/2023 944 2^876202-17 263764 Stefano Morozzi 07/2022 945 (14*10^263720-11)/3 263721 Robert Price 08/2022 946 2^875748-461129 263627 Enzo Doria 07/2015 947 2^875518-15 263558 Stefano Morozzi 07/2022 948 (29*10^263523-17)/3 263524 Robert Price 01/2023 949 2^875181-2789923 263456 Enzo Doria 12/2015 950 2^875101-350083 263432 Enzo Doria 08/2015 951 2^874684+1883587 263307 Enzo Doria 01/2017 952 2^874616+1872211 263286 Enzo Doria 05/2016 953 3^551491+16 263129 Robert Price 04/2020 954 2^874073+2792957 263123 Enzo Doria 02/2016 955 2^873628+1878751 262989 Enzo Doria 08/2016 956 2^873497+20837 262949 Enzo Doria 08/2023 957 2^873288-269 262886 Yves Minet 01/2015 958 (2*10^262874+7)/9 262874 Rytis Slatkevicius 01/2023 959 (28*10^262655-43)/3 262656 Robert Price 04/2023 960 (2*10^262603-11)/9 262603 Serge Batalov 11/2022 961 2^871991-4207 262496 Yves Minet 03/2021 962 (23*10^262324+7)/3 262325 Robert Price 05/2023 963 2^871146-3173 262242 Yves Minet 07/2016 964 2^869601-163 261776 Yves Minet 01/2015 965 (2*10^261704+61)/9 261704 Serge Batalov 11/2022 966 2^869326+282859 261694 Enzo Doria 11/2016 967 2^869035-114181 261606 Enzo Doria 12/2014 968 4*10^261248+91 261249 Robert Price 11/2022 969 2^865715+80303 260607 Enzo Doria 07/2016 970 2^865048+1882411 260406 Enzo Doria 12/2016 971 2^864899-113871 260361 Enzo Doria 10/2014 972 (16*10^260256-91)/3 260257 Robert Price 11/2022 973 (7*10^260198-61)/9 260198 Erik Branger 11/2011 974 2^864298-2788421 260180 Enzo Doria 12/2015 975 2^864039-2791357 260102 Enzo Doria 01/2016 976 2^863621-113833 259976 Enzo Doria 10/2014 977 10^259945-11 259945 Mischa Rodermond 04/2023 978 (28*10^259897+113)/3 259898 Robert Price 06/2023 979 2^862837+75767 259740 Enzo Doria 05/2016 980 2^862637-31 259680 Jorge Menendez 05/2019 981 2^862088+1874941 259515 Enzo Doria 06/2016 982 2^861987-134557 259484 Hans Havermann 10/2018 983 (14*10^259431-143)/3 259432 Robert Price 05/2023 984 2^861516-1854029 259343 Enzo Doria 09/2015 985 2^860975-1853977 259180 Enzo Doria 09/2015 986 3^543128+16 259138 Robert Price 04/2020 987 2^860625-1858843 259074 Enzo Doria 10/2015 988 2^860110+77689 258919 Enzo Doria 05/2016 989 2^859600+1880371 258766 Enzo Doria 10/2016 990 2^859433+494711 258716 Makoto Morimoto 10/2013 991 (2^859433-44)/(2^2*3) 258715 Makoto Morimoto 08/2019 992 (2^859431-11)/3 258715 Stefano Morozzi 08/2022 993 (13*10^258710-43)/3 258711 Robert Price 08/2023 994 (2^859433+39899)/(73*3907*46301) 258705 Makoto Morimoto 10/2016 995 2^859240+1875271 258658 Enzo Doria 06/2016 996 Tau(971^15738) 258571 Nik Lygeros / Olivier Rozier 05/2015 997 (23*10^258494-47)/3 258495 Robert Price 09/2023 998 (144^119671+1)/145 258292 Paul Bourdelais 08/2019 999 2^857608+105 258166 Stefano Morozzi 05/2021 1000 (11*2^857159-13)/15 258031 Renaud Lifchitz 08/2011

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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