## PRP Records

### Probable Primes Top 10000

#### (295158 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 ? 751 2^1136462+1887289 342110 Enzo Doria 05/2017 752 F(1636007) 341905 Henri Lifchitz 03/2009 753 (2^1135567+13)/3 341840 Stefano Morozzi 09/2022 754 2^1133678+782569 341272 Enzo Doria 11/2016 755 (11^327001+1)/12 340536 Paul Bourdelais 09/2013 756 2^1129361+221597 339972 Enzo Doria 04/2024 757 2^1128621+25919 339749 Enzo Doria 12/2023 758 (2^1127239+2^563620+1)/5 339333 Borys Jaworski 11/2006 759 Tau(907^20848) 339132 Nik Lygeros / Olivier Rozier 01/2016 760 2^1126380-3 339075 Paul Bourdelais 06/2019 761 2^1125784+24331 338895 Enzo Doria 10/2023 762 2^1125446+1885099 338794 Enzo Doria 08/2017 763 (63^188147+1)/64 338539 Paul Bourdelais 12/2020 764 2^1124549+143807 338523 Enzo Doria 10/2016 765 (4*10^338476+23)/9 338476 Serge Batalov 11/2022 766 2^1121187+1886783 337511 Enzo Doria 04/2017 767 (48^200443-1)/47 336992 Paul Bourdelais 08/2020 768 (2*10^336405+43)/9 336405 Rytis Slatkevicius 01/2023 769 (94^170371-1)/93 336162 Paul Bourdelais 09/2020 770 2^1116184+1883521 336005 Enzo Doria 02/2017 771 2^1115727+27683 335868 Enzo Doria 01/2024 772 2^1114974+28759 335641 Enzo Doria 02/2024 773 2^1114517+1880087 335504 Enzo Doria 10/2016 774 (5*10^335480+31)/9 335480 Serge Batalov 11/2022 775 5*3^701688+2^701688 334791 Jon Grantham 08/2023 776 (101^166849+1)/102 334418 Paul Bourdelais 12/2020 777 (3^700897+1)/4 334413 Paul Bourdelais 04/2010 778 2^1109200+223201 333903 Enzo Doria 05/2024 779 2^1108463+32513 333681 Enzo Doria 05/2024 780 2^1104500+22411 332488 Enzo Doria 10/2023 781 2^1104408-114539 332460 Enzo Doria 03/2015 782 2^1101921+82085 331712 Enzo Doria 10/2016 783 2^1101895+29963 331704 Enzo Doria 03/2024 784 2^1100655+683513 331331 Enzo Doria 01/2017 785 (10^330906+71)/9 330906 Serge Batalov 07/2015 786 2^1098346+482899 330636 Enzo Doria 11/2016 787 (2^1096212+19)/5 329992 Stefano Morozzi 09/2022 788 2^1095679+1878713 329833 Enzo Doria 09/2016 789 2^1094874+27499 329590 Enzo Doria 01/2024 790 2^1094740-1851539 329550 Enzo Doria 08/2015 791 2^1092242+19 328798 Stefano Morozzi 10/2022 792 2^1091469-379369 328565 Enzo Doria 03/2014 793 2^1090801+24227 328364 Enzo Doria 10/2023 794 (69^178093-1)/68 327485 Paul Bourdelais 08/2020 795 (10^326884+7)/421 326882 Alfred Reich 12/2021 796 2^1085750+582349 326844 Enzo Doria 11/2016 797 (54308^69169-1)/(54308^263-1) 326261 Ryan Propper 11/2023 798 2^1083596+483061 326195 Enzo Doria 12/2016 799 (2^541456-1)*10^162995+2^541455-1 325990 paolo galliani 01/2019 800 2^1082908+583561 325988 Enzo Doria 05/2017 801 30^220411-29^220411 325574 Jean-Louis Charton 10/2018 802 2^1081308+7 325507 Stefano Morozzi 10/2022 803 2^1080032+25171 325123 Enzo Doria 11/2023 804 2^1078242+1881649 324584 Enzo Doria 11/2016 805 2^1077737+1880117 324432 Enzo Doria 10/2016 806 3^679017-5*2^679017 323974 Jon Grantham 08/2023 807 2^1076006+29539 323911 Enzo Doria 03/2024 808 2^1075573+32417 323780 Enzo Doria 05/2024 809 2^1075425+1880117 323736 Enzo Doria 10/2016 810 (28^223381+1)/29 323267 Paul Bourdelais 12/2020 811 10^322999+187071 323000 Stefano Morozzi 03/2019 812 10^322999-143151 322999 Patrick De Geest 05/2020 813 2^1072744+32641 322929 Enzo Doria 05/2024 814 2^1072146+1886869 322749 Enzo Doria 04/2017 815 2^1072118-7321953 322740 Enzo Doria 02/2015 816 2^1071026+1886869 322411 Enzo Doria 04/2017 817 2^1070539+1880633 322265 Enzo Doria 10/2016 818 2^1069788+26587 322039 Enzo Doria 12/2023 819 2^1069293-1147195 321890 Enzo Doria 05/2015 820 2^1065968+1880941 320889 Enzo Doria 10/2016 821 2^1065897-1147195 320867 Enzo Doria 05/2015 822 2^1063427+1882103 320124 Enzo Doria 12/2016 823 2^1061095-1061095 319422 Henri Lifchitz 10/2013 824 2^1060950+653119 319378 Enzo Doria 12/2016 825 2^1060363+782753 319202 Enzo Doria 11/2016 826 2^1060028+31771 319101 Enzo Doria 04/2024 827 (71^172259-1)/70 318895 Paul Bourdelais 08/2020 828 -30*Bern(85996)/236037521 318354 Sergey Batalov 10/2023 829 2^1055665+30407 317787 Enzo Doria 03/2024 830 2^1054736+483061 317508 Enzo Doria 12/2016 831 2^1053965+1879667 317276 Enzo Doria 10/2016 832 (43^194119-1)/42 317086 Paul Bourdelais 08/2020 833 2^1052186-458165 316740 Enzo Doria 03/2015 834 11^303909+2 316489 Paul Bourdelais 08/2023 835 2^1049026+214609 315789 Enzo Doria 11/2023 836 2^1046613-114685 315062 Enzo Doria 04/2015 837 2^1045625-459373 314765 Enzo Doria 06/2015 838 10^(2*157363+1)-8*10^157363-1 314727 Robert Price 07/2023 839 (7*10^314564-61)/9 314564 Erik Branger 09/2016 840 2^1044206+7 314338 Stefano Morozzi 10/2022 841 (7^371669-1)/6 314096 Paul Bourdelais 02/2010 842 (53^181981-1)/52 313784 Paul Bourdelais 08/2020 843 (8^347437-5^347437)/3 313767 Jon Grantham 08/2023 844 (10^313741+1)/11/11294677 313733 Alfred Reich 04/2024 845 2^1041944+283051 313657 Enzo Doria 12/2016 846 (1624^97969-1)/(1624^313-1) 313533 Sergey Batalov 11/2023 847 2^1041153-114391 313419 Enzo Doria 02/2015 848 (2^1039700+9)/5 312981 Stefano Morozzi 09/2022 849 (74^167311+1)/75 312742 Paul Bourdelais 12/2020 850 2^1038871+1866983 312732 Enzo Doria 04/2016 851 2^1038545+71657 312634 Enzo Doria 08/2023 852 (55^179573-1)/54 312521 Paul Bourdelais 08/2020 853 2^1037647+1881263 312363 Enzo Doria 11/2016 854 2^1037226+1879699 312237 Enzo Doria 10/2016 855 2^1036867+1865843 312129 Enzo Doria 02/2016 856 (76^165947+1)/77 312114 Paul Bourdelais 01/2021 857 2^1036020-114539 311874 Enzo Doria 02/2015 858 (90^159463-1)/89 311628 Paul Bourdelais 08/2020 859 2^1034546+28819 311430 Enzo Doria 02/2024 860 2^1032240+1883431 310736 Enzo Doria 01/2017 861 64211^64588+64588^64211 310514 Norbert Schneider 11/2023 862 2^1031450+29629 310498 Enzo Doria 03/2024 863 2^1030352+1870021 310167 Enzo Doria 06/2016 864 2^1030046+1882843 310075 Enzo Doria 11/2016 865 3^648872+16 309591 Robert Price 04/2020 866 (16976^73441-1)/(16976^271-1) 309498 Ryan Propper 11/2023 867 64221^64366+64366^64221 309451 Norbert Schneider 06/2023 868 (11121^76729-1)/(11121^277-1) 309336 Ryan Propper 11/2023 869 2^1027478+219259 309302 Enzo Doria 02/2024 870 2^1026999+20513 309158 Enzo Doria 07/2023 871 5^442281+2 309142 Paul Bourdelais 01/2021 872 2^1026204+22741 308919 Enzo Doria 09/2023 873 2^1026190+15 308914 Stefano Morozzi 10/2022 874 2^1025108+20851 308589 Enzo Doria 08/2023 875 A352736(16) 306985 Kellen Shenton 05/2022 876 2^1019777+213947 306984 Enzo Doria 10/2023 877 (11^293831-1)/10 305993 Paul Bourdelais 03/2010 878 (67^167449-1)/66 305773 Paul Bourdelais 08/2020 879 (62^170539+1)/63 305671 Paul Bourdelais 12/2020 880 2^1015321-1015321 305643 Henri Lifchitz 08/2013 881 2^1014775+27113 305478 Enzo Doria 12/2023 882 2^1014450+7 305380 Stefano Morozzi 10/2022 883 2^1014336+215731 305346 Enzo Doria 12/2023 884 2^1014224-2791229 305312 Enzo Doria 01/2016 885 (10^304986+7)/673 304984 Alfred Reich 11/2021 886 65473^45250+45250^65473 304818 Hans Havermann 02/2022 887 66012^41423+41423^66012 304794 Hans Havermann 03/2022 888 65073^48202+48202^65073 304742 Hans Havermann 04/2022 889 238176^19+19^238176 304569 Hans Havermann 03/2022 890 73122^14615+14615^73122 304539 Hans Havermann 05/2022 891 64492^52639+52639^64492 304487 Hans Havermann 03/2022 892 65955^41288+41288^65955 304437 Hans Havermann 04/2022 893 71729^17530+17530^71729 304403 Hans Havermann 03/2022 894 70170^21733+21733^70170 304336 Hans Havermann 03/2022 895 2^1010751-107709 304267 Enzo Doria 03/2014 896 84473^3994+3994^84473 304222 Hans Havermann 03/2022 897 (2^1010623-1)/12602017578957977 304212 Tony Prest / Never Odd Or Even 02/2014 898 74442^12125+12125^74442 303998 Hans Havermann 02/2022 899 77842^8039+8039^77842 303989 Hans Havermann 01/2022 900 64209^54140+54140^64209 303935 Hans Havermann 02/2022 901 2^1009577+1869587 303913 Enzo Doria 06/2016 902 67389^32338+32338^67389 303906 Hans Havermann 02/2022 903 8^336419-7^336419 303817 Jean-Louis Charton 01/2008 904 2^1009168+15 303790 Stefano Morozzi 10/2022 905 80766^5771+5771^80766 303782 Hans Havermann 01/2022 906 66094^39385+39385^66094 303724 Hans Havermann 01/2022 907 69147^24574+24574^69147 303589 Hans Havermann 02/2022 908 78390^7459+7459^78390 303580 Hans Havermann 01/2022 909 2^1008301+1869377 303529 Enzo Doria 06/2016 910 65008^46615+46615^65008 303492 Hans Havermann 02/2022 911 (2^1007838+5)/3 303389 Serge Batalov 08/2015 912 65018^46293+46293^65018 303343 Hans Havermann 01/2022 913 6^389756+5 303290 Paul Bourdelais 02/2021 914 71016^18649+18649^71016 303285 Hans Havermann 01/2022 915 2^1007065+29231 303157 Enzo Doria 03/2024 916 80160^6047+6047^80160 303129 Hans Havermann 01/2022 917 67434^31237+31237^67434 303094 Hans Havermann 03/2022 918 65537^42102+42102^65537 303063 Hans Havermann 02/2022 919 71790^16553+16553^71790 302874 Hans Havermann 11/2021 920 65208^44129+44129^65208 302874 Hans Havermann 11/2021 921 84181^3960+3960^84181 302858 Hans Havermann 11/2021 922 (13703^73441-1)/(13703^271-1) 302691 Ryan Propper 11/2023 923 71956^16087+16087^71956 302682 Hans Havermann 11/2021 924 2^1005326+383059 302634 Enzo Doria 12/2016 925 2^1004929+1877567 302514 Enzo Doria 08/2016 926 69341^22978+22978^69341 302418 Hans Havermann 12/2021 927 111443^516+516^111443 302306 Hans Havermann 12/2021 928 67638^29387+29387^67638 302218 Hans Havermann 11/2021 929 2^1003494+1874899 302082 Enzo Doria 06/2016 930 75189^10400+10400^75189 302037 Hans Havermann 12/2021 931 67237^31042+31042^67237 302026 Hans Havermann 12/2021 932 64540^47791+47791^64540 302005 Hans Havermann 11/2021 933 2^1003046+60529 301947 Enzo Doria 04/2016 934 83278^4209+4209^83278 301815 Hans Havermann 09/2021 935 64431^48250+48250^64431 301763 Hans Havermann 09/2021 936 67237^30714+30714^67237 301716 Hans Havermann 09/2021 937 64641^46288+46288^64641 301581 Hans Havermann 09/2021 938 71513^16482+16482^71513 301572 Hans Havermann 10/2021 939 72017^15396+15396^72017 301565 Hans Havermann 09/2021 940 65534^39927+39927^65534 301540 Hans Havermann 10/2021 941 (23^221411-1)/22 301501 Paul Bourdelais 08/2020 942 63169^59152+59152^63169 301441 Hans Havermann 09/2021 943 75055^10348+10348^75055 301336 Hans Havermann 09/2021 944 2^1000647+1881353 301225 Enzo Doria 11/2016 945 83686^3961+3961^83686 301086 Hans Havermann 10/2021 946 68529^24742+24742^68529 301078 Hans Havermann 09/2021 947 65207^41416+41416^65207 301072 Hans Havermann 10/2021 949 2^1000000+821751 301030 Tony Prest / Never Odd Or Even 10/2015 948 2^999999+77151 301030 Norman Luhn 09/2023 950 90762^2071+2071^90762 300984 Hans Havermann 06/2021 951 63909^51142+51142^63909 300934 Hans Havermann 08/2021 952 2^999646+1874029 300924 Enzo Doria 06/2016 953 66280^34607+34607^66280 300856 Hans Havermann 06/2021 954 65534^38925+38925^65534 300817 Hans Havermann 07/2021 955 63296^56517+56517^63296 300794 Hans Havermann 06/2021 956 110610^523+523^110610 300694 Hans Havermann 06/2021 957 66428^33609+33609^66428 300684 Hans Havermann 06/2021 958 74247^11210+11210^74247 300672 Hans Havermann 06/2021 959 (59^169777-1)/58 300649 Paul Bourdelais 08/2020 960 10^300476+3 300477 Ed Trice 10/2012 961 10^300476-530913 300476 Patrick De Geest 03/2016 962 66703^31960+31960^66703 300471 Hans Havermann 06/2021 963 63722^51915+51915^63722 300468 Hans Havermann 06/2021 964 2^998053+1879667 300444 Enzo Doria 09/2016 965 77018^7959+7959^77018 300437 Hans Havermann 07/2021 966 314738^9+9^314738 300337 Anatoly F. Selevich 02/2011 967 2^997689+217787 300335 Enzo Doria 01/2024 968 69478^20987+20987^69478 300281 Hans Havermann 07/2021 969 64088^48393+48393^64088 300239 Hans Havermann 07/2021 970 64605^44146+44146^64605 300084 Hans Havermann 08/2021 971 2^996845+29027 300081 Enzo Doria 02/2024 972 7^355039-6^355039 300043 Jean-Louis Charton 05/2011 973 67594^27465+27465^67594 300035 Hans Havermann 06/2021 974 10^300000+287389 300001 Patrick De Geest 10/2019 975 10^300000-83657 300000 Patrick De Geest 10/2019 976 70599^17756+17756^70599 300000 Hans Havermann 06/2021 977 numbpart(72526161452) 299999 Serge Batalov 04/2017 978 2^996182-114431 299881 Enzo Doria 02/2015 979 3*2^996126+5 299865 Jon Grantham 07/2023 980 2^996034-17 299837 Stefano Morozzi 07/2022 981 (19*10^299640+77)/3 299641 Robert Price 03/2023 982 2^995214-2788361 299590 Enzo Doria 12/2015 983 2^994791-114319 299462 Enzo Doria 01/2015 984 2^994490-1863791 299372 Enzo Doria 01/2016 985 2^993322+1885729 299020 Enzo Doria 03/2017 986 (36395^65536+36393^65536)/2 298913 Kellen Shenton 04/2022 987 2^992711-2788807 298836 Enzo Doria 12/2015 988 2^992525-114199 298780 Enzo Doria 12/2014 989 (7^353501-3^353501)/4 298743 Jon Grantham 08/2023 990 2^992329+1884707 298721 Enzo Doria 02/2017 991 2^992052+215491 298638 Enzo Doria 11/2023 992 2^991968-23 298613 Stefano Morozzi 07/2022 993 2^991715-19 298536 Stefano Morozzi 07/2022 994 (10^298414+7)/191/823/56921/1334467 298398 Alfred Reich 10/2021 995 2^989562+25 297888 Stefano Morozzi 05/2021 996 2^988580+214051 297593 Enzo Doria 10/2023 997 2^988537+218837 297580 Enzo Doria 03/2024 998 (19*10^297497+77)/3 297498 Robert Price 03/2023 999 (2*10^297488-23)/3 297488 Robert Price 10/2022 1000 (2^986191+1)/3 296873 Vincent Diepeveen 06/2008

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

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