## PRP Records

### Probable Primes Top 10000

#### (295765 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 2^1200202+216499 361297 Enzo Doria 12/2023 752 (2^1200182+274462)/2 361291 Stefano Morozzi 01/2021 753 2^1200178+149193 361290 Stefano Morozzi 07/2022 754 2^1200168+140403 361287 Stefano Morozzi 03/2022 755 (2^1200162+275910)/2 361285 Stefano Morozzi 03/2021 756 2^1200157+168927 361284 Stefano Morozzi 02/2023 757 2^1200134+141385 361277 Stefano Morozzi 08/2022 758 (2^1200131+360150)/2 361276 Stefano Morozzi 10/2020 759 (2^1200118+290718)/2 361272 Stefano Morozzi 01/2021 760 2^1200022+192777 361243 Stefano Morozzi 09/2022 761 2^1200021+149777 361243 Stefano Morozzi 10/2022 762 (64*10^360173-1)/243 360173 Serge Batalov 09/2014 763 (59^203309+1)/60 360029 Paul Bourdelais 09/2021 764 (2*10^359860-11)/9 359860 Rytis Slatkevicius 01/2023 765 2^1195093+1882577 359759 Enzo Doria 12/2016 766 3^753451+5*2^753451 359488 Jon Grantham 08/2023 767 2^1192258+36739 358906 Enzo Doria 09/2024 768 (6^461108-11)/5 358812 Paul Bourdelais 04/2019 769 2^1191375+8543 358640 Phil Moore 06/2008 770 2^1190972+1880191 358519 Enzo Doria 11/2016 771 2^1189930+28549 358205 Enzo Doria 03/2024 772 (45^216551-1)/44 358004 Paul Bourdelais 08/2020 773 (50^210319-1)/49 357324 Paul Bourdelais 08/2020 774 (531^131072+25^131072)/2 357184 Kellen Shenton 03/2021 775 2^1186366+226747 357132 Enzo Doria 09/2024 776 2^1184565+21227 356590 Enzo Doria 08/2023 777 2^1180159+22823 355264 Enzo Doria 11/2023 778 2^1179836+1885021 355167 Enzo Doria 02/2017 779 2^1178942+32269 354897 Enzo Doria 04/2024 780 2^1177053+28607 354329 Enzo Doria 02/2024 781 (19*10^353884-91)/9 353885 Alfred Reich 02/2023 782 (10^353884*19-91)/9 353885 Alfred Reich 10/2023 783 20^271951+3 353817 Paul Bourdelais 01/2021 784 72722^72722+7^7 353551 Serge Batalov 04/2024 785 2^1173095+21 353137 Stefano Morozzi 10/2022 786 2^1170959+218945 352494 Enzo Doria 03/2024 787 2^1170915+382623 352481 Boyan Hu 08/2024 788 (63^195893-1)/62 352477 Paul Bourdelais 08/2020 789 2^1170331+27293 352305 Enzo Doria 01/2024 790 2^1170326+7 352304 Stefano Morozzi 10/2022 791 numbpart(100000135540) 352269 Serge Batalov 04/2017 792 (10^352237-1)/9/10567111/950335427 352221 Maksym Voznyy 01/2015 793 5*3^737931-2^737931 352084 Jon Grantham 08/2023 794 2^1168851+223613 351860 Enzo Doria 06/2024 795 2^1168554+783529 351770 Enzo Doria 01/2017 796 (2^1168183-1)/54763676838381762583 351639 Matthias Wurtinger 01/2011 797 2^1166950+30409 351287 Enzo Doria 03/2024 798 2^1166563+223103 351171 Enzo Doria 05/2024 799 2^1166152+1882411 351047 Enzo Doria 12/2016 800 2^1163972+20971 350391 Enzo Doria 08/2023 801 2^1163272+22411 350180 Enzo Doria 10/2023 802 10^350071+7 350072 Alfred Reich 05/2021 803 2^1162154+1890207 349844 Enzo Doria 08/2017 804 (7*10^348724-61)/9 348724 Erik Branger 09/2016 805 (4*10^348453+41)/9 348453 Serge Batalov 11/2022 806 (127^165601-1)/126 348390 Alexander Zhirkov 09/2015 807 2^1155085+213377 347716 Enzo Doria 09/2023 808 2^1153083+1883693 347113 Enzo Doria 04/2017 809 2^1152186+225529 346843 Enzo Doria 07/2024 810 (2^1148729+2^574365+1)/5 345802 Borys Jaworski 03/2007 811 2^1145882+80779 344945 Enzo Doria 09/2016 812 2^1143425+221177 344206 Enzo Doria 03/2024 813 2^1141813+27047 343720 Enzo Doria 12/2023 814 2^1141114+221869 343510 Enzo Doria 04/2024 815 2^1138296+27541 342662 Enzo Doria 01/2024 816 2^1136462+1887289 342110 Enzo Doria 05/2017 817 F(1636007) 341905 Henri Lifchitz 03/2009 818 (2^1135567+13)/3 341840 Stefano Morozzi 09/2022 819 2^1134873+223637 341631 Enzo Doria 06/2024 820 2^1133678+782569 341272 Enzo Doria 11/2016 821 (11^327001+1)/12 340536 Paul Bourdelais 09/2013 822 2^1129965+223667 340154 Enzo Doria 06/2024 823 2^1129361+221597 339972 Enzo Doria 04/2024 824 2^1128706+225529 339775 Enzo Doria 07/2024 825 2^1128621+25919 339749 Enzo Doria 12/2023 826 (2^1127239+2^563620+1)/5 339333 Borys Jaworski 11/2006 827 Tau(907^20848) 339132 Nik Lygeros / Olivier Rozier 01/2016 828 2^1126380-3 339075 Paul Bourdelais 06/2019 829 2^1125784+24331 338895 Enzo Doria 10/2023 830 2^1125446+1885099 338794 Enzo Doria 08/2017 831 (63^188147+1)/64 338539 Paul Bourdelais 12/2020 832 2^1124549+143807 338523 Enzo Doria 10/2016 833 (4*10^338476+23)/9 338476 Serge Batalov 11/2022 834 2^1121187+1886783 337511 Enzo Doria 04/2017 835 (48^200443-1)/47 336992 Paul Bourdelais 08/2020 836 (2*10^336405+43)/9 336405 Rytis Slatkevicius 01/2023 837 (94^170371-1)/93 336162 Paul Bourdelais 09/2020 838 2^1116184+1883521 336005 Enzo Doria 02/2017 839 2^1115727+27683 335868 Enzo Doria 01/2024 840 2^1114974+28759 335641 Enzo Doria 02/2024 841 2^1114517+1880087 335504 Enzo Doria 10/2016 842 (5*10^335480+31)/9 335480 Serge Batalov 11/2022 843 5*3^701688+2^701688 334791 Jon Grantham 08/2023 844 (101^166849+1)/102 334418 Paul Bourdelais 12/2020 845 (3^700897+1)/4 334413 Paul Bourdelais 04/2010 846 2^1109200+223201 333903 Enzo Doria 05/2024 847 2^1108463+32513 333681 Enzo Doria 05/2024 848 2^1104500+22411 332488 Enzo Doria 10/2023 849 2^1104408-114539 332460 Enzo Doria 03/2015 850 2^1101921+82085 331712 Enzo Doria 10/2016 851 2^1101895+29963 331704 Enzo Doria 03/2024 852 2^1101167-1101167^2 331485 Henri Lifchitz 07/2024 853 2^1101091+224153 331462 Enzo Doria 06/2024 854 2^1100655+683513 331331 Enzo Doria 01/2017 855 (10^330906+71)/9 330906 Serge Batalov 07/2015 856 2^1098346+482899 330636 Enzo Doria 11/2016 857 (2^1096212+19)/5 329992 Stefano Morozzi 09/2022 858 2^1095679+1878713 329833 Enzo Doria 09/2016 859 2^1094874+27499 329590 Enzo Doria 01/2024 860 2^1094740-1851539 329550 Enzo Doria 08/2015 861 2^1092242+19 328798 Stefano Morozzi 10/2022 862 2^1091469-379369 328565 Enzo Doria 03/2014 863 2^1090801+24227 328364 Enzo Doria 10/2023 864 (69^178093-1)/68 327485 Paul Bourdelais 08/2020 865 (10^326884+7)/421 326882 Alfred Reich 12/2021 866 2^1085750+582349 326844 Enzo Doria 11/2016 867 (54308^69169-1)/(54308^263-1) 326261 Ryan Propper 11/2023 868 2^1083596+483061 326195 Enzo Doria 12/2016 869 (2^541456-1)*10^162995+2^541455-1 325990 paolo galliani 01/2019 870 2^1082908+583561 325988 Enzo Doria 05/2017 871 30^220411-29^220411 325574 Jean-Louis Charton 10/2018 872 2^1081308+7 325507 Stefano Morozzi 10/2022 873 2^1080151+225413 325158 Enzo Doria 08/2024 874 2^1080032+25171 325123 Enzo Doria 11/2023 875 2^1078242+1881649 324584 Enzo Doria 11/2016 876 2^1077737+1880117 324432 Enzo Doria 10/2016 877 3^679017-5*2^679017 323974 Jon Grantham 08/2023 878 2^1076006+29539 323911 Enzo Doria 03/2024 879 2^1075573+32417 323780 Enzo Doria 05/2024 880 2^1075425+1880117 323736 Enzo Doria 10/2016 881 (28^223381+1)/29 323267 Paul Bourdelais 12/2020 882 10^322999+187071 323000 Stefano Morozzi 03/2019 883 10^322999-143151 322999 Patrick De Geest 05/2020 884 2^1072744+32641 322929 Enzo Doria 05/2024 885 2^1072146+1886869 322749 Enzo Doria 04/2017 886 2^1072118-7321953 322740 Enzo Doria 02/2015 887 2^1071026+1886869 322411 Enzo Doria 04/2017 888 2^1070539+1880633 322265 Enzo Doria 10/2016 889 2^1069788+26587 322039 Enzo Doria 12/2023 890 2^1069293-1147195 321890 Enzo Doria 05/2015 891 2^1065968+1880941 320889 Enzo Doria 10/2016 892 2^1065897-1147195 320867 Enzo Doria 05/2015 893 2^1063427+1882103 320124 Enzo Doria 12/2016 894 2^1061095-1061095 319422 Henri Lifchitz 10/2013 895 2^1060950+653119 319378 Enzo Doria 12/2016 896 2^1060363+782753 319202 Enzo Doria 11/2016 897 2^1060028+31771 319101 Enzo Doria 04/2024 898 (71^172259-1)/70 318895 Paul Bourdelais 08/2020 899 -30*Bern(85996)/236037521 318354 Sergey Batalov 10/2023 900 2^1055665+30407 317787 Enzo Doria 03/2024 901 2^1054736+483061 317508 Enzo Doria 12/2016 902 2^1053965+1879667 317276 Enzo Doria 10/2016 903 (43^194119-1)/42 317086 Paul Bourdelais 08/2020 904 2^1052899+225413 316955 Enzo Doria 08/2024 905 2^1052186-458165 316740 Enzo Doria 03/2015 906 11^303909+2 316489 Paul Bourdelais 08/2023 907 2^1049026+214609 315789 Enzo Doria 11/2023 908 2^1048576+69661 315653 Boyan Hu 08/2024 909 2^1046613-114685 315062 Enzo Doria 04/2015 910 2^1045625-459373 314765 Enzo Doria 06/2015 911 10^(2*157363+1)-8*10^157363-1 314727 Robert Price 07/2023 912 (7*10^314564-61)/9 314564 Erik Branger 09/2016 913 2^1044206+7 314338 Stefano Morozzi 10/2022 914 (7^371669-1)/6 314096 Paul Bourdelais 02/2010 915 (53^181981-1)/52 313784 Paul Bourdelais 08/2020 916 (8^347437-5^347437)/3 313767 Jon Grantham 08/2023 917 (10^313741+1)/11/11294677 313733 Alfred Reich 04/2024 918 2^1041944+283051 313657 Enzo Doria 12/2016 919 (1624^97969-1)/(1624^313-1) 313533 Sergey Batalov 11/2023 920 2^1041153-114391 313419 Enzo Doria 02/2015 921 (2^1039700+9)/5 312981 Stefano Morozzi 09/2022 922 (74^167311+1)/75 312742 Paul Bourdelais 12/2020 923 2^1038871+1866983 312732 Enzo Doria 04/2016 924 2^1038545+71657 312634 Enzo Doria 08/2023 925 (55^179573-1)/54 312521 Paul Bourdelais 08/2020 926 2^1037647+1881263 312363 Enzo Doria 11/2016 927 2^1037226+1879699 312237 Enzo Doria 10/2016 928 2^1036867+1865843 312129 Enzo Doria 02/2016 929 (76^165947+1)/77 312114 Paul Bourdelais 01/2021 930 2^1036020-114539 311874 Enzo Doria 02/2015 931 (90^159463-1)/89 311628 Paul Bourdelais 08/2020 932 2^1034546+28819 311430 Enzo Doria 02/2024 933 2^1032240+1883431 310736 Enzo Doria 01/2017 934 64211^64588+64588^64211 310514 Norbert Schneider 11/2023 935 2^1031450+29629 310498 Enzo Doria 03/2024 936 2^1030352+1870021 310167 Enzo Doria 06/2016 937 2^1030046+1882843 310075 Enzo Doria 11/2016 938 3^648872+16 309591 Robert Price 04/2020 939 (16976^73441-1)/(16976^271-1) 309498 Ryan Propper 11/2023 940 64221^64366+64366^64221 309451 Norbert Schneider 06/2023 941 (11121^76729-1)/(11121^277-1) 309336 Ryan Propper 11/2023 942 2^1027478+219259 309302 Enzo Doria 02/2024 943 2^1026999+20513 309158 Enzo Doria 07/2023 944 5^442281+2 309142 Paul Bourdelais 01/2021 945 2^1026204+22741 308919 Enzo Doria 09/2023 946 2^1026190+15 308914 Stefano Morozzi 10/2022 947 2^1025108+20851 308589 Enzo Doria 08/2023 948 A352736(16) 306985 Kellen Shenton 05/2022 949 2^1019777+213947 306984 Enzo Doria 10/2023 950 (11^293831-1)/10 305993 Paul Bourdelais 03/2010 951 (67^167449-1)/66 305773 Paul Bourdelais 08/2020 952 (62^170539+1)/63 305671 Paul Bourdelais 12/2020 953 2^1015321-1015321 305643 Henri Lifchitz 08/2013 954 2^1014775+27113 305478 Enzo Doria 12/2023 955 2^1014450+7 305380 Stefano Morozzi 10/2022 956 2^1014336+215731 305346 Enzo Doria 12/2023 957 2^1014224-2791229 305312 Enzo Doria 01/2016 958 (10^304986+7)/673 304984 Alfred Reich 11/2021 959 65473^45250+45250^65473 304818 Hans Havermann 02/2022 960 66012^41423+41423^66012 304794 Hans Havermann 03/2022 961 65073^48202+48202^65073 304742 Hans Havermann 04/2022 962 2^1012054+31669 304659 Enzo Doria 06/2024 963 238176^19+19^238176 304569 Hans Havermann 03/2022 964 73122^14615+14615^73122 304539 Hans Havermann 05/2022 965 64492^52639+52639^64492 304487 Hans Havermann 03/2022 966 65955^41288+41288^65955 304437 Hans Havermann 04/2022 967 71729^17530+17530^71729 304403 Hans Havermann 03/2022 968 70170^21733+21733^70170 304336 Hans Havermann 03/2022 969 2^1010751-107709 304267 Enzo Doria 03/2014 970 84473^3994+3994^84473 304222 Hans Havermann 03/2022 971 (2^1010623-1)/12602017578957977 304212 Tony Prest / Never Odd Or Even 02/2014 972 74442^12125+12125^74442 303998 Hans Havermann 02/2022 973 77842^8039+8039^77842 303989 Hans Havermann 01/2022 974 64209^54140+54140^64209 303935 Hans Havermann 02/2022 975 2^1009577+1869587 303913 Enzo Doria 06/2016 976 67389^32338+32338^67389 303906 Hans Havermann 02/2022 977 8^336419-7^336419 303817 Jean-Louis Charton 01/2008 978 2^1009168+15 303790 Stefano Morozzi 10/2022 979 80766^5771+5771^80766 303782 Hans Havermann 01/2022 980 66094^39385+39385^66094 303724 Hans Havermann 01/2022 981 69147^24574+24574^69147 303589 Hans Havermann 02/2022 982 78390^7459+7459^78390 303580 Hans Havermann 01/2022 983 2^1008301+1869377 303529 Enzo Doria 06/2016 984 65008^46615+46615^65008 303492 Hans Havermann 02/2022 985 (2^1007838+5)/3 303389 Serge Batalov 08/2015 986 65018^46293+46293^65018 303343 Hans Havermann 01/2022 987 6^389756+5 303290 Paul Bourdelais 02/2021 988 71016^18649+18649^71016 303285 Hans Havermann 01/2022 989 2^1007065+29231 303157 Enzo Doria 03/2024 990 80160^6047+6047^80160 303129 Hans Havermann 01/2022 991 67434^31237+31237^67434 303094 Hans Havermann 03/2022 992 65537^42102+42102^65537 303063 Hans Havermann 02/2022 993 71790^16553+16553^71790 302874 Hans Havermann 11/2021 994 65208^44129+44129^65208 302874 Hans Havermann 11/2021 995 84181^3960+3960^84181 302858 Hans Havermann 11/2021 996 (13703^73441-1)/(13703^271-1) 302691 Ryan Propper 11/2023 997 71956^16087+16087^71956 302682 Hans Havermann 11/2021 998 2^1005326+383059 302634 Enzo Doria 12/2016 999 2^1004929+1877567 302514 Enzo Doria 08/2016 1000 69341^22978+22978^69341 302418 Hans Havermann 12/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 13 2024 17:43 (Time in France)

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