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
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
751 | (53^158341+1)/54 | 273022 | Paul Bourdelais | 07/2019 |
752 | 2^906594-113201 | 272912 | Enzo Doria | 08/2014 |
753 | 2^904773+1872167 | 272364 | Enzo Doria | 06/2016 |
754 | 6^349903+5 | 272278 | Paul Bourdelais | 02/2021 |
755 | 2^904149-1862473 | 272176 | Enzo Doria | 12/2015 |
756 | (7*10^271757-61)/9 | 271757 | Erik Branger | 03/2012 |
757 | 2^902497+1880117 | 271679 | Enzo Doria | 09/2016 |
758 | 2^901858+77689 | 271487 | Enzo Doria | 06/2016 |
759 | 2^901372+1875301 | 271341 | Enzo Doria | 06/2016 |
760 | 23*10^270799-7 | 270801 | Robert Price | 10/2022 |
761 | 2^899121-115033 | 270663 | Enzo Doria | 07/2015 |
762 | 2^898900+883021 | 270596 | Enzo Doria | 12/2016 |
763 | 2^898762-251511 | 270555 | Enzo Doria | 12/2013 |
764 | 2^898589+47 | 270503 | Lelio R Paula | 03/2016 |
765 | 187322*10^270343-187321 | 270349 | Danilo Nitsche | 09/2013 |
766 | 48358*10^270343-48357 | 270348 | Danilo Nitsche | 09/2013 |
767 | (10^270343-1)/9 | 270343 | Maksym Voznyy | 07/2007 |
768 | 2^897867-3217 | 270285 | Yves Minet | 12/2016 |
769 | 2^897849-115273 | 270280 | Enzo Doria | 07/2015 |
770 | 2^896616-114179 | 269909 | Enzo Doria | 12/2014 |
771 | 2^894928+583561 | 269401 | Enzo Doria | 04/2017 |
772 | 2^894673-39343 | 269324 | Enzo Doria | 08/2015 |
773 | F(1285607) | 268676 | Henri Lifchitz | 11/2008 |
774 | 2^892112+187663 | 268553 | Enzo Doria | 08/2016 |
775 | (10^268207+1)/11 | 268206 | Paul Bourdelais | 02/2010 |
776 | 2^890957-69583 | 268205 | Enzo Doria | 12/2015 |
777 | 32841!^2+32840!^2+...+2!^2+1!^2 | 268128 | Serge Batalov | 07/2017 |
778 | 2^890122-351401 | 267954 | Enzo Doria | 07/2015 |
779 | (19^209359-1)/18 | 267718 | Paul Bourdelais | 08/2010 |
780 | (85^138647+1)/86 | 267507 | Paul Bourdelais | 07/2019 |
781 | (485^99523-1)/484 | 267291 | Michael Stocker | 05/2020 |
782 | 2^886324+77791 | 266811 | Enzo Doria | 06/2016 |
783 | 7*10^266731+87 | 266732 | Robert Price | 11/2022 |
784 | 2^884714+1880527 | 266326 | Enzo Doria | 10/2016 |
785 | 11^255426+255426^11 | 265999 | Serge Batalov | 05/2014 |
786 | 2^883462-343421 | 265949 | Enzo Doria | 07/2015 |
787 | 2^883442+1875019 | 265943 | Enzo Doria | 06/2016 |
788 | 2^883333-291583 | 265910 | Enzo Doria | 07/2015 |
789 | (2*10^265321-17)/3 | 265321 | Serge Batalov | 11/2022 |
790 | (16*10^265052-91)/3 | 265053 | Robert Price | 11/2022 |
791 | 2^880411+1882673 | 265031 | Enzo Doria | 12/2016 |
792 | (14*10^264791-11)/3 | 264792 | Robert Price | 08/2022 |
793 | 2^879530-2788031 | 264765 | Enzo Doria | 12/2015 |
794 | (2*10^264539+61)/9 | 264539 | Serge Batalov | 11/2022 |
795 | 2^878118+2793079 | 264340 | Enzo Doria | 02/2016 |
796 | (2^878073-7)/5 | 264326 | Stefano Morozzi | 08/2022 |
797 | (37^168527-1)/36 | 264283 | Paul Bourdelais | 08/2019 |
798 | 2^876202-17 | 263764 | Stefano Morozzi | 07/2022 |
799 | (14*10^263720-11)/3 | 263721 | Robert Price | 08/2022 |
800 | 2^875748-461129 | 263627 | Enzo Doria | 07/2015 |
801 | 2^875518-15 | 263558 | Stefano Morozzi | 07/2022 |
802 | (29*10^263523-17)/3 | 263524 | Robert Price | 01/2023 |
803 | 2^875181-2789923 | 263456 | Enzo Doria | 12/2015 |
804 | 2^875101-350083 | 263432 | Enzo Doria | 08/2015 |
805 | 2^874684+1883587 | 263307 | Enzo Doria | 01/2017 |
806 | 2^874616+1872211 | 263286 | Enzo Doria | 05/2016 |
807 | 3^551491+16 | 263129 | Robert Price | 04/2020 |
808 | 2^874073+2792957 | 263123 | Enzo Doria | 02/2016 |
809 | 2^873628+1878751 | 262989 | Enzo Doria | 08/2016 |
810 | 2^873288-269 | 262886 | Yves Minet | 01/2015 |
811 | (2*10^262874+7)/9 | 262874 | Rytis Slatkevicius | 01/2023 |
812 | (2*10^262603-11)/9 | 262603 | Serge Batalov | 11/2022 |
813 | 2^871991-4207 | 262496 | Yves Minet | 03/2021 |
814 | 2^871146-3173 | 262242 | Yves Minet | 07/2016 |
815 | 2^869601-163 | 261776 | Yves Minet | 01/2015 |
816 | (2*10^261704+61)/9 | 261704 | Serge Batalov | 11/2022 |
817 | 2^869326+282859 | 261694 | Enzo Doria | 11/2016 |
818 | 2^869035-114181 | 261606 | Enzo Doria | 12/2014 |
819 | 4*10^261248+91 | 261249 | Robert Price | 11/2022 |
820 | 2^865715+80303 | 260607 | Enzo Doria | 07/2016 |
821 | 2^865048+1882411 | 260406 | Enzo Doria | 12/2016 |
822 | 2^864899-113871 | 260361 | Enzo Doria | 10/2014 |
823 | (16*10^260256-91)/3 | 260257 | Robert Price | 11/2022 |
824 | (7*10^260198-61)/9 | 260198 | Erik Branger | 11/2011 |
825 | 2^864298-2788421 | 260180 | Enzo Doria | 12/2015 |
826 | 2^864039-2791357 | 260102 | Enzo Doria | 01/2016 |
827 | 2^863621-113833 | 259976 | Enzo Doria | 10/2014 |
828 | 2^862837+75767 | 259740 | Enzo Doria | 05/2016 |
829 | 2^862637-31 | 259680 | Jorge Menendez | 05/2019 |
830 | 2^862088+1874941 | 259515 | Enzo Doria | 06/2016 |
831 | 2^861987-134557 | 259484 | Hans Havermann | 10/2018 |
832 | 2^861516-1854029 | 259343 | Enzo Doria | 09/2015 |
833 | 2^860975-1853977 | 259180 | Enzo Doria | 09/2015 |
834 | 3^543128+16 | 259138 | Robert Price | 04/2020 |
835 | 2^860625-1858843 | 259074 | Enzo Doria | 10/2015 |
836 | 2^860110+77689 | 258919 | Enzo Doria | 05/2016 |
837 | 2^859600+1880371 | 258766 | Enzo Doria | 10/2016 |
838 | 2^859433+494711 | 258716 | Makoto Morimoto | 10/2013 |
839 | (2^859433-44)/(2^2*3) | 258715 | Makoto Morimoto | 08/2019 |
840 | (2^859431-11)/3 | 258715 | Stefano Morozzi | 08/2022 |
841 | (2^859433+39899)/(73*3907*46301) | 258705 | Makoto Morimoto | 10/2016 |
842 | 2^859240+1875271 | 258658 | Enzo Doria | 06/2016 |
843 | Tau(971^15738) | 258571 | Nik Lygeros / Olivier Rozier | 05/2015 |
844 | (144^119671+1)/145 | 258292 | Paul Bourdelais | 08/2019 |
845 | 2^857608+105 | 258166 | Stefano Morozzi | 05/2021 |
846 | (11*2^857159-13)/15 | 258031 | Renaud Lifchitz | 08/2011 |
847 | 2^857016-633113 | 257988 | Enzo Doria | 12/2013 |
848 | 2^855732-113969 | 257602 | Enzo Doria | 10/2014 |
849 | 2^853682-3911 | 256984 | Enzo Doria | 05/2014 |
850 | 11^246668-90 | 256879 | Enzo Doria | 12/2012 |
851 | 2^851904-113939 | 256449 | Enzo Doria | 10/2014 |
852 | 2^851725-851725^2 | 256395 | Henri Lifchitz | 03/2019 |
853 | 11^246167-90 | 256357 | Enzo Doria | 12/2012 |
854 | (85*10^256301-1)/3 | 256303 | Robert Price | 12/2022 |
855 | (10^256187+7)/63443/148782853 | 256175 | Alfred Reich | 10/2021 |
856 | 2^850700-569049 | 256087 | Enzo Doria | 11/2013 |
857 | 2^850675+153 | 256079 | Stefano Morozzi | 05/2021 |
858 | 21^193601-20^193601 | 255983 | Jean-Louis Charton | 02/2015 |
859 | (37^163193+1)/38 | 255918 | Paul Bourdelais | 07/2019 |
860 | (14*10^255805-83)/3 | 255806 | Robert Price | 11/2022 |
861 | 2^849177-114025 | 255628 | Enzo Doria | 12/2014 |
862 | 2^848502-3173 | 255425 | Yves Minet | 07/2016 |
863 | 2^848178-140291 | 255328 | Enzo Doria | 01/2014 |
864 | 7*10^255167+87 | 255168 | Robert Price | 11/2022 |
865 | 2^847622-2441 | 255160 | Yves Minet | 02/2016 |
866 | 2^847291+182843 | 255061 | Enzo Doria | 11/2016 |
867 | 2^847174+1879429 | 255025 | Enzo Doria | 09/2016 |
868 | 24*29^174239+13361 | 254809 | Curtis Bright | 04/2015 |
869 | 22*10^254639+7 | 254641 | Robert Price | 10/2022 |
870 | 2^845633-933075 | 254561 | Paul Bourdelais | 11/2021 |
871 | 2^845610-1868591 | 254554 | Enzo Doria | 04/2016 |
872 | 2^845484+81931 | 254517 | Enzo Doria | 08/2016 |
873 | 2^845402-114761 | 254492 | Enzo Doria | 05/2015 |
874 | 2^844334-2792441 | 254170 | Enzo Doria | 02/2016 |
875 | 11^243796-90 | 253888 | Enzo Doria | 12/2012 |
876 | (10^253891+7)/44777/79843/16940711 | 253875 | Alfred Reich | 10/2021 |
877 | 30^171733-29^171733 | 253671 | Jean-Louis Charton | 10/2018 |
878 | 2^842209+1876037 | 253531 | Enzo Doria | 07/2016 |
879 | 2^842123-59197 | 253505 | Enzo Doria | 10/2015 |
880 | (8*10^253313-53)/9 | 253313 | Serge Batalov | 11/2022 |
881 | 2^840797-3 | 253106 | Paul Bourdelais | 06/2019 |
882 | 2^840716-2969 | 253081 | Yves Minet | 05/2016 |
883 | 2^840358-462491 | 252973 | Enzo Doria | 08/2015 |
884 | 2^840310+1878379 | 252959 | Enzo Doria | 08/2016 |
885 | 2^840203-21 | 252927 | Stefano Morozzi | 07/2022 |
886 | 11^242579-60 | 252620 | Enzo Doria | 10/2012 |
887 | 45^152659+2 | 252378 | Robert Price | 09/2015 |
888 | (95^127583+1)/96 | 252322 | Paul Bourdelais | 07/2019 |
889 | 7*10^252209-17 | 252210 | Robert Price | 12/2022 |
890 | 2^837725+1869377 | 252181 | Enzo Doria | 05/2016 |
891 | 2^837536-311039 | 252124 | Enzo Doria | 06/2015 |
892 | 21^190632-2 | 252058 | Robert Price | 07/2015 |
893 | 2^837242+1873297 | 252035 | Enzo Doria | 06/2016 |
894 | 2^836656-2787929 | 251859 | Enzo Doria | 11/2015 |
895 | 2^836380+1875541 | 251776 | Enzo Doria | 07/2016 |
896 | (359^98327-1)/358 | 251233 | Alexander Zhirkov | 11/2017 |
897 | tau(41^28288) | 250924 | Nik Lygeros / Olivier Rozier | 10/2013 |
898 | 2^832511-461197 | 250611 | Enzo Doria | 07/2015 |
899 | 2^832505+1881137 | 250609 | Enzo Doria | 11/2016 |
900 | 2^832363+583295 | 250567 | Enzo Doria | 12/2016 |
901 | 2^832244-403635 | 250531 | Enzo Doria | 01/2014 |
902 | (14*10^250336-41)/9 | 250337 | Serge Batalov | 01/2023 |
903 | 2^831157+1880657 | 250204 | Enzo Doria | 11/2016 |
904 | 2^831088-7200899 | 250183 | Enzo Doria | 01/2015 |
905 | 2^830956-1349 | 250143 | Yves Minet | 07/2015 |
906 | 2^830037+282317 | 249867 | Enzo Doria | 09/2016 |
907 | 2^829589-113653 | 249732 | Enzo Doria | 09/2014 |
908 | (4*10^249550-7)/3 | 249551 | Serge Batalov | 01/2023 |
909 | 2^828281-3193 | 249338 | Yves Minet | 08/2016 |
910 | (2^828140-19)/3 | 249295 | Stefano Morozzi | 08/2022 |
911 | 2^828064-2785619 | 249273 | Enzo Doria | 10/2015 |
912 | 2^827602+60409 | 249134 | Enzo Doria | 03/2016 |
913 | 10^249010+348861 | 249011 | Patrick De Geest | 04/2016 |
914 | 10^249010-21 | 249010 | Serge Batalov | 12/2014 |
915 | 2^826733+1882907 | 248872 | Enzo Doria | 12/2016 |
916 | 2^825682+1876549 | 248556 | Enzo Doria | 07/2016 |
917 | 2^824991-114121 | 248348 | Enzo Doria | 12/2014 |
918 | 2^824642-362727 | 248242 | Enzo Doria | 12/2013 |
919 | 2^824565-114265 | 248219 | Enzo Doria | 01/2015 |
920 | (73*10^248145-1)/9 | 248146 | Robert Price | 01/2015 |
921 | (2^823337+1)/(3*362268281) | 247841 | Gord Palameta | 08/2018 |
922 | (2^822971-1)/6583769/28211445881/21255852651726486149207 | 247700 | Robert Kinser | 09/2016 |
923 | 2^822296+76501 | 247536 | Enzo Doria | 05/2016 |
924 | 2^821590-114167 | 247324 | Enzo Doria | 12/2014 |
925 | 2^821512-2790659 | 247300 | Enzo Doria | 12/2015 |
926 | 2^820077+382847 | 246868 | Enzo Doria | 11/2016 |
927 | 2^820001+81269 | 246845 | Enzo Doria | 07/2016 |
928 | 2^819463-59197 | 246683 | Enzo Doria | 10/2015 |
929 | 2^819296+80581 | 246633 | Enzo Doria | 07/2016 |
930 | 2^817160-350369 | 245990 | Enzo Doria | 06/2015 |
931 | 2^816039-19 | 245653 | Stefano Morozzi | 07/2022 |
932 | (71*10^245558-17)/9 | 245559 | Serge Batalov | 01/2023 |
933 | 88093#+(653879#)/(88093#) | 245374 | Makoto Morimoto | 11/2017 |
934 | 2^815111-113857 | 245373 | Enzo Doria | 10/2014 |
935 | 2^814914-4001 | 245314 | Yves Minet | 05/2017 |
936 | 846^83761-845^83761 | 245200 | Jean-Louis Charton | 12/2012 |
937 | 2^814356-2790449 | 245146 | Enzo Doria | 12/2015 |
938 | 2^814276-459029 | 245122 | Enzo Doria | 04/2015 |
939 | 2^814023+180923 | 245046 | Enzo Doria | 07/2016 |
940 | (3^513059-2^513059)/(1026119*5430216457) | 244776 | Mike Oakes | 03/2017 |
941 | 3^513007+16 | 244767 | Robert Price | 04/2020 |
942 | 2^811842-113675 | 244389 | Enzo Doria | 09/2014 |
943 | 2^811132-2787929 | 244176 | Enzo Doria | 11/2015 |
944 | 2^809746-2790971 | 243758 | Enzo Doria | 01/2016 |
945 | 2^808767-3295 | 243464 | Yves Minet | 12/2016 |
946 | 2^808621-113809 | 243420 | Enzo Doria | 09/2014 |
947 | 2^807724+1879621 | 243150 | Enzo Doria | 09/2016 |
948 | 20^186554-3 | 242713 | Paul Bourdelais | 12/2020 |
949 | 2^805843-113611 | 242583 | Enzo Doria | 08/2014 |
950 | 2^805745-459763 | 242554 | Enzo Doria | 05/2015 |
951 | 2^805353+782687 | 242436 | Enzo Doria | 11/2016 |
952 | 6^311257+5 | 242206 | Paul Bourdelais | 02/2021 |
953 | 2^804277-417933 | 242112 | Enzo Doria | 01/2014 |
954 | 2^803468-269039 | 241868 | Enzo Doria | 10/2013 |
955 | 2^803172+80851 | 241779 | Enzo Doria | 07/2016 |
956 | 3^506233-2 | 241535 | Robert Price | 11/2013 |
957 | 2^802025-25999 | 241434 | Enzo Doria | 10/2013 |
958 | (3^505823+3^252912+1)/7 | 241339 | Serge Batalov | 03/2014 |
959 | 2^801303+1872923 | 241217 | Enzo Doria | 05/2016 |
960 | 2^800579-1862947 | 240999 | Enzo Doria | 12/2015 |
961 | 3^504206+2 | 240568 | Luke W. Richards | 03/2018 |
962 | 2^798973-26283 | 240515 | Enzo Doria | 10/2013 |
963 | 2^798671-69487 | 240424 | Enzo Doria | 12/2015 |
964 | 2^797220+79831 | 239988 | Enzo Doria | 06/2016 |
965 | 2^796910-26001 | 239894 | Enzo Doria | 10/2013 |
966 | 2^796598+653119 | 239800 | Enzo Doria | 12/2016 |
967 | 2^796432-1859729 | 239750 | Enzo Doria | 11/2015 |
968 | 2^796002-1852211 | 239621 | Enzo Doria | 08/2015 |
969 | 2^795709+75767 | 239533 | Enzo Doria | 04/2016 |
970 | 2^795708+81721 | 239532 | Enzo Doria | 08/2016 |
971 | 2^795468-2786249 | 239460 | Enzo Doria | 10/2015 |
972 | 2^795442+80779 | 239452 | Enzo Doria | 07/2016 |
973 | 2^795075-1852057 | 239342 | Enzo Doria | 08/2015 |
974 | (86^123677+1)/87 | 239252 | Paul Bourdelais | 01/2019 |
975 | 2^794043+1875023 | 239031 | Enzo Doria | 06/2016 |
976 | 2^793347-69577 | 238822 | Enzo Doria | 01/2016 |
977 | 2^792988-344429 | 238714 | Enzo Doria | 08/2015 |
978 | 2^792700-2786369 | 238627 | Enzo Doria | 11/2015 |
979 | 2^792663-1844797 | 238616 | Enzo Doria | 06/2015 |
980 | 2^792605-291943 | 238598 | Enzo Doria | 07/2015 |
981 | (2^792061-2^396031+1)/5 | 238434 | Thomas Ritschel | 03/2014 |
982 | 4*10^238163+21 | 238164 | Robert Price | 12/2022 |
983 | 2^789373+1869377 | 237625 | Enzo Doria | 05/2016 |
984 | ((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961 | 237544 | Serge Batalov | 04/2015 |
985 | 2^788942+1866409 | 237496 | Enzo Doria | 02/2016 |
986 | 2^788844-114329 | 237466 | Enzo Doria | 01/2015 |
987 | 2^788705-1859713 | 237424 | Enzo Doria | 11/2015 |
988 | 2^786180+1871971 | 236664 | Enzo Doria | 05/2016 |
989 | 11^227092-90 | 236492 | Enzo Doria | 11/2012 |
990 | 2^785260+1866361 | 236387 | Enzo Doria | 02/2016 |
991 | 2^785220+1880611 | 236375 | Enzo Doria | 10/2016 |
992 | (2^784689-15)/7 | 236215 | Stefano Morozzi | 08/2022 |
993 | 19^184650-2 | 236122 | Robert Price | 10/2014 |
994 | 10^236059+216513 | 236060 | Patrick De Geest | 04/2016 |
995 | 10^236059-20909 | 236059 | Robert Price | 09/2015 |
996 | 2^783893-21 | 235976 | Stefano Morozzi | 07/2022 |
997 | (87^121487-1)/86 | 235625 | Paul Bourdelais | 12/2018 |
998 | 2^782634-113981 | 235597 | Enzo Doria | 11/2014 |
999 | 2^782423+1879733 | 235533 | Enzo Doria | 09/2016 |
1000 | 2^781682-2789543 | 235310 | Enzo Doria | 12/2015 |