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 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
752 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
753 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
754 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
755 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
756 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
757 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
758 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
759 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
760 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |
761 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
762 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
763 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
764 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
765 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
766 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
767 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
768 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
769 | 2^667894+1875589 | 201057 | Enzo Doria | 06/2016 |
770 | 2^667569-1836559 | 200959 | Enzo Doria | 05/2015 |
771 | (172*10^200746-1)/9 | 200748 | Serge Batalov | 12/2014 |
772 | 2^666430+782569 | 200616 | Enzo Doria | 10/2016 |
773 | (86^103471+1)/87 | 200163 | Paul Bourdelais | 05/2018 |
775 | 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 | 200003 | Robert Price | 05/2017 |
774 | 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 | 200003 | Robert Price | 01/2018 |
776 | numbpart(32235776596) | 200002 | Serge Batalov | 04/2017 |
777 | (10^200001+149)/3 | 200001 | Serge Batalov | 12/2014 |
778 | (14*10^199447+73)/3 | 199448 | Robert Price | 12/2018 |
779 | 2^662103-29287 | 199313 | Enzo Doria | 08/2015 |
780 | (2*10^199283+457)/9 | 199283 | Robert Price | 01/2018 |
781 | (10^199248-19)/9 | 199248 | Robert Price | 01/2018 |
782 | 2^660482-2891 | 198825 | Yves Minet | 05/2016 |
783 | 2^659583+1879223 | 198555 | Enzo Doria | 08/2016 |
784 | (53*10^198529+1)/9 | 198530 | Serge Batalov | 07/2010 |
785 | 2^658828-29819 | 198327 | Enzo Doria | 08/2015 |
786 | 2^658776-2791229 | 198312 | Enzo Doria | 01/2016 |
787 | (35*10^198294-377)/9 | 198295 | Robert Price | 07/2018 |
788 | (4*10^198268+137)/3 | 198269 | Robert Price | 03/2018 |
789 | 2^658544-1854029 | 198242 | Enzo Doria | 09/2015 |
790 | (157^90239-1)/156 | 198154 | Alexander Zhirkov | 06/2016 |
791 | (4*10^197778+173)/3 | 197779 | Robert Price | 02/2018 |
792 | 2^656462+1874419 | 197615 | Enzo Doria | 06/2016 |
793 | (89^101363+1)/90 | 197595 | Paul Bourdelais | 11/2017 |
794 | 2^655893-344563 | 197444 | Enzo Doria | 07/2015 |
795 | 2^655875+71333 | 197439 | Enzo Doria | 04/2016 |
796 | 2^655845-9 | 197430 | Robert Price | 01/2017 |
797 | 2^655682-1849121 | 197380 | Enzo Doria | 08/2015 |
798 | 4*10^197268-89 | 197269 | Robert Price | 11/2018 |
799 | 2^655045-49603 | 197189 | Enzo Doria | 10/2015 |
800 | 2^655000-2784089 | 197175 | Enzo Doria | 10/2015 |
801 | (18^157051-1)/17 | 197141 | Paul Bourdelais | 03/2010 |
802 | 2^654400-39719 | 196995 | Enzo Doria | 09/2015 |
803 | (14*10^196965-221)/9 | 196966 | Robert Price | 04/2018 |
804 | 2^654216-459995 | 196939 | Enzo Doria | 06/2015 |
805 | (17*10^196921+31)/3 | 196922 | Robert Price | 01/2019 |
806 | 3*10^196881-59 | 196882 | Robert Price | 09/2018 |
807 | 2^653851+82295 | 196829 | Enzo Doria | 09/2016 |
808 | (38*10^196792+691)/9 | 196793 | Robert Price | 10/2018 |
809 | 2^653636-29429 | 196765 | Enzo Doria | 08/2015 |
810 | 2^653601-69673 | 196754 | Enzo Doria | 02/2016 |
811 | (44*10^196684+1)/9 | 196685 | Serge Batalov | 07/2010 |
812 | 2^652786-1852571 | 196509 | Enzo Doria | 08/2015 |
813 | 2^652752-1325 | 196498 | Yves Minet | 07/2015 |
814 | 2^652470-1859141 | 196414 | Enzo Doria | 10/2015 |
815 | 2^652307+1877483 | 196364 | Enzo Doria | 08/2016 |
816 | 2^652293-115273 | 196360 | Enzo Doria | 06/2015 |
817 | 2^651218-1868201 | 196037 | Enzo Doria | 04/2016 |
818 | 2^651047-49687 | 195985 | Enzo Doria | 10/2015 |
819 | 2^650285-2785333 | 195756 | Enzo Doria | 10/2015 |
820 | (69^106397-1)/68 | 195647 | Paul Bourdelais | 10/2017 |
821 | 2^649811+1877573 | 195613 | Enzo Doria | 08/2016 |
822 | 2^649662-170531 | 195568 | Hans Havermann | 10/2018 |
823 | 2^649586+182839 | 195545 | Enzo Doria | 11/2016 |
824 | 2^649537-1867363 | 195531 | Enzo Doria | 04/2016 |
825 | 2^649536-1861499 | 195530 | Enzo Doria | 12/2015 |
826 | (103*10^195478-1)/3 | 195480 | Serge Batalov | 12/2014 |
827 | 2^649102-59351 | 195400 | Enzo Doria | 10/2015 |
828 | (2*10^195399+529)/9 | 195399 | Robert Price | 01/2018 |
829 | 2^648988+1178971 | 195365 | Enzo Doria | 06/2016 |
830 | 2^648975-114319 | 195361 | Enzo Doria | 02/2015 |
831 | (11*10^195350-137)/9 | 195351 | Robert Price | 01/2018 |
832 | 2^648619-24835 | 195254 | Enzo Doria | 09/2013 |
833 | (14*10^195234-83)/3 | 195235 | Robert Price | 12/2018 |
834 | 2^648190-24737 | 195125 | Enzo Doria | 09/2013 |
835 | (57^111119+1)/58 | 195110 | Paul Bourdelais | 10/2017 |
836 | 11^187185-90 | 194934 | Enzo Doria | 09/2012 |
837 | 2^647068+77281 | 194787 | Enzo Doria | 05/2016 |
838 | 15^165559-14^165559 | 194713 | Jean-Louis Charton | 03/2011 |
839 | F(931517) | 194676 | Henri Lifchitz | 09/2008 |
840 | 4*10^194668+49 | 194669 | Robert Price | 01/2019 |
841 | 2^646589+1179407 | 194643 | Enzo Doria | 06/2016 |
842 | 2^646289-114621 | 194553 | Enzo Doria | 05/2015 |
843 | 2^646236-39659 | 194537 | Enzo Doria | 09/2015 |
844 | 2^646161-59833 | 194514 | Enzo Doria | 11/2015 |
845 | (17*10^194502+31)/3 | 194503 | Robert Price | 01/2019 |
846 | 2*10^194413+3 | 194414 | Robert Price | 07/2015 |
847 | 2^645360-1848599 | 194273 | Enzo Doria | 08/2015 |
848 | (112*10^194150-1)/3 | 194152 | Serge Batalov | 12/2014 |
849 | 2*10^193981-43 | 193982 | Robert Price | 04/2018 |
850 | 2^644382+75169 | 193979 | Enzo Doria | 04/2016 |
851 | 2^644304-1861409 | 193955 | Enzo Doria | 11/2015 |
852 | 5*10^193907-9 | 193908 | Robert Price | 05/2015 |
853 | 2^644043+1876703 | 193877 | Enzo Doria | 07/2016 |
854 | 2^643735+1879733 | 193784 | Enzo Doria | 09/2016 |
855 | (5^277183+1)/6 | 193742 | Paul Bourdelais | 07/2010 |
856 | 2^643216-286565 | 193628 | Enzo Doria | 07/2015 |
857 | 2^642888-24965 | 193529 | Enzo Doria | 09/2013 |
858 | 2^642448-114825 | 193397 | Enzo Doria | 05/2015 |
859 | 2^642437-1856623 | 193393 | Enzo Doria | 10/2015 |
860 | 2^642039-59797 | 193273 | Enzo Doria | 11/2015 |
861 | 10^193230+513861 | 193231 | Patrick De Geest | 07/2018 |
862 | 10^193230-8001 | 193230 | Robert Price | 03/2018 |
863 | 2^641692-286349 | 193169 | Enzo Doria | 07/2015 |
864 | 2^641690-24737 | 193168 | Enzo Doria | 09/2013 |
865 | 2^641514+1876549 | 193115 | Enzo Doria | 07/2016 |
866 | 2^640888-2785619 | 192927 | Enzo Doria | 10/2015 |
867 | 2^640874-2783741 | 192923 | Enzo Doria | 09/2015 |
868 | 2^640181+467 | 192714 | Lelio R Paula | 08/2013 |
869 | 2^639536-1850249 | 192520 | Enzo Doria | 08/2015 |
870 | 5*10^192422-43 | 192423 | Robert Price | 01/2019 |
871 | 2^639110-2792441 | 192392 | Enzo Doria | 02/2016 |
872 | 2^638955-29827 | 192345 | Enzo Doria | 08/2015 |
873 | 2^638713-2784223 | 192272 | Enzo Doria | 10/2015 |
874 | 2^638490-113507 | 192205 | Enzo Doria | 08/2014 |
875 | 2^638189-39943 | 192115 | Enzo Doria | 09/2015 |
876 | 2^638110+1877119 | 192091 | Enzo Doria | 07/2016 |
877 | 2^638066-2785211 | 192078 | Enzo Doria | 10/2015 |
878 | 2^637475-115309 | 191900 | Enzo Doria | 07/2015 |
879 | 2^636661+1876577 | 191655 | Enzo Doria | 07/2016 |
880 | (34^125101-1)/33 | 191589 | Paul Bourdelais | 11/2017 |
881 | 2^636177-1855123 | 191509 | Enzo Doria | 09/2015 |
882 | 2^636158-113627 | 191503 | Enzo Doria | 08/2014 |
883 | (37*25^136966+63)/4 | 191472 | Curtis Bright | 05/2015 |
884 | 2^636035+79823 | 191466 | Enzo Doria | 06/2016 |
885 | 2^636011-1860847 | 191459 | Enzo Doria | 11/2015 |
886 | 2^635926-1860611 | 191433 | Enzo Doria | 11/2015 |
887 | 3*10^191152-7 | 191153 | Robert Price | 08/2015 |
888 | 2^634883-1865677 | 191119 | Enzo Doria | 02/2016 |
889 | 2^634801+1871957 | 191095 | Enzo Doria | 05/2016 |
890 | (35*10^191073+1)/9 | 191074 | Serge Batalov | 07/2010 |
891 | 2^634470-59861 | 190995 | Enzo Doria | 11/2015 |
892 | 2^634368-29519 | 190964 | Enzo Doria | 08/2015 |
893 | 2^634188-350609 | 190910 | Enzo Doria | 06/2015 |
894 | (13*10^190732-61)/3 | 190733 | Robert Price | 11/2018 |
895 | (7*10^190683+143)/3 | 190684 | Robert Price | 03/2018 |
896 | 2^633088-113879 | 190579 | Enzo Doria | 10/2014 |
897 | 2^633064+1874911 | 190572 | Enzo Doria | 06/2016 |
898 | (43*10^190547+83)/9 | 190548 | Robert Price | 11/2018 |
899 | 2^632795-351205 | 190491 | Enzo Doria | 06/2015 |
900 | (43*10^190351+101)/9 | 190352 | Robert Price | 11/2018 |
901 | 2^632156+78391 | 190298 | Enzo Doria | 06/2016 |
902 | 2^632082-1851971 | 190276 | Enzo Doria | 08/2015 |
903 | 2^632020+1880311 | 190257 | Enzo Doria | 09/2016 |
904 | 2^631637-462373 | 190142 | Enzo Doria | 08/2015 |
905 | 2^631122-39251 | 189987 | Enzo Doria | 08/2015 |
906 | (26*10^189928-89)/9 | 189929 | Robert Price | 06/2018 |
907 | 2^630839-97 | 189902 | Yves Minet | 07/2017 |
908 | 2^630359+1788953 | 189757 | Enzo Doria | 05/2016 |
909 | 2^630228+1871971 | 189718 | Enzo Doria | 05/2016 |
910 | 2^630108+781 | 189682 | Lelio R Paula | 08/2013 |
911 | 2^629870-1867811 | 189610 | Enzo Doria | 04/2016 |
912 | (359^74189-1)/358 | 189558 | Alexander Zhirkov | 11/2017 |
913 | 2^629326+2792929 | 189447 | Enzo Doria | 02/2016 |
914 | (10^189385-61)/3 | 189385 | Serge Batalov | 12/2014 |
915 | 2^629036+1874011 | 189359 | Enzo Doria | 06/2016 |
916 | 2^628930+80779 | 189327 | Enzo Doria | 07/2016 |
917 | 2^628582+1179439 | 189223 | Enzo Doria | 06/2016 |
918 | (44*10^188999-503)/9 | 189000 | Robert Price | 12/2018 |
919 | 2^627037-2785843 | 188757 | Enzo Doria | 10/2015 |
920 | L(901657) | 188436 | Renaud Lifchitz | 11/2008 |
921 | 2^625651+74213 | 188340 | Enzo Doria | 04/2016 |
922 | 2^625584-460919 | 188320 | Enzo Doria | 06/2015 |
923 | (10^188164+359)/9 | 188164 | Serge Batalov | 12/2014 |
924 | 2^624481-113611 | 187988 | Enzo Doria | 08/2014 |
925 | 2^624077-112723 | 187866 | Enzo Doria | 07/2014 |
926 | 2^624008+1874941 | 187846 | Enzo Doria | 06/2016 |
927 | 2^623870+78679 | 187804 | Enzo Doria | 05/2016 |
928 | 2^623714-114035 | 187757 | Enzo Doria | 11/2014 |
929 | 2^623651-1834251 | 187738 | Enzo Doria | 07/2015 |
930 | (7*10^187645+53)/3 | 187646 | Robert Price | 05/2018 |
931 | 2^623146+1879609 | 187586 | Enzo Doria | 09/2016 |
932 | (5*10^187471+91)/3 | 187472 | Robert Price | 04/2018 |
933 | 2^622500+81931 | 187392 | Enzo Doria | 08/2016 |
934 | 2^622300-1861739 | 187331 | Enzo Doria | 12/2015 |
935 | (38*10^187281+349)/9 | 187282 | Robert Price | 10/2018 |
936 | 2^622052+76771 | 187257 | Enzo Doria | 05/2016 |
937 | 2^622005-24091 | 187243 | Enzo Doria | 08/2013 |
938 | 2^621879-351787 | 187205 | Enzo Doria | 07/2015 |
939 | 2^621700+79411 | 187151 | Enzo Doria | 06/2016 |
940 | (2*10^187062-71)/3 | 187062 | Robert Price | 12/2017 |
941 | 2^620929-113203 | 186919 | Enzo Doria | 07/2014 |
942 | 10^186842+168223 | 186843 | Patrick De Geest | 07/2018 |
943 | 10^186842-8001 | 186842 | Robert Price | 03/2018 |
944 | 2^620347-1777 | 186744 | Lelio R Paula | 07/2013 |
945 | 11^179143-4170 | 186559 | Enzo Doria | 12/2012 |
946 | (5^266863+1)/6 | 186529 | Paul Bourdelais | 07/2010 |
947 | 2^619297-2792353 | 186427 | Enzo Doria | 02/2016 |
948 | 2^618940-460139 | 186320 | Enzo Doria | 06/2015 |
949 | 2^618046+74179 | 186051 | Enzo Doria | 04/2016 |
950 | 3*10^186019+11 | 186020 | Robert Price | 07/2018 |
951 | 2*10^185930-3 | 185931 | Robert Price | 07/2015 |
952 | (82^97151+1)/83 | 185928 | Paul Bourdelais | 10/2017 |
953 | 4*10^185905+91 | 185906 | Robert Price | 08/2018 |
954 | (37*10^185811+377)/9 | 185812 | Robert Price | 11/2018 |
955 | 2^617250+9385 | 185811 | Lelio R Paula | 07/2013 |
956 | 39^116749+2 | 185756 | Robert Price | 04/2015 |
957 | 2^616924-39719 | 185713 | Enzo Doria | 09/2015 |
958 | 2^616712+1867621 | 185649 | Enzo Doria | 04/2016 |
959 | (3^388897+2^388897)/5 | 185551 | Jean-Louis Charton | 09/2011 |
960 | 4*10^185355+9 | 185356 | Robert Price | 05/2015 |
961 | 2^615622+76639 | 185321 | Enzo Doria | 05/2016 |
962 | 2^615591+1879223 | 185312 | Enzo Doria | 08/2016 |
963 | 2^615503+1876643 | 185285 | Enzo Doria | 07/2016 |
964 | 5^265007-4^265007 | 185232 | Jean-Louis Charton | 02/2013 |
965 | (4*10^185221-91)/3 | 185222 | Robert Price | 03/2018 |
966 | 2^614783-2790097 | 185069 | Enzo Doria | 12/2015 |
967 | 2^614745-29323 | 185057 | Enzo Doria | 07/2015 |
968 | (((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840 | 185052 | Serge Batalov | 07/2013 |
969 | (14*10^184950+211)/9 | 184951 | Robert Price | 04/2018 |
970 | 2^614315+81353 | 184928 | Enzo Doria | 08/2016 |
971 | 2^614294-1849961 | 184921 | Enzo Doria | 08/2015 |
972 | 2^614266+1877809 | 184913 | Enzo Doria | 08/2016 |
973 | 2^613715-1860727 | 184747 | Enzo Doria | 11/2015 |
974 | 2*10^184723+41 | 184724 | Robert Price | 05/2018 |
975 | 2^613487-349987 | 184678 | Enzo Doria | 07/2015 |
976 | (95^93377+1)/96 | 184672 | Paul Bourdelais | 11/2017 |
977 | 14^161089-161089^14 | 184629 | Serge Batalov | 05/2016 |
978 | 2^613033-114621 | 184542 | Enzo Doria | 05/2015 |
979 | (9^193247+1)/10 | 184404 | Paul Bourdelais | 02/2010 |
980 | 2^612341-1604809 | 184334 | Enzo Doria | 05/2015 |
981 | (2^611999-1)/18464214225958267477777390354183 | 184199 | Dario Alpern | 06/2017 |
982 | (14*10^184150+37)/3 | 184151 | Robert Price | 12/2018 |
983 | 2^611731-4837 | 184150 | Yves Minet | 08/2018 |
984 | 3*10^184124-7 | 184125 | Robert Price | 08/2015 |
985 | 2^611628-24537 | 184119 | Enzo Doria | 08/2013 |
986 | 3*10^184110+13 | 184111 | Robert Price | 07/2018 |
987 | 2^611460+71881 | 184068 | Enzo Doria | 04/2016 |
988 | 4*10^184004-63 | 184005 | Robert Price | 10/2018 |
989 | 2^610982-1867301 | 183924 | Enzo Doria | 03/2016 |
990 | 3*10^183872-49 | 183873 | Robert Price | 07/2018 |
991 | 2^610597+1178897 | 183809 | Enzo Doria | 05/2016 |
992 | (17*10^183764+31)/3 | 183765 | Robert Price | 01/2019 |
993 | (28*10^183760-1)/9 | 183761 | Serge Batalov | 10/2014 |
994 | 2^610401+1277 | 183750 | Lelio R Paula | 07/2013 |
995 | 2^610356-1849019 | 183736 | Enzo Doria | 08/2015 |
996 | (63^102103+1)/64 | 183717 | Paul Bourdelais | 10/2017 |
997 | (2^610289+1)/(3*528882550291) | 183704 | Gord Palameta | 08/2018 |
998 | (4*10^183659+149)/9 | 183659 | Robert Price | 04/2018 |
999 | 2^609846-1834251 | 183582 | Enzo Doria | 07/2015 |
1000 | 11^176176-240 | 183469 | Enzo Doria | 11/2012 |