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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
7751 | (61*10^101986+47)/9 | 101987 | Robert Price | 07/2022 |
7752 | 2^338787+53309 | 101986 | Stefano Morozzi | 01/2022 |
7753 | 2^338787-153817 | 101986 | Stefano Morozzi | 01/2022 |
7754 | 2^338789+56229 | 101986 | Stefano Morozzi | 01/2022 |
7755 | 2^338790+6429 | 101986 | Stefano Morozzi | 01/2022 |
7756 | 2^338788+131701 | 101986 | Stefano Morozzi | 02/2022 |
7757 | 2^338785+104639 | 101985 | Stefano Morozzi | 01/2022 |
7758 | 2^338784+37591 | 101985 | Stefano Morozzi | 04/2022 |
7759 | 2^338786-9831 | 101985 | Stefano Morozzi | 04/2022 |
7760 | 2^338783+109065 | 101984 | Stefano Morozzi | 03/2022 |
7761 | 2^338779+86711 | 101983 | Stefano Morozzi | 04/2022 |
7762 | 2^338778+113589 | 101983 | Stefano Morozzi | 05/2022 |
7763 | 2^338775-30369 | 101982 | Stefano Morozzi | 02/2022 |
7764 | 2^338774+159135 | 101982 | Stefano Morozzi | 03/2022 |
7765 | 2^338776+113001 | 101982 | Stefano Morozzi | 04/2022 |
7766 | 2^338774+117039 | 101982 | Stefano Morozzi | 09/2022 |
7767 | 2^338775+167109 | 101982 | Stefano Morozzi | 09/2022 |
7768 | 2^338774+147595 | 101982 | Stefano Morozzi | 11/2022 |
7769 | 2^338772+42733 | 101981 | Stefano Morozzi | 09/2022 |
7770 | 2^338771-138805 | 101981 | Stefano Morozzi | 12/2022 |
7771 | 2^338768-181007 | 101980 | Stefano Morozzi | 02/2022 |
7772 | 2^338768+108807 | 101980 | Stefano Morozzi | 03/2022 |
7773 | 2^338767+169155 | 101980 | Stefano Morozzi | 09/2022 |
7774 | 2^338769+95369 | 101980 | Stefano Morozzi | 11/2022 |
7775 | 2^338769+195965 | 101980 | Stefano Morozzi | 11/2022 |
7776 | 2^338770-12725 | 101980 | Stefano Morozzi | 12/2022 |
7777 | 2^338768-140843 | 101980 | Stefano Morozzi | 01/2023 |
7778 | 2^338764+138013 | 101979 | Stefano Morozzi | 04/2022 |
7779 | 2^338765-160323 | 101979 | Stefano Morozzi | 06/2022 |
7780 | 2^338765+124545 | 101979 | Stefano Morozzi | 02/2023 |
7786 | lucasU(1373,1,32502)-lucasU(1373,1,32501) | 101978 | Mike Oakes | 05/2009 |
7781 | 2^338761+103671 | 101978 | Stefano Morozzi | 01/2022 |
7782 | 2^338763-7651 | 101978 | Stefano Morozzi | 03/2022 |
7783 | 2^338763+65591 | 101978 | Stefano Morozzi | 06/2022 |
7784 | 2^338762-111875 | 101978 | Stefano Morozzi | 12/2022 |
7785 | 2^338762-192237 | 101978 | Stefano Morozzi | 02/2023 |
7787 | 2^338757-5151 | 101977 | Stefano Morozzi | 02/2022 |
7788 | 2^338760-79037 | 101977 | Stefano Morozzi | 02/2022 |
7789 | 2^338757-82143 | 101977 | Stefano Morozzi | 03/2022 |
7790 | 2^338757+137007 | 101977 | Stefano Morozzi | 04/2022 |
7791 | 2^338755+158531 | 101976 | Stefano Morozzi | 03/2022 |
7792 | 2^338755+74081 | 101976 | Stefano Morozzi | 02/2023 |
7793 | 2^338752-153353 | 101975 | Stefano Morozzi | 01/2022 |
7794 | 2^338751+8001 | 101975 | Stefano Morozzi | 02/2022 |
7795 | 2^338752+32977 | 101975 | Stefano Morozzi | 02/2022 |
7796 | 2^338753-79233 | 101975 | Stefano Morozzi | 02/2022 |
7797 | 2^338752-88157 | 101975 | Stefano Morozzi | 12/2022 |
7798 | 2^338750-175625 | 101974 | Stefano Morozzi | 12/2021 |
7799 | 2^338747-2731 | 101974 | Stefano Morozzi | 12/2021 |
7800 | 2^338750-29597 | 101974 | Stefano Morozzi | 02/2022 |
7801 | 2^338748+35095 | 101974 | Stefano Morozzi | 03/2022 |
7802 | 2^338747+137475 | 101974 | Stefano Morozzi | 04/2022 |
7803 | 2^338747+162005 | 101974 | Stefano Morozzi | 04/2022 |
7804 | 2^338750+162237 | 101974 | Stefano Morozzi | 04/2022 |
7805 | 2^338747-184365 | 101974 | Stefano Morozzi | 04/2022 |
7806 | 2^338748+64341 | 101974 | Stefano Morozzi | 05/2022 |
7807 | 2^338750+24445 | 101974 | Stefano Morozzi | 02/2023 |
7808 | 2^338746+59577 | 101973 | Stefano Morozzi | 03/2022 |
7809 | 2^338746+62055 | 101973 | Stefano Morozzi | 04/2022 |
7810 | 2^338744+194065 | 101973 | Stefano Morozzi | 09/2022 |
7811 | 2^338741+25359 | 101972 | Stefano Morozzi | 12/2021 |
7812 | 2^338743+176981 | 101972 | Stefano Morozzi | 12/2021 |
7813 | 2^338741+183029 | 101972 | Stefano Morozzi | 02/2022 |
7814 | 2^338743-130309 | 101972 | Stefano Morozzi | 02/2022 |
7815 | 2^338741+86349 | 101972 | Stefano Morozzi | 04/2022 |
7816 | 2^338741+111561 | 101972 | Stefano Morozzi | 04/2022 |
7817 | 2^338743+172301 | 101972 | Stefano Morozzi | 11/2022 |
7818 | 2^338741-189969 | 101972 | Stefano Morozzi | 01/2023 |
7819 | 2^338739+76959 | 101971 | Stefano Morozzi | 12/2021 |
7820 | 2^338739-105957 | 101971 | Stefano Morozzi | 02/2022 |
7821 | 2^338739+190149 | 101971 | Stefano Morozzi | 05/2022 |
7822 | 2^338738+64947 | 101971 | Stefano Morozzi | 05/2022 |
7823 | 2^338740+119947 | 101971 | Stefano Morozzi | 11/2022 |
7824 | 2^338740-186837 | 101971 | Stefano Morozzi | 12/2022 |
7825 | 2^338737+127547 | 101970 | Stefano Morozzi | 12/2021 |
7826 | 2^338737+128591 | 101970 | Stefano Morozzi | 01/2022 |
7827 | 2^338735-153165 | 101970 | Stefano Morozzi | 01/2022 |
7828 | 2^338734+13719 | 101970 | Stefano Morozzi | 05/2022 |
7829 | 2^338734-138225 | 101970 | Stefano Morozzi | 12/2022 |
7830 | 2^338735-186129 | 101970 | Stefano Morozzi | 12/2022 |
7836 | 25295^10744+10744^25295 | 101969 | Hans Havermann | 01/2019 |
7837 | 25712^9243+9243^25712 | 101969 | Hans Havermann | 01/2019 |
7831 | 2^338731-150895 | 101969 | Stefano Morozzi | 12/2021 |
7832 | 2^338731+54911 | 101969 | Stefano Morozzi | 01/2022 |
7833 | 2^338731+85863 | 101969 | Stefano Morozzi | 03/2022 |
7834 | 2^338732+185047 | 101969 | Stefano Morozzi | 03/2022 |
7835 | 2^338733+193791 | 101969 | Stefano Morozzi | 09/2022 |
7838 | 2^338729+69221 | 101968 | Stefano Morozzi | 09/2022 |
7839 | 2^338728+123355 | 101968 | Stefano Morozzi | 11/2022 |
7840 | 2^338730-87063 | 101968 | Stefano Morozzi | 12/2022 |
7841 | 2^338726+128199 | 101967 | Stefano Morozzi | 01/2022 |
7842 | 2^338727+127745 | 101967 | Stefano Morozzi | 01/2022 |
7843 | 2^338724+32971 | 101967 | Stefano Morozzi | 02/2022 |
7844 | 2^338727+189683 | 101967 | Stefano Morozzi | 05/2022 |
7845 | 2^338727+118293 | 101967 | Stefano Morozzi | 09/2022 |
7846 | 2^338723-76651 | 101966 | Stefano Morozzi | 12/2021 |
7847 | 2^338721+79037 | 101966 | Stefano Morozzi | 01/2022 |
7848 | 2^338723-132621 | 101966 | Stefano Morozzi | 03/2022 |
7849 | 2^338722+137313 | 101966 | Stefano Morozzi | 04/2022 |
7850 | 2^338722+162915 | 101966 | Stefano Morozzi | 04/2022 |
7851 | 2^338723+199161 | 101966 | Stefano Morozzi | 02/2023 |
7852 | 2^338718-126861 | 101965 | Stefano Morozzi | 12/2021 |
7853 | 2^338718-109127 | 101965 | Stefano Morozzi | 04/2022 |
7858 | (71^55079-1)/70 | 101964 | Paul Bourdelais | 08/2017 |
7854 | 2^338714+30835 | 101964 | Stefano Morozzi | 01/2022 |
7855 | 2^338714+156715 | 101964 | Stefano Morozzi | 02/2022 |
7856 | 2^338715+19923 | 101964 | Stefano Morozzi | 09/2022 |
7857 | 2^338716+173253 | 101964 | Stefano Morozzi | 11/2022 |
7859 | 2^338711+125399 | 101963 | Stefano Morozzi | 12/2021 |
7860 | 2^338713-30895 | 101963 | Stefano Morozzi | 02/2022 |
7861 | 2^338712-132545 | 101963 | Stefano Morozzi | 03/2022 |
7862 | 2^338713+87825 | 101963 | Stefano Morozzi | 04/2022 |
7863 | 2^338712+190333 | 101963 | Stefano Morozzi | 06/2022 |
7864 | 2^338709-154429 | 101962 | Stefano Morozzi | 02/2022 |
7865 | 2^338710+140545 | 101962 | Stefano Morozzi | 06/2022 |
7866 | 2^338706-102917 | 101961 | Stefano Morozzi | 01/2022 |
7867 | 2^338705+34727 | 101961 | Stefano Morozzi | 03/2022 |
7868 | 2^338706-165633 | 101961 | Stefano Morozzi | 01/2023 |
7869 | 2^338707-116115 | 101961 | Stefano Morozzi | 01/2023 |
7870 | 2^338698+104083 | 101959 | Stefano Morozzi | 01/2022 |
7871 | 2^338700-184565 | 101959 | Stefano Morozzi | 04/2022 |
7872 | 2^338700+189777 | 101959 | Stefano Morozzi | 05/2022 |
7873 | 2^338698+41779 | 101959 | Stefano Morozzi | 09/2022 |
7874 | 2^338699+148533 | 101959 | Stefano Morozzi | 11/2022 |
7875 | 2^338700+97381 | 101959 | Stefano Morozzi | 11/2022 |
7876 | 2^338698-142181 | 101959 | Stefano Morozzi | 02/2023 |
7877 | 2^338696+181671 | 101958 | Stefano Morozzi | 02/2022 |
7878 | 2^338697+146651 | 101958 | Stefano Morozzi | 11/2022 |
7879 | 2^338695-116977 | 101958 | Stefano Morozzi | 02/2023 |
7880 | 2^338692+106297 | 101957 | Stefano Morozzi | 01/2022 |
7881 | 2^338692+33195 | 101957 | Stefano Morozzi | 02/2022 |
7882 | 2^338692+110505 | 101957 | Stefano Morozzi | 03/2022 |
7883 | 2^338692+190093 | 101957 | Stefano Morozzi | 05/2022 |
7884 | 2^338692+173343 | 101957 | Stefano Morozzi | 11/2022 |
7885 | 2^338693+144975 | 101957 | Stefano Morozzi | 11/2022 |
7886 | 2^338692+149281 | 101957 | Stefano Morozzi | 02/2023 |
7887 | 2^338688+82203 | 101956 | Stefano Morozzi | 02/2022 |
7888 | 2^338689+82365 | 101956 | Stefano Morozzi | 02/2022 |
7889 | 2^338688-92159 | 101956 | Stefano Morozzi | 02/2023 |
7890 | 2^338686-81303 | 101955 | Stefano Morozzi | 03/2022 |
7891 | 2^338687+40461 | 101955 | Stefano Morozzi | 06/2022 |
7892 | 2^338687+65283 | 101955 | Stefano Morozzi | 06/2022 |
7898 | 2^338682-19865 | 101954 | Enzo Doria | 06/2013 |
7899 | (2^(112895*3+1)+243)/7 | 101954 | Kevin Acres | 12/2013 |
7893 | (8*10^101954-269)/9 | 101954 | Robert Price | 09/2021 |
7894 | 2^338683+50303 | 101954 | Stefano Morozzi | 11/2021 |
7895 | 2^338682-107205 | 101954 | Stefano Morozzi | 03/2022 |
7896 | 2^338682+13839 | 101954 | Stefano Morozzi | 05/2022 |
7897 | 2^338683-42837 | 101954 | Stefano Morozzi | 02/2023 |
7900 | 2^338678-180005 | 101953 | Stefano Morozzi | 02/2022 |
7901 | 2^338680+15855 | 101953 | Stefano Morozzi | 06/2022 |
7902 | 2^338678+93175 | 101953 | Stefano Morozzi | 09/2022 |
7903 | 2^338680+99217 | 101953 | Stefano Morozzi | 02/2023 |
7904 | 2^338674-175967 | 101952 | Stefano Morozzi | 12/2021 |
7905 | 2^338677-177373 | 101952 | Stefano Morozzi | 12/2021 |
7906 | 2^338677+102999 | 101952 | Stefano Morozzi | 01/2022 |
7907 | 2^338676+33381 | 101952 | Stefano Morozzi | 03/2022 |
7908 | 2^338677-82699 | 101952 | Stefano Morozzi | 03/2022 |
7909 | 2^338676-34299 | 101952 | Stefano Morozzi | 04/2022 |
7910 | 2^338675+188445 | 101952 | Stefano Morozzi | 05/2022 |
7911 | 2^338676+165271 | 101952 | Stefano Morozzi | 06/2022 |
7912 | 2^338674-187551 | 101952 | Stefano Morozzi | 12/2022 |
7913 | 2^338676-42243 | 101952 | Stefano Morozzi | 02/2023 |
7914 | 2^338671-55041 | 101951 | Stefano Morozzi | 02/2022 |
7915 | 2^338673-80203 | 101951 | Stefano Morozzi | 02/2022 |
7916 | 2^338672-182063 | 101951 | Stefano Morozzi | 03/2022 |
7917 | 2^338672+36667 | 101951 | Stefano Morozzi | 04/2022 |
7918 | 2^338668+2583 | 101950 | Stefano Morozzi | 12/2021 |
7919 | 2^338670-157001 | 101950 | Stefano Morozzi | 03/2022 |
7920 | 2^338669-8353 | 101950 | Stefano Morozzi | 04/2022 |
7921 | 2^338670+40635 | 101950 | Stefano Morozzi | 06/2022 |
7929 | (2^338666+3154)/2 | 101949 | Stefano Morozzi | 09/2020 |
7922 | 2^338665+1577 | 101949 | Stefano Morozzi | 12/2021 |
7923 | 2^338665-51133 | 101949 | Stefano Morozzi | 12/2021 |
7924 | 2^338664+4345 | 101949 | Stefano Morozzi | 01/2022 |
7925 | 2^338666-128943 | 101949 | Stefano Morozzi | 01/2022 |
7926 | 2^338664+131535 | 101949 | Stefano Morozzi | 01/2022 |
7927 | 2^338667+14943 | 101949 | Stefano Morozzi | 05/2022 |
7928 | 2^338665+166637 | 101949 | Stefano Morozzi | 09/2022 |
7930 | 2^338662+31587 | 101948 | Stefano Morozzi | 02/2022 |
7931 | 2^338663-58375 | 101948 | Stefano Morozzi | 04/2022 |
7932 | 2^338663-107869 | 101948 | Stefano Morozzi | 04/2022 |
7933 | 2^338663+90435 | 101948 | Stefano Morozzi | 06/2022 |
7934 | 2^338661+70457 | 101948 | Stefano Morozzi | 11/2022 |
7935 | 2^338662+70519 | 101948 | Stefano Morozzi | 11/2022 |
7936 | 2^338663-39447 | 101948 | Stefano Morozzi | 01/2023 |
7937 | 2^338658-159191 | 101947 | Stefano Morozzi | 04/2022 |
7938 | 2^338659-159687 | 101947 | Stefano Morozzi | 04/2022 |
7939 | 2^338659+15543 | 101947 | Stefano Morozzi | 05/2022 |
7940 | 2^338658+44395 | 101947 | Stefano Morozzi | 09/2022 |
7941 | 2^338658+192537 | 101947 | Stefano Morozzi | 09/2022 |
7942 | 2^338659-90531 | 101947 | Stefano Morozzi | 01/2023 |
7943 | 2^338659-114759 | 101947 | Stefano Morozzi | 01/2023 |
7944 | 2^338659+124079 | 101947 | Stefano Morozzi | 02/2023 |
7945 | 2^338654+51027 | 101946 | Stefano Morozzi | 12/2021 |
7946 | 2^338656-152115 | 101946 | Stefano Morozzi | 12/2021 |
7947 | 2^338654+32415 | 101946 | Stefano Morozzi | 02/2022 |
7948 | 2^338654+39799 | 101946 | Stefano Morozzi | 05/2022 |
7949 | 2^338655+144579 | 101946 | Stefano Morozzi | 09/2022 |
7950 | 2^338657+97509 | 101946 | Stefano Morozzi | 11/2022 |
7951 | 2^338653+126629 | 101945 | Stefano Morozzi | 12/2021 |
7952 | 2^338653+33279 | 101945 | Stefano Morozzi | 02/2022 |
7953 | 2^338652-107097 | 101945 | Stefano Morozzi | 03/2022 |
7954 | 2^338653+94475 | 101945 | Stefano Morozzi | 09/2022 |
7955 | 2^338651+194073 | 101945 | Stefano Morozzi | 09/2022 |
7956 | 2^338652-89157 | 101945 | Stefano Morozzi | 01/2023 |
7957 | 2^338649-154663 | 101944 | Stefano Morozzi | 02/2022 |
7958 | 2^338650+61399 | 101944 | Stefano Morozzi | 04/2022 |
7959 | 2^338650-35655 | 101944 | Stefano Morozzi | 06/2022 |
7960 | 2^338650+169623 | 101944 | Stefano Morozzi | 09/2022 |
7961 | 2^338649-40743 | 101944 | Stefano Morozzi | 01/2023 |
7962 | 2^338645+150311 | 101943 | Stefano Morozzi | 11/2021 |
7963 | 2^338645+28481 | 101943 | Stefano Morozzi | 01/2022 |
7964 | 2^338647-77895 | 101943 | Stefano Morozzi | 01/2022 |
7965 | 2^338647-84607 | 101943 | Stefano Morozzi | 04/2022 |
7966 | 2^338647+164523 | 101943 | Stefano Morozzi | 05/2022 |
7967 | 2^338645+64845 | 101943 | Stefano Morozzi | 05/2022 |
7968 | 2^338644-35969 | 101943 | Stefano Morozzi | 12/2022 |
7969 | 2^338645-15715 | 101943 | Stefano Morozzi | 01/2023 |
7970 | 2^338641-152541 | 101942 | Stefano Morozzi | 12/2021 |
7971 | 2^338643-56487 | 101942 | Stefano Morozzi | 03/2022 |
7972 | 2^338642-186525 | 101942 | Stefano Morozzi | 12/2022 |
7973 | 2^338643-41715 | 101942 | Stefano Morozzi | 02/2023 |
7974 | 2^338638+100575 | 101941 | Stefano Morozzi | 12/2021 |
7975 | 2^338639-127461 | 101941 | Stefano Morozzi | 12/2021 |
7976 | 2^338640+187657 | 101941 | Stefano Morozzi | 04/2022 |
7977 | 2^338640+44431 | 101941 | Stefano Morozzi | 09/2022 |
7978 | 2^338635+1961 | 101940 | Stefano Morozzi | 12/2021 |
7979 | 2^338637+102125 | 101940 | Stefano Morozzi | 12/2021 |
7980 | 2^338636-135329 | 101940 | Stefano Morozzi | 06/2022 |
7981 | 2^338635+199485 | 101940 | Stefano Morozzi | 02/2023 |
7986 | 28594^3673+3673^28594 | 101939 | Hans Havermann | 02/2019 |
7982 | 2^338631+110741 | 101939 | Stefano Morozzi | 03/2022 |
7983 | 2^338631+112119 | 101939 | Stefano Morozzi | 04/2022 |
7984 | 2^338634-83097 | 101939 | Stefano Morozzi | 04/2022 |
7985 | 2^338633+139701 | 101939 | Stefano Morozzi | 05/2022 |
7987 | 2^338630-150341 | 101938 | Stefano Morozzi | 12/2021 |
7988 | 2^338630+12867 | 101938 | Stefano Morozzi | 04/2022 |
7989 | 2^338629+42147 | 101938 | Stefano Morozzi | 09/2022 |
7990 | 2^338628+121083 | 101938 | Stefano Morozzi | 11/2022 |
7991 | 2^338630+147235 | 101938 | Stefano Morozzi | 11/2022 |
7992 | 2^338628-37679 | 101938 | Stefano Morozzi | 12/2022 |
7993 | 2^338629-41383 | 101938 | Stefano Morozzi | 01/2023 |
7994 | 2^338628-91877 | 101938 | Stefano Morozzi | 02/2023 |
7995 | 2^338626-105875 | 101937 | Stefano Morozzi | 02/2022 |
7996 | 2^338625-111729 | 101937 | Stefano Morozzi | 12/2022 |
7997 | 2^338627+49299 | 101937 | Stefano Morozzi | 02/2023 |
7998 | 2^338621+33069 | 101936 | Stefano Morozzi | 02/2022 |
7999 | 2^338623-106405 | 101936 | Stefano Morozzi | 03/2022 |
8000 | 2^338621+61751 | 101936 | Stefano Morozzi | 04/2022 |