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 ? |
9751 | 2^338543-140677 | 101912 | Stefano Morozzi | 01/2023 |
9752 | 2^338541+152721 | 101911 | Stefano Morozzi | 01/2022 |
9753 | 2^338539+60825 | 101911 | Stefano Morozzi | 03/2022 |
9754 | 2^338539+160881 | 101911 | Stefano Morozzi | 03/2022 |
9755 | 2^338541-182523 | 101911 | Stefano Morozzi | 03/2022 |
9756 | 2^338540+87645 | 101911 | Stefano Morozzi | 04/2022 |
9757 | 2^338541+148305 | 101911 | Stefano Morozzi | 11/2022 |
9758 | 2^338541-163075 | 101911 | Stefano Morozzi | 12/2022 |
9759 | 2^338536-100785 | 101910 | Stefano Morozzi | 12/2021 |
9760 | 2^338535-51837 | 101910 | Stefano Morozzi | 12/2021 |
9761 | 2^338535-158745 | 101910 | Stefano Morozzi | 04/2022 |
9762 | 2^338536-189977 | 101910 | Stefano Morozzi | 01/2023 |
9763 | 2^338537-65623 | 101910 | Stefano Morozzi | 01/2023 |
9764 | 2^338532+39445 | 101909 | Stefano Morozzi | 05/2022 |
9765 | 2^338532+141415 | 101909 | Stefano Morozzi | 06/2022 |
9766 | 2^338532-136037 | 101909 | Stefano Morozzi | 06/2022 |
9767 | 2^338531+81081 | 101908 | Stefano Morozzi | 01/2022 |
9768 | 2^338530+59835 | 101908 | Stefano Morozzi | 03/2022 |
9769 | 2^338529+186551 | 101908 | Stefano Morozzi | 04/2022 |
9770 | 2^338531+61313 | 101908 | Stefano Morozzi | 04/2022 |
9771 | 2^338531-9277 | 101908 | Stefano Morozzi | 04/2022 |
9772 | 2^338528-92727 | 101908 | Stefano Morozzi | 02/2023 |
9773 | 2^338527+191205 | 101907 | Stefano Morozzi | 06/2022 |
9774 | 2^338525+99621 | 101907 | Stefano Morozzi | 02/2023 |
9775 | 2^338524+54421 | 101906 | Stefano Morozzi | 01/2022 |
9776 | 2^338522-155811 | 101906 | Stefano Morozzi | 02/2022 |
9777 | 2^338523-16291 | 101906 | Stefano Morozzi | 01/2023 |
9778 | 2^338522-142137 | 101906 | Stefano Morozzi | 02/2023 |
9779 | 2^338521+183131 | 101905 | Stefano Morozzi | 02/2022 |
9780 | 2^338520+34945 | 101905 | Stefano Morozzi | 03/2022 |
9781 | 2^338518-182885 | 101905 | Stefano Morozzi | 04/2022 |
9782 | 2^338518+114633 | 101905 | Stefano Morozzi | 05/2022 |
9783 | 2^338518-12621 | 101905 | Stefano Morozzi | 12/2022 |
9784 | 2^338518-187325 | 101905 | Stefano Morozzi | 12/2022 |
9792 | (9*2^338520+1)/365 | 101904 | Lelio R Paula | 12/2013 |
9785 | 2^338517-125955 | 101904 | Stefano Morozzi | 12/2021 |
9786 | 2^338517+126437 | 101904 | Stefano Morozzi | 12/2021 |
9787 | 2^338517-53499 | 101904 | Stefano Morozzi | 01/2022 |
9788 | 2^338515+30369 | 101904 | Stefano Morozzi | 01/2022 |
9789 | 2^338517-184623 | 101904 | Stefano Morozzi | 04/2022 |
9790 | 2^338515+89333 | 101904 | Stefano Morozzi | 05/2022 |
9791 | 2^338515+198813 | 101904 | Stefano Morozzi | 02/2023 |
9795 | 24502^14419+14419^24502 | 101903 | Hans Havermann | 01/2019 |
9793 | 2^338512-827 | 101903 | Stefano Morozzi | 12/2021 |
9794 | 2^338514-6611 | 101903 | Stefano Morozzi | 03/2022 |
9796 | 2^338509+5139 | 101902 | Stefano Morozzi | 01/2022 |
9797 | 2^338509+40205 | 101902 | Stefano Morozzi | 06/2022 |
9798 | 2^338511+19959 | 101902 | Stefano Morozzi | 09/2022 |
9799 | 2^338510-37877 | 101902 | Stefano Morozzi | 12/2022 |
9800 | 2^338507-188655 | 101901 | Stefano Morozzi | 12/2022 |
9801 | 2^338507-114457 | 101901 | Stefano Morozzi | 01/2023 |
9802 | 2^338504-152615 | 101900 | Stefano Morozzi | 01/2022 |
9803 | 2^338502-4587 | 101900 | Stefano Morozzi | 02/2022 |
9804 | 2^338502-166275 | 101900 | Stefano Morozzi | 01/2023 |
9805 | 2^338500-26865 | 101899 | Stefano Morozzi | 12/2021 |
9806 | 2^338501-177471 | 101899 | Stefano Morozzi | 12/2021 |
9807 | 2^338499-3915 | 101899 | Stefano Morozzi | 01/2022 |
9808 | 2^338501+32051 | 101899 | Stefano Morozzi | 02/2022 |
9809 | 2^338499+183533 | 101899 | Stefano Morozzi | 03/2022 |
9810 | 2^338500+35625 | 101899 | Stefano Morozzi | 03/2022 |
9811 | 2^338499+87579 | 101899 | Stefano Morozzi | 04/2022 |
9812 | 2^338498-117683 | 101899 | Stefano Morozzi | 02/2023 |
9815 | 2^338497-17041 | 101898 | Enzo Doria | 05/2013 |
9813 | 2^338497+150405 | 101898 | Stefano Morozzi | 11/2021 |
9814 | 2^338495+100533 | 101898 | Stefano Morozzi | 12/2021 |
9816 | 2^338494+36057 | 101897 | Stefano Morozzi | 03/2022 |
9817 | 2^338492+39015 | 101897 | Stefano Morozzi | 05/2022 |
9818 | 2^338494+168007 | 101897 | Stefano Morozzi | 09/2022 |
9819 | 2^338490+61149 | 101896 | Stefano Morozzi | 03/2022 |
9820 | 2^338489+161369 | 101896 | Stefano Morozzi | 04/2022 |
9821 | 2^338491+22961 | 101896 | Stefano Morozzi | 11/2022 |
9822 | 2^338487-3555 | 101895 | Stefano Morozzi | 01/2022 |
9823 | 2^338487-183129 | 101895 | Stefano Morozzi | 04/2022 |
9824 | 2^338484+128767 | 101894 | Stefano Morozzi | 01/2022 |
9825 | 2^338484-31895 | 101894 | Stefano Morozzi | 03/2022 |
9826 | 2^338483-67899 | 101894 | Stefano Morozzi | 02/2023 |
9827 | 2^338483-192129 | 101894 | Stefano Morozzi | 02/2023 |
9828 | 2^338478+10893 | 101893 | Stefano Morozzi | 03/2022 |
9829 | 2^338479+87243 | 101893 | Stefano Morozzi | 04/2022 |
9830 | 2^338479+167619 | 101893 | Stefano Morozzi | 09/2022 |
9831 | 2^338480+197503 | 101893 | Stefano Morozzi | 11/2022 |
9832 | 2^338481-11421 | 101893 | Stefano Morozzi | 12/2022 |
9833 | 2^338479-89649 | 101893 | Stefano Morozzi | 01/2023 |
9834 | (29*34^66532-12833)/33 | 101893 | Eric Chen | 03/2023 |
9837 | 2^338475+54615 | 101892 | Lelio R Paula | 10/2016 |
9835 | 2^338475-59775 | 101892 | Stefano Morozzi | 04/2022 |
9836 | 2^338476-134237 | 101892 | Stefano Morozzi | 04/2022 |
9838 | 2^338474+100767 | 101891 | Stefano Morozzi | 11/2021 |
9839 | 2^338474+81165 | 101891 | Stefano Morozzi | 01/2022 |
9840 | 2^338474+41137 | 101891 | Stefano Morozzi | 06/2022 |
9841 | 2^338472-110445 | 101891 | Stefano Morozzi | 06/2022 |
9842 | 2^338473-89535 | 101891 | Stefano Morozzi | 01/2023 |
9843 | 2^338470+27777 | 101890 | Stefano Morozzi | 01/2022 |
9844 | 2^338468+31351 | 101890 | Stefano Morozzi | 01/2022 |
9845 | 2^338469-106339 | 101890 | Stefano Morozzi | 03/2022 |
9846 | 2^338471+187469 | 101890 | Stefano Morozzi | 04/2022 |
9847 | 2^338468+96613 | 101890 | Stefano Morozzi | 11/2022 |
9848 | 2^338469+46167 | 101890 | Stefano Morozzi | 11/2022 |
9849 | 2^338470+71527 | 101890 | Stefano Morozzi | 11/2022 |
9850 | 2^338469-112783 | 101890 | Stefano Morozzi | 12/2022 |
9851 | 2^338470-115665 | 101890 | Stefano Morozzi | 01/2023 |
9852 | 2^338467-25665 | 101889 | Stefano Morozzi | 12/2021 |
9853 | 2^338465+152139 | 101889 | Stefano Morozzi | 12/2021 |
9854 | 2^338466-28643 | 101889 | Stefano Morozzi | 01/2022 |
9855 | 2^338465+181517 | 101889 | Stefano Morozzi | 01/2022 |
9856 | 2^338466+115917 | 101889 | Stefano Morozzi | 06/2022 |
9857 | 2^338465-88291 | 101889 | Stefano Morozzi | 12/2022 |
9858 | 2^338464-104009 | 101888 | Stefano Morozzi | 02/2022 |
9859 | 2^338463+185169 | 101888 | Stefano Morozzi | 03/2022 |
9860 | 2^338464+60595 | 101888 | Stefano Morozzi | 03/2022 |
9861 | 2^338464-66377 | 101888 | Stefano Morozzi | 01/2023 |
9862 | 2^338458+60273 | 101887 | Stefano Morozzi | 03/2022 |
9863 | 2^338461+135867 | 101887 | Stefano Morozzi | 03/2022 |
9864 | 2^338455-4621 | 101886 | Stefano Morozzi | 02/2022 |
9865 | 2^338457+187827 | 101886 | Stefano Morozzi | 04/2022 |
9866 | 2^338455+173349 | 101886 | Stefano Morozzi | 11/2022 |
9867 | 2^338454+133737 | 101885 | Stefano Morozzi | 03/2022 |
9868 | 2^338454-158501 | 101885 | Stefano Morozzi | 04/2022 |
9869 | 2^338454-184217 | 101885 | Stefano Morozzi | 04/2022 |
9870 | 2^338453+164451 | 101885 | Stefano Morozzi | 05/2022 |
9871 | 2^338452-136137 | 101885 | Stefano Morozzi | 12/2022 |
9872 | 2^338450+106275 | 101884 | Stefano Morozzi | 01/2022 |
9873 | 2^338450+168439 | 101884 | Stefano Morozzi | 09/2022 |
9874 | (133*10^101881+17)/3 | 101883 | Robert Price | 11/2021 |
9875 | 2^338445-80461 | 101883 | Stefano Morozzi | 02/2022 |
9876 | 2^338446-131211 | 101883 | Stefano Morozzi | 02/2022 |
9877 | 2^338448+187167 | 101883 | Stefano Morozzi | 04/2022 |
9878 | 2^338446-160115 | 101883 | Stefano Morozzi | 06/2022 |
9879 | 2^338447-164157 | 101883 | Stefano Morozzi | 01/2023 |
9880 | 2^338447-191001 | 101883 | Stefano Morozzi | 01/2023 |
9881 | 2^338444+127623 | 101882 | Stefano Morozzi | 12/2021 |
9882 | 2^338443-113827 | 101882 | Stefano Morozzi | 12/2022 |
9883 | 2^338441-5893 | 101881 | Stefano Morozzi | 02/2022 |
9884 | 2^338439-162565 | 101881 | Stefano Morozzi | 12/2022 |
9885 | 2^338436+153657 | 101880 | Stefano Morozzi | 01/2022 |
9886 | 2^338437-153159 | 101880 | Stefano Morozzi | 01/2022 |
9887 | 2^338436-83783 | 101880 | Stefano Morozzi | 04/2022 |
9888 | 2^338435+89109 | 101880 | Stefano Morozzi | 05/2022 |
9889 | 2^338435+13871 | 101880 | Stefano Morozzi | 05/2022 |
9890 | 2^338436+149691 | 101880 | Stefano Morozzi | 02/2023 |
9891 | 2^338434+81537 | 101879 | Stefano Morozzi | 01/2022 |
9892 | 2^338432+33495 | 101879 | Stefano Morozzi | 03/2022 |
9893 | 2^338432-7043 | 101879 | Stefano Morozzi | 03/2022 |
9894 | 2^338433-32629 | 101879 | Stefano Morozzi | 03/2022 |
9895 | 2^338430-9903 | 101878 | Stefano Morozzi | 04/2022 |
9903 | 2^338426-19797 | 101877 | Enzo Doria | 06/2013 |
9896 | 2^338427-77797 | 101877 | Stefano Morozzi | 01/2022 |
9897 | 2^338427-178687 | 101877 | Stefano Morozzi | 01/2022 |
9898 | 2^338428-54873 | 101877 | Stefano Morozzi | 02/2022 |
9899 | 2^338425+41357 | 101877 | Stefano Morozzi | 06/2022 |
9900 | 2^338428+90855 | 101877 | Stefano Morozzi | 06/2022 |
9901 | 2^338428-39807 | 101877 | Stefano Morozzi | 01/2023 |
9902 | 2^338425-192381 | 101877 | Stefano Morozzi | 02/2023 |
9904 | 2^338422-188787 | 101876 | Stefano Morozzi | 12/2022 |
9905 | 2^338423-187755 | 101876 | Stefano Morozzi | 12/2022 |
9906 | 2^338422-115865 | 101876 | Stefano Morozzi | 01/2023 |
9907 | 2^338420-178829 | 101875 | Stefano Morozzi | 01/2022 |
9908 | 2^338421-105423 | 101875 | Stefano Morozzi | 02/2022 |
9909 | 2^338419-82761 | 101875 | Stefano Morozzi | 03/2022 |
9910 | 2^338420+193143 | 101875 | Stefano Morozzi | 09/2022 |
9911 | 2^338419+199641 | 101875 | Stefano Morozzi | 02/2023 |
9912 | 2^338420-143103 | 101875 | Stefano Morozzi | 02/2023 |
9913 | 2^338418-50903 | 101874 | Stefano Morozzi | 12/2021 |
9914 | 2^338418+158355 | 101874 | Stefano Morozzi | 02/2022 |
9915 | 2^338418+159339 | 101874 | Stefano Morozzi | 03/2022 |
9916 | 2^338416+14953 | 101874 | Stefano Morozzi | 05/2022 |
9917 | 2^338416+166051 | 101874 | Stefano Morozzi | 06/2022 |
9918 | 2^338418-138765 | 101874 | Stefano Morozzi | 12/2022 |
9919 | 2^338417+49737 | 101874 | Stefano Morozzi | 02/2023 |
9920 | 2^338413-125919 | 101873 | Stefano Morozzi | 12/2021 |
9921 | 2^338414+26083 | 101873 | Stefano Morozzi | 12/2021 |
9922 | 2^338412-152379 | 101873 | Stefano Morozzi | 12/2021 |
9923 | 2^338413+54797 | 101873 | Stefano Morozzi | 01/2022 |
9924 | 2^338412+157951 | 101873 | Stefano Morozzi | 02/2022 |
9925 | 2^338414+81627 | 101873 | Stefano Morozzi | 02/2022 |
9926 | 2^338413+133679 | 101873 | Stefano Morozzi | 03/2022 |
9927 | 2^338413+197735 | 101873 | Stefano Morozzi | 11/2022 |
9928 | 2^338413-114301 | 101873 | Stefano Morozzi | 01/2023 |
9929 | 11*32^67682+395 | 101873 | Eric Chen | 04/2023 |
9930 | 2^338409-52183 | 101872 | Stefano Morozzi | 12/2021 |
9931 | 2^338411-3789 | 101872 | Stefano Morozzi | 01/2022 |
9932 | 2^338409+173237 | 101872 | Stefano Morozzi | 11/2022 |
9933 | 2^338406-184175 | 101871 | Stefano Morozzi | 04/2022 |
9934 | 2^338405+94451 | 101871 | Stefano Morozzi | 09/2022 |
9935 | 2^338406-161217 | 101871 | Stefano Morozzi | 12/2022 |
9936 | 2^338406+199929 | 101871 | Stefano Morozzi | 02/2023 |
9937 | 2^338404+55717 | 101870 | Stefano Morozzi | 01/2022 |
9938 | 2^338403+36261 | 101870 | Stefano Morozzi | 04/2022 |
9939 | 2^338402-34431 | 101870 | Stefano Morozzi | 04/2022 |
9940 | 2^338404-159215 | 101870 | Stefano Morozzi | 04/2022 |
9941 | 2^338403+18363 | 101870 | Stefano Morozzi | 09/2022 |
9942 | 2^338403+170235 | 101870 | Stefano Morozzi | 11/2022 |
9943 | 2^338399+23045 | 101869 | Stefano Morozzi | 11/2022 |
9944 | 2^338399-65535 | 101869 | Stefano Morozzi | 01/2023 |
9945 | 2^338395-127449 | 101868 | Stefano Morozzi | 12/2021 |
9946 | 2^338398-127637 | 101868 | Stefano Morozzi | 01/2022 |
9947 | 2^338398-166533 | 101868 | Stefano Morozzi | 01/2023 |
9948 | 2^338394+100317 | 101867 | Stefano Morozzi | 11/2021 |
9949 | 2^338393-152749 | 101867 | Stefano Morozzi | 01/2022 |
9950 | 2^338393+163025 | 101867 | Stefano Morozzi | 04/2022 |
9951 | 2^338393+89229 | 101867 | Stefano Morozzi | 05/2022 |
9952 | 2^338393+99647 | 101867 | Stefano Morozzi | 02/2023 |
9953 | 2^338394-192471 | 101867 | Stefano Morozzi | 02/2023 |
9954 | 2^338390+76627 | 101866 | Stefano Morozzi | 12/2021 |
9955 | 2^338389-85081 | 101866 | Stefano Morozzi | 06/2022 |
9956 | 2^338390+148113 | 101866 | Stefano Morozzi | 11/2022 |
9957 | 2^338389-14253 | 101866 | Stefano Morozzi | 01/2023 |
9958 | 2^338390-114297 | 101866 | Stefano Morozzi | 01/2023 |
9959 | 2^338391-64225 | 101866 | Stefano Morozzi | 01/2023 |
9960 | 2^338389-16971 | 101866 | Stefano Morozzi | 02/2023 |
9961 | 2^338387-75685 | 101865 | Stefano Morozzi | 12/2021 |
9962 | 2^338388-53459 | 101865 | Stefano Morozzi | 01/2022 |
9963 | 2^338388-36575 | 101865 | Stefano Morozzi | 12/2022 |
9964 | 2^338385-190311 | 101865 | Stefano Morozzi | 01/2023 |
9965 | 2^338384+131563 | 101864 | Stefano Morozzi | 01/2022 |
9966 | 2^338382+109069 | 101864 | Stefano Morozzi | 03/2022 |
9967 | 2^338384+168987 | 101864 | Stefano Morozzi | 09/2022 |
9968 | 2^338383-42367 | 101864 | Stefano Morozzi | 02/2023 |
9969 | 2^338380+77125 | 101863 | Stefano Morozzi | 12/2021 |
9970 | 2^338381-35539 | 101863 | Stefano Morozzi | 06/2022 |
9971 | 2^338378-125841 | 101862 | Stefano Morozzi | 12/2021 |
9972 | 2^338375+27815 | 101862 | Stefano Morozzi | 01/2022 |
9973 | 2^338375-28509 | 101862 | Stefano Morozzi | 01/2022 |
9974 | 2^338375+29985 | 101862 | Stefano Morozzi | 01/2022 |
9975 | 2^338377+157881 | 101862 | Stefano Morozzi | 02/2022 |
9976 | 2^338375+59589 | 101862 | Stefano Morozzi | 03/2022 |
9977 | 2^338378+36399 | 101862 | Stefano Morozzi | 04/2022 |
9978 | 2^338378-159773 | 101862 | Stefano Morozzi | 04/2022 |
9979 | 2^338378+14883 | 101862 | Stefano Morozzi | 05/2022 |
9980 | 2^338376+140173 | 101862 | Stefano Morozzi | 06/2022 |
9981 | 2^338375+18761 | 101862 | Stefano Morozzi | 09/2022 |
9982 | 2^338373-75103 | 101861 | Stefano Morozzi | 12/2021 |
9983 | 2^338372+128877 | 101861 | Stefano Morozzi | 01/2022 |
9984 | 2^338374-28731 | 101861 | Stefano Morozzi | 01/2022 |
9985 | 2^338374-128427 | 101861 | Stefano Morozzi | 01/2022 |
9986 | 2^338372+37875 | 101861 | Stefano Morozzi | 04/2022 |
9987 | 2^338373+161541 | 101861 | Stefano Morozzi | 04/2022 |
9988 | 2^338374+37759 | 101861 | Stefano Morozzi | 04/2022 |
9989 | 2^338372+93235 | 101861 | Stefano Morozzi | 09/2022 |
9990 | 2^338373-63273 | 101861 | Stefano Morozzi | 12/2022 |
9991 | 2^338369+29427 | 101860 | Stefano Morozzi | 01/2022 |
9992 | 2^338370+179133 | 101860 | Stefano Morozzi | 01/2022 |
9993 | 2^338369+131501 | 101860 | Stefano Morozzi | 01/2022 |
9994 | 2^338369+181649 | 101860 | Stefano Morozzi | 02/2022 |
9995 | 2^338370-4787 | 101860 | Stefano Morozzi | 02/2022 |
9996 | 2^338371-133491 | 101860 | Stefano Morozzi | 04/2022 |
9997 | 2^338371+42023 | 101860 | Stefano Morozzi | 09/2022 |
9998 | 2^338371+145323 | 101860 | Stefano Morozzi | 11/2022 |
9999 | 2^338371-138145 | 101860 | Stefano Morozzi | 12/2022 |
10000 | 2^338366+53853 | 101859 | Stefano Morozzi | 01/2022 |