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 ? |
7001 | 2^338518+114633 | 101905 | Stefano Morozzi | 05/2022 |
7002 | 2^338518-12621 | 101905 | Stefano Morozzi | 12/2022 |
7003 | 2^338518-187325 | 101905 | Stefano Morozzi | 12/2022 |
7011 | (9*2^338520+1)/365 | 101904 | Lelio R Paula | 12/2013 |
7004 | 2^338517-125955 | 101904 | Stefano Morozzi | 12/2021 |
7005 | 2^338517+126437 | 101904 | Stefano Morozzi | 12/2021 |
7006 | 2^338517-53499 | 101904 | Stefano Morozzi | 01/2022 |
7007 | 2^338515+30369 | 101904 | Stefano Morozzi | 01/2022 |
7008 | 2^338517-184623 | 101904 | Stefano Morozzi | 04/2022 |
7009 | 2^338515+89333 | 101904 | Stefano Morozzi | 05/2022 |
7010 | 2^338515+198813 | 101904 | Stefano Morozzi | 02/2023 |
7014 | 24502^14419+14419^24502 | 101903 | Hans Havermann | 01/2019 |
7012 | 2^338512-827 | 101903 | Stefano Morozzi | 12/2021 |
7013 | 2^338514-6611 | 101903 | Stefano Morozzi | 03/2022 |
7015 | 2^338509+5139 | 101902 | Stefano Morozzi | 01/2022 |
7016 | 2^338509+40205 | 101902 | Stefano Morozzi | 06/2022 |
7017 | 2^338511+19959 | 101902 | Stefano Morozzi | 09/2022 |
7018 | 2^338510-37877 | 101902 | Stefano Morozzi | 12/2022 |
7019 | 2^338507-188655 | 101901 | Stefano Morozzi | 12/2022 |
7020 | 2^338507-114457 | 101901 | Stefano Morozzi | 01/2023 |
7021 | 2^338504-152615 | 101900 | Stefano Morozzi | 01/2022 |
7022 | 2^338502-4587 | 101900 | Stefano Morozzi | 02/2022 |
7023 | 2^338502-166275 | 101900 | Stefano Morozzi | 01/2023 |
7024 | 2^338500-26865 | 101899 | Stefano Morozzi | 12/2021 |
7025 | 2^338501-177471 | 101899 | Stefano Morozzi | 12/2021 |
7026 | 2^338499-3915 | 101899 | Stefano Morozzi | 01/2022 |
7027 | 2^338501+32051 | 101899 | Stefano Morozzi | 02/2022 |
7028 | 2^338499+183533 | 101899 | Stefano Morozzi | 03/2022 |
7029 | 2^338500+35625 | 101899 | Stefano Morozzi | 03/2022 |
7030 | 2^338499+87579 | 101899 | Stefano Morozzi | 04/2022 |
7031 | 2^338498-117683 | 101899 | Stefano Morozzi | 02/2023 |
7034 | 2^338497-17041 | 101898 | Enzo Doria | 05/2013 |
7032 | 2^338497+150405 | 101898 | Stefano Morozzi | 11/2021 |
7033 | 2^338495+100533 | 101898 | Stefano Morozzi | 12/2021 |
7035 | 2^338494+36057 | 101897 | Stefano Morozzi | 03/2022 |
7036 | 2^338492+39015 | 101897 | Stefano Morozzi | 05/2022 |
7037 | 2^338494+168007 | 101897 | Stefano Morozzi | 09/2022 |
7038 | 2^338490+61149 | 101896 | Stefano Morozzi | 03/2022 |
7039 | 2^338489+161369 | 101896 | Stefano Morozzi | 04/2022 |
7040 | 2^338491+22961 | 101896 | Stefano Morozzi | 11/2022 |
7041 | 2^338487-3555 | 101895 | Stefano Morozzi | 01/2022 |
7042 | 2^338487-183129 | 101895 | Stefano Morozzi | 04/2022 |
7043 | 2^338484+128767 | 101894 | Stefano Morozzi | 01/2022 |
7044 | 2^338484-31895 | 101894 | Stefano Morozzi | 03/2022 |
7045 | 2^338483-67899 | 101894 | Stefano Morozzi | 02/2023 |
7046 | 2^338483-192129 | 101894 | Stefano Morozzi | 02/2023 |
7047 | 2^338478+10893 | 101893 | Stefano Morozzi | 03/2022 |
7048 | 2^338479+87243 | 101893 | Stefano Morozzi | 04/2022 |
7049 | 2^338479+167619 | 101893 | Stefano Morozzi | 09/2022 |
7050 | 2^338480+197503 | 101893 | Stefano Morozzi | 11/2022 |
7051 | 2^338481-11421 | 101893 | Stefano Morozzi | 12/2022 |
7052 | 2^338479-89649 | 101893 | Stefano Morozzi | 01/2023 |
7053 | (29*34^66532-12833)/33 | 101893 | Eric Chen | 03/2023 |
7056 | 2^338475+54615 | 101892 | Lelio R Paula | 10/2016 |
7054 | 2^338475-59775 | 101892 | Stefano Morozzi | 04/2022 |
7055 | 2^338476-134237 | 101892 | Stefano Morozzi | 04/2022 |
7057 | 2^338474+100767 | 101891 | Stefano Morozzi | 11/2021 |
7058 | 2^338474+81165 | 101891 | Stefano Morozzi | 01/2022 |
7059 | 2^338474+41137 | 101891 | Stefano Morozzi | 06/2022 |
7060 | 2^338472-110445 | 101891 | Stefano Morozzi | 06/2022 |
7061 | 2^338473-89535 | 101891 | Stefano Morozzi | 01/2023 |
7062 | 2^338470+27777 | 101890 | Stefano Morozzi | 01/2022 |
7063 | 2^338468+31351 | 101890 | Stefano Morozzi | 01/2022 |
7064 | 2^338469-106339 | 101890 | Stefano Morozzi | 03/2022 |
7065 | 2^338471+187469 | 101890 | Stefano Morozzi | 04/2022 |
7066 | 2^338468+96613 | 101890 | Stefano Morozzi | 11/2022 |
7067 | 2^338469+46167 | 101890 | Stefano Morozzi | 11/2022 |
7068 | 2^338470+71527 | 101890 | Stefano Morozzi | 11/2022 |
7069 | 2^338469-112783 | 101890 | Stefano Morozzi | 12/2022 |
7070 | 2^338470-115665 | 101890 | Stefano Morozzi | 01/2023 |
7071 | 2^338467-25665 | 101889 | Stefano Morozzi | 12/2021 |
7072 | 2^338465+152139 | 101889 | Stefano Morozzi | 12/2021 |
7073 | 2^338466-28643 | 101889 | Stefano Morozzi | 01/2022 |
7074 | 2^338465+181517 | 101889 | Stefano Morozzi | 01/2022 |
7075 | 2^338466+115917 | 101889 | Stefano Morozzi | 06/2022 |
7076 | 2^338465-88291 | 101889 | Stefano Morozzi | 12/2022 |
7077 | 2^338464-104009 | 101888 | Stefano Morozzi | 02/2022 |
7078 | 2^338463+185169 | 101888 | Stefano Morozzi | 03/2022 |
7079 | 2^338464+60595 | 101888 | Stefano Morozzi | 03/2022 |
7080 | 2^338464-66377 | 101888 | Stefano Morozzi | 01/2023 |
7081 | 2^338458+60273 | 101887 | Stefano Morozzi | 03/2022 |
7082 | 2^338461+135867 | 101887 | Stefano Morozzi | 03/2022 |
7083 | 2^338455-4621 | 101886 | Stefano Morozzi | 02/2022 |
7084 | 2^338457+187827 | 101886 | Stefano Morozzi | 04/2022 |
7085 | 2^338455+173349 | 101886 | Stefano Morozzi | 11/2022 |
7086 | 2^338454+133737 | 101885 | Stefano Morozzi | 03/2022 |
7087 | 2^338454-158501 | 101885 | Stefano Morozzi | 04/2022 |
7088 | 2^338454-184217 | 101885 | Stefano Morozzi | 04/2022 |
7089 | 2^338453+164451 | 101885 | Stefano Morozzi | 05/2022 |
7090 | 2^338452-136137 | 101885 | Stefano Morozzi | 12/2022 |
7091 | 2^338450+106275 | 101884 | Stefano Morozzi | 01/2022 |
7092 | 2^338450+168439 | 101884 | Stefano Morozzi | 09/2022 |
7093 | (133*10^101881+17)/3 | 101883 | Robert Price | 11/2021 |
7094 | 2^338445-80461 | 101883 | Stefano Morozzi | 02/2022 |
7095 | 2^338446-131211 | 101883 | Stefano Morozzi | 02/2022 |
7096 | 2^338448+187167 | 101883 | Stefano Morozzi | 04/2022 |
7097 | 2^338446-160115 | 101883 | Stefano Morozzi | 06/2022 |
7098 | 2^338447-164157 | 101883 | Stefano Morozzi | 01/2023 |
7099 | 2^338447-191001 | 101883 | Stefano Morozzi | 01/2023 |
7100 | 2^338444+127623 | 101882 | Stefano Morozzi | 12/2021 |
7101 | 2^338443-113827 | 101882 | Stefano Morozzi | 12/2022 |
7102 | 2^338441-5893 | 101881 | Stefano Morozzi | 02/2022 |
7103 | 2^338439-162565 | 101881 | Stefano Morozzi | 12/2022 |
7104 | 2^338436+153657 | 101880 | Stefano Morozzi | 01/2022 |
7105 | 2^338437-153159 | 101880 | Stefano Morozzi | 01/2022 |
7106 | 2^338436-83783 | 101880 | Stefano Morozzi | 04/2022 |
7107 | 2^338435+89109 | 101880 | Stefano Morozzi | 05/2022 |
7108 | 2^338435+13871 | 101880 | Stefano Morozzi | 05/2022 |
7109 | 2^338436+149691 | 101880 | Stefano Morozzi | 02/2023 |
7110 | 2^338434+81537 | 101879 | Stefano Morozzi | 01/2022 |
7111 | 2^338432+33495 | 101879 | Stefano Morozzi | 03/2022 |
7112 | 2^338432-7043 | 101879 | Stefano Morozzi | 03/2022 |
7113 | 2^338433-32629 | 101879 | Stefano Morozzi | 03/2022 |
7114 | 2^338430-9903 | 101878 | Stefano Morozzi | 04/2022 |
7122 | 2^338426-19797 | 101877 | Enzo Doria | 06/2013 |
7115 | 2^338427-77797 | 101877 | Stefano Morozzi | 01/2022 |
7116 | 2^338427-178687 | 101877 | Stefano Morozzi | 01/2022 |
7117 | 2^338428-54873 | 101877 | Stefano Morozzi | 02/2022 |
7118 | 2^338425+41357 | 101877 | Stefano Morozzi | 06/2022 |
7119 | 2^338428+90855 | 101877 | Stefano Morozzi | 06/2022 |
7120 | 2^338428-39807 | 101877 | Stefano Morozzi | 01/2023 |
7121 | 2^338425-192381 | 101877 | Stefano Morozzi | 02/2023 |
7123 | 2^338422-188787 | 101876 | Stefano Morozzi | 12/2022 |
7124 | 2^338423-187755 | 101876 | Stefano Morozzi | 12/2022 |
7125 | 2^338422-115865 | 101876 | Stefano Morozzi | 01/2023 |
7126 | 2^338420-178829 | 101875 | Stefano Morozzi | 01/2022 |
7127 | 2^338421-105423 | 101875 | Stefano Morozzi | 02/2022 |
7128 | 2^338419-82761 | 101875 | Stefano Morozzi | 03/2022 |
7129 | 2^338420+193143 | 101875 | Stefano Morozzi | 09/2022 |
7130 | 2^338419+199641 | 101875 | Stefano Morozzi | 02/2023 |
7131 | 2^338420-143103 | 101875 | Stefano Morozzi | 02/2023 |
7132 | 2^338418-50903 | 101874 | Stefano Morozzi | 12/2021 |
7133 | 2^338418+158355 | 101874 | Stefano Morozzi | 02/2022 |
7134 | 2^338418+159339 | 101874 | Stefano Morozzi | 03/2022 |
7135 | 2^338416+14953 | 101874 | Stefano Morozzi | 05/2022 |
7136 | 2^338416+166051 | 101874 | Stefano Morozzi | 06/2022 |
7137 | 2^338418-138765 | 101874 | Stefano Morozzi | 12/2022 |
7138 | 2^338417+49737 | 101874 | Stefano Morozzi | 02/2023 |
7139 | 2^338413-125919 | 101873 | Stefano Morozzi | 12/2021 |
7140 | 2^338414+26083 | 101873 | Stefano Morozzi | 12/2021 |
7141 | 2^338412-152379 | 101873 | Stefano Morozzi | 12/2021 |
7142 | 2^338413+54797 | 101873 | Stefano Morozzi | 01/2022 |
7143 | 2^338412+157951 | 101873 | Stefano Morozzi | 02/2022 |
7144 | 2^338414+81627 | 101873 | Stefano Morozzi | 02/2022 |
7145 | 2^338413+133679 | 101873 | Stefano Morozzi | 03/2022 |
7146 | 2^338413+197735 | 101873 | Stefano Morozzi | 11/2022 |
7147 | 2^338413-114301 | 101873 | Stefano Morozzi | 01/2023 |
7148 | 2^338409-52183 | 101872 | Stefano Morozzi | 12/2021 |
7149 | 2^338411-3789 | 101872 | Stefano Morozzi | 01/2022 |
7150 | 2^338409+173237 | 101872 | Stefano Morozzi | 11/2022 |
7151 | 2^338406-184175 | 101871 | Stefano Morozzi | 04/2022 |
7152 | 2^338405+94451 | 101871 | Stefano Morozzi | 09/2022 |
7153 | 2^338406-161217 | 101871 | Stefano Morozzi | 12/2022 |
7154 | 2^338406+199929 | 101871 | Stefano Morozzi | 02/2023 |
7155 | 2^338404+55717 | 101870 | Stefano Morozzi | 01/2022 |
7156 | 2^338403+36261 | 101870 | Stefano Morozzi | 04/2022 |
7157 | 2^338402-34431 | 101870 | Stefano Morozzi | 04/2022 |
7158 | 2^338404-159215 | 101870 | Stefano Morozzi | 04/2022 |
7159 | 2^338403+18363 | 101870 | Stefano Morozzi | 09/2022 |
7160 | 2^338403+170235 | 101870 | Stefano Morozzi | 11/2022 |
7161 | 2^338399+23045 | 101869 | Stefano Morozzi | 11/2022 |
7162 | 2^338399-65535 | 101869 | Stefano Morozzi | 01/2023 |
7163 | 2^338395-127449 | 101868 | Stefano Morozzi | 12/2021 |
7164 | 2^338398-127637 | 101868 | Stefano Morozzi | 01/2022 |
7165 | 2^338398-166533 | 101868 | Stefano Morozzi | 01/2023 |
7166 | 2^338394+100317 | 101867 | Stefano Morozzi | 11/2021 |
7167 | 2^338393-152749 | 101867 | Stefano Morozzi | 01/2022 |
7168 | 2^338393+163025 | 101867 | Stefano Morozzi | 04/2022 |
7169 | 2^338393+89229 | 101867 | Stefano Morozzi | 05/2022 |
7170 | 2^338393+99647 | 101867 | Stefano Morozzi | 02/2023 |
7171 | 2^338394-192471 | 101867 | Stefano Morozzi | 02/2023 |
7172 | 2^338390+76627 | 101866 | Stefano Morozzi | 12/2021 |
7173 | 2^338389-85081 | 101866 | Stefano Morozzi | 06/2022 |
7174 | 2^338390+148113 | 101866 | Stefano Morozzi | 11/2022 |
7175 | 2^338389-14253 | 101866 | Stefano Morozzi | 01/2023 |
7176 | 2^338390-114297 | 101866 | Stefano Morozzi | 01/2023 |
7177 | 2^338391-64225 | 101866 | Stefano Morozzi | 01/2023 |
7178 | 2^338389-16971 | 101866 | Stefano Morozzi | 02/2023 |
7179 | 2^338387-75685 | 101865 | Stefano Morozzi | 12/2021 |
7180 | 2^338388-53459 | 101865 | Stefano Morozzi | 01/2022 |
7181 | 2^338388-36575 | 101865 | Stefano Morozzi | 12/2022 |
7182 | 2^338385-190311 | 101865 | Stefano Morozzi | 01/2023 |
7183 | 2^338384+131563 | 101864 | Stefano Morozzi | 01/2022 |
7184 | 2^338382+109069 | 101864 | Stefano Morozzi | 03/2022 |
7185 | 2^338384+168987 | 101864 | Stefano Morozzi | 09/2022 |
7186 | 2^338383-42367 | 101864 | Stefano Morozzi | 02/2023 |
7187 | 2^338380+77125 | 101863 | Stefano Morozzi | 12/2021 |
7188 | 2^338381-35539 | 101863 | Stefano Morozzi | 06/2022 |
7189 | 2^338378-125841 | 101862 | Stefano Morozzi | 12/2021 |
7190 | 2^338375+27815 | 101862 | Stefano Morozzi | 01/2022 |
7191 | 2^338375-28509 | 101862 | Stefano Morozzi | 01/2022 |
7192 | 2^338375+29985 | 101862 | Stefano Morozzi | 01/2022 |
7193 | 2^338377+157881 | 101862 | Stefano Morozzi | 02/2022 |
7194 | 2^338375+59589 | 101862 | Stefano Morozzi | 03/2022 |
7195 | 2^338378+36399 | 101862 | Stefano Morozzi | 04/2022 |
7196 | 2^338378-159773 | 101862 | Stefano Morozzi | 04/2022 |
7197 | 2^338378+14883 | 101862 | Stefano Morozzi | 05/2022 |
7198 | 2^338376+140173 | 101862 | Stefano Morozzi | 06/2022 |
7199 | 2^338375+18761 | 101862 | Stefano Morozzi | 09/2022 |
7200 | 2^338373-75103 | 101861 | Stefano Morozzi | 12/2021 |
7201 | 2^338372+128877 | 101861 | Stefano Morozzi | 01/2022 |
7202 | 2^338374-28731 | 101861 | Stefano Morozzi | 01/2022 |
7203 | 2^338374-128427 | 101861 | Stefano Morozzi | 01/2022 |
7204 | 2^338372+37875 | 101861 | Stefano Morozzi | 04/2022 |
7205 | 2^338373+161541 | 101861 | Stefano Morozzi | 04/2022 |
7206 | 2^338374+37759 | 101861 | Stefano Morozzi | 04/2022 |
7207 | 2^338372+93235 | 101861 | Stefano Morozzi | 09/2022 |
7208 | 2^338373-63273 | 101861 | Stefano Morozzi | 12/2022 |
7209 | 2^338369+29427 | 101860 | Stefano Morozzi | 01/2022 |
7210 | 2^338370+179133 | 101860 | Stefano Morozzi | 01/2022 |
7211 | 2^338369+131501 | 101860 | Stefano Morozzi | 01/2022 |
7212 | 2^338369+181649 | 101860 | Stefano Morozzi | 02/2022 |
7213 | 2^338370-4787 | 101860 | Stefano Morozzi | 02/2022 |
7214 | 2^338371-133491 | 101860 | Stefano Morozzi | 04/2022 |
7215 | 2^338371+42023 | 101860 | Stefano Morozzi | 09/2022 |
7216 | 2^338371+145323 | 101860 | Stefano Morozzi | 11/2022 |
7217 | 2^338371-138145 | 101860 | Stefano Morozzi | 12/2022 |
7224 | 2^338368-20369 | 101859 | Enzo Doria | 06/2013 |
7225 | 2^338366+74179 | 101859 | Enzo Doria | 04/2016 |
7218 | 2^338366+53853 | 101859 | Stefano Morozzi | 01/2022 |
7219 | 2^338365-31665 | 101859 | Stefano Morozzi | 03/2022 |
7220 | 2^338368-156345 | 101859 | Stefano Morozzi | 03/2022 |
7221 | 2^338366-159867 | 101859 | Stefano Morozzi | 04/2022 |
7222 | 2^338368-63509 | 101859 | Stefano Morozzi | 12/2022 |
7223 | 2^338365-190975 | 101859 | Stefano Morozzi | 01/2023 |
7226 | 2^338362-180845 | 101858 | Stefano Morozzi | 02/2022 |
7227 | 2^338364-155769 | 101858 | Stefano Morozzi | 02/2022 |
7228 | 2^338362+142843 | 101858 | Stefano Morozzi | 09/2022 |
7229 | 2^338362+170019 | 101858 | Stefano Morozzi | 11/2022 |
7230 | 2^338361-100875 | 101857 | Stefano Morozzi | 12/2021 |
7231 | 2^338361+154169 | 101857 | Stefano Morozzi | 01/2022 |
7232 | 2^338359-189645 | 101857 | Stefano Morozzi | 01/2023 |
7233 | 2^338356+101271 | 101856 | Stefano Morozzi | 12/2021 |
7234 | 2^338356+53383 | 101856 | Stefano Morozzi | 01/2022 |
7235 | 2^338355+59393 | 101856 | Stefano Morozzi | 03/2022 |
7236 | 2^338356+60775 | 101856 | Stefano Morozzi | 03/2022 |
7237 | 2^338356-106257 | 101856 | Stefano Morozzi | 03/2022 |
7238 | 2^338357-58921 | 101856 | Stefano Morozzi | 04/2022 |
7239 | 2^338356+94605 | 101856 | Stefano Morozzi | 09/2022 |
7240 | 2^338356+117813 | 101856 | Stefano Morozzi | 09/2022 |
7241 | 2^338358-38475 | 101856 | Stefano Morozzi | 12/2022 |
7242 | 2^338353-190291 | 101855 | Stefano Morozzi | 01/2023 |
7243 | 2^338350-152933 | 101854 | Stefano Morozzi | 01/2022 |
7244 | 2^338350+6337 | 101854 | Stefano Morozzi | 01/2022 |
7245 | 2^338350+168759 | 101854 | Stefano Morozzi | 09/2022 |
7248 | 27088^5755+5755^27088 | 101853 | Hans Havermann | 01/2019 |
7246 | 2^338347+125901 | 101853 | Stefano Morozzi | 11/2021 |
7247 | 2^338346-10643 | 101853 | Stefano Morozzi | 06/2022 |
7249 | 2^338343+152271 | 101852 | Stefano Morozzi | 12/2021 |
7250 | 2^338345+154107 | 101852 | Stefano Morozzi | 01/2022 |