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 ? |
6001 | 2^338936+84147 | 102030 | Stefano Morozzi | 03/2022 |
6002 | 2^338931+2349 | 102029 | Stefano Morozzi | 12/2021 |
6003 | 2^338933+79935 | 102029 | Stefano Morozzi | 01/2022 |
6004 | 2^338930+33819 | 102029 | Stefano Morozzi | 03/2022 |
6005 | 2^338931-31555 | 102029 | Stefano Morozzi | 03/2022 |
6006 | 2^338933+64169 | 102029 | Stefano Morozzi | 05/2022 |
6007 | 2^338928+2367 | 102028 | Stefano Morozzi | 12/2021 |
6008 | 2^338927+52779 | 102028 | Stefano Morozzi | 01/2022 |
6009 | 2^338927-79539 | 102028 | Stefano Morozzi | 02/2022 |
6010 | 2^338929+60819 | 102028 | Stefano Morozzi | 03/2022 |
6011 | 2^338928-156959 | 102028 | Stefano Morozzi | 03/2022 |
6012 | 2^338925+106631 | 102027 | Stefano Morozzi | 01/2022 |
6013 | 2^338926+80235 | 102027 | Stefano Morozzi | 01/2022 |
6014 | 2^338922-27291 | 102026 | Stefano Morozzi | 12/2021 |
6015 | 2^338919-103849 | 102025 | Stefano Morozzi | 01/2022 |
6016 | 2^338919+130221 | 102025 | Stefano Morozzi | 01/2022 |
6017 | 2^338914-79121 | 102024 | Stefano Morozzi | 02/2022 |
6018 | 2^338916+134047 | 102024 | Stefano Morozzi | 03/2022 |
6019 | 2^338910+81027 | 102023 | Stefano Morozzi | 01/2022 |
6020 | 2^338912+179821 | 102023 | Stefano Morozzi | 01/2022 |
6021 | 2^338909+100769 | 102022 | Stefano Morozzi | 11/2021 |
6022 | 2^338908-100839 | 102022 | Stefano Morozzi | 12/2021 |
6023 | 2^338909-25951 | 102022 | Stefano Morozzi | 12/2021 |
6024 | 2^338906-25823 | 102021 | Stefano Morozzi | 12/2021 |
6025 | 2^338904+75951 | 102021 | Stefano Morozzi | 12/2021 |
6026 | 2^338906+6685 | 102021 | Stefano Morozzi | 01/2022 |
6027 | 2^338905+160365 | 102021 | Stefano Morozzi | 03/2022 |
6028 | 2^338903+4155 | 102020 | Stefano Morozzi | 01/2022 |
6029 | 2^338901+55571 | 102020 | Stefano Morozzi | 01/2022 |
6030 | 2^338901-55479 | 102020 | Stefano Morozzi | 02/2022 |
6031 | 2^338903+33555 | 102020 | Stefano Morozzi | 03/2022 |
6032 | 2^338901+39777 | 102020 | Stefano Morozzi | 05/2022 |
6033 | 2^338899-150051 | 102019 | Stefano Morozzi | 12/2021 |
6034 | 2^338899+125951 | 102019 | Stefano Morozzi | 12/2021 |
6035 | 2^338898+179623 | 102019 | Stefano Morozzi | 01/2022 |
6036 | 2^338899-154467 | 102019 | Stefano Morozzi | 02/2022 |
6037 | 2^338894-133295 | 102018 | Stefano Morozzi | 04/2022 |
6045 | 2^338891-18885 | 102017 | Enzo Doria | 05/2013 |
6038 | 2^338891+26499 | 102017 | Stefano Morozzi | 12/2021 |
6039 | 2^338891-2625 | 102017 | Stefano Morozzi | 12/2021 |
6040 | 2^338893+128727 | 102017 | Stefano Morozzi | 01/2022 |
6041 | 2^338890-52965 | 102017 | Stefano Morozzi | 01/2022 |
6042 | 2^338892-55467 | 102017 | Stefano Morozzi | 02/2022 |
6043 | 2^338892-83393 | 102017 | Stefano Morozzi | 04/2022 |
6044 | 2^338893+13649 | 102017 | Stefano Morozzi | 05/2022 |
6046 | 2^338887+154029 | 102016 | Stefano Morozzi | 01/2022 |
6047 | 2^338889-104293 | 102016 | Stefano Morozzi | 02/2022 |
6048 | 2^338886+177159 | 102015 | Stefano Morozzi | 12/2021 |
6049 | 2^338880+11341 | 102014 | Stefano Morozzi | 03/2022 |
6050 | 2^338879-1059 | 102013 | Stefano Morozzi | 12/2021 |
6051 | 2^338879-54525 | 102013 | Stefano Morozzi | 02/2022 |
6052 | 2^338877-82813 | 102013 | Stefano Morozzi | 03/2022 |
6053 | 2^338871+7679 | 102011 | Stefano Morozzi | 02/2022 |
6054 | 2^338872+61141 | 102011 | Stefano Morozzi | 03/2022 |
6055 | 2^338872-183923 | 102011 | Stefano Morozzi | 04/2022 |
6056 | 2^338868-5985 | 102010 | Stefano Morozzi | 02/2022 |
6057 | 2^338867+38079 | 102010 | Stefano Morozzi | 05/2022 |
6058 | 2^338864+158191 | 102009 | Stefano Morozzi | 02/2022 |
6059 | 2^338862+60433 | 102008 | Stefano Morozzi | 03/2022 |
6060 | 2^338861-9453 | 102008 | Stefano Morozzi | 04/2022 |
6061 | 2^338855+102141 | 102006 | Stefano Morozzi | 12/2021 |
6062 | 2^338856-27173 | 102006 | Stefano Morozzi | 12/2021 |
6063 | 2^338856-102839 | 102006 | Stefano Morozzi | 01/2022 |
6064 | 2^338855+79629 | 102006 | Stefano Morozzi | 01/2022 |
6065 | 2^338850+27987 | 102005 | Stefano Morozzi | 01/2022 |
6066 | 2^338853+111791 | 102005 | Stefano Morozzi | 04/2022 |
6067 | 2^338847+176013 | 102004 | Stefano Morozzi | 12/2021 |
6068 | 2^338847-2365 | 102004 | Stefano Morozzi | 12/2021 |
6069 | 2^338848+158941 | 102004 | Stefano Morozzi | 03/2022 |
6070 | 2^338845+135831 | 102003 | Stefano Morozzi | 03/2022 |
6071 | 2^338846+85695 | 102003 | Stefano Morozzi | 03/2022 |
6072 | 2^338845+186525 | 102003 | Stefano Morozzi | 04/2022 |
6073 | 2^338843-127261 | 102002 | Stefano Morozzi | 12/2021 |
6074 | 2^338843+107205 | 102002 | Stefano Morozzi | 02/2022 |
6075 | 2^338842-33185 | 102002 | Stefano Morozzi | 04/2022 |
6076 | 2^338842+14227 | 102002 | Stefano Morozzi | 05/2022 |
6078 | 8*10^102000+51 | 102001 | Robert Price | 08/2019 |
6077 | 2^338838+150837 | 102001 | Stefano Morozzi | 11/2021 |
6079 | 2^338835-150625 | 102000 | Stefano Morozzi | 12/2021 |
6080 | 2^338834-32877 | 102000 | Stefano Morozzi | 04/2022 |
6083 | (2^338832+642)/2 | 101999 | Stefano Morozzi | 09/2020 |
6081 | 2^338833-100905 | 101999 | Stefano Morozzi | 12/2021 |
6082 | 2^338831+54419 | 101999 | Stefano Morozzi | 01/2022 |
6089 | 2^338829-113239 | 101998 | Enzo Doria | 07/2014 |
6090 | 2^338828-113297 | 101998 | Enzo Doria | 07/2014 |
6084 | 2^338830+25017 | 101998 | Stefano Morozzi | 11/2021 |
6085 | 2^338831+321 | 101998 | Stefano Morozzi | 11/2021 |
6086 | 2^338827-26197 | 101998 | Stefano Morozzi | 12/2021 |
6087 | 2^338829+52727 | 101998 | Stefano Morozzi | 01/2022 |
6088 | 2^338827-55461 | 101998 | Stefano Morozzi | 02/2022 |
6091 | 2^338825-27453 | 101997 | Stefano Morozzi | 12/2021 |
6092 | 2^338824+89355 | 101997 | Stefano Morozzi | 05/2022 |
6093 | 2^338822+111175 | 101996 | Stefano Morozzi | 03/2022 |
6094 | 2^338822+187819 | 101996 | Stefano Morozzi | 04/2022 |
6095 | 2^338823+139545 | 101996 | Stefano Morozzi | 05/2022 |
6096 | 2^338815+151175 | 101994 | Stefano Morozzi | 12/2021 |
6097 | 2^338814-30011 | 101994 | Stefano Morozzi | 02/2022 |
6098 | 2^338814+12309 | 101994 | Stefano Morozzi | 04/2022 |
6099 | 2^338811-126999 | 101993 | Stefano Morozzi | 12/2021 |
6100 | 2^338811+131621 | 101993 | Stefano Morozzi | 02/2022 |
6101 | 2^338812-107637 | 101993 | Stefano Morozzi | 03/2022 |
6102 | 2^338809-152755 | 101992 | Stefano Morozzi | 01/2022 |
6103 | 2^338808+156531 | 101992 | Stefano Morozzi | 01/2022 |
6104 | 2^338808+7885 | 101992 | Stefano Morozzi | 02/2022 |
6105 | 2^338808-105797 | 101992 | Stefano Morozzi | 02/2022 |
6106 | 2^338805+29879 | 101991 | Stefano Morozzi | 01/2022 |
6107 | 2^338805+157925 | 101991 | Stefano Morozzi | 02/2022 |
6108 | 2^338804-6809 | 101991 | Stefano Morozzi | 03/2022 |
6109 | 2^338806-157095 | 101991 | Stefano Morozzi | 03/2022 |
6110 | 2^338804-133173 | 101991 | Stefano Morozzi | 04/2022 |
6111 | 2^338802+150403 | 101990 | Stefano Morozzi | 11/2021 |
6112 | 2^338801+154587 | 101990 | Stefano Morozzi | 01/2022 |
6113 | 2^338802-180603 | 101990 | Stefano Morozzi | 02/2022 |
6114 | 2^338803-31921 | 101990 | Stefano Morozzi | 03/2022 |
6115 | 2^338803-81735 | 101990 | Stefano Morozzi | 03/2022 |
6116 | 2^338800+160141 | 101989 | Stefano Morozzi | 03/2022 |
6117 | 2^338797-82489 | 101989 | Stefano Morozzi | 03/2022 |
6122 | 2^338796+93 | 101988 | Donovan Johnson | 06/2008 |
6118 | 2^338795+455 | 101988 | Stefano Morozzi | 11/2021 |
6119 | 2^338795-102075 | 101988 | Stefano Morozzi | 12/2021 |
6120 | 2^338794-3483 | 101988 | Stefano Morozzi | 01/2022 |
6121 | 2^338796+179641 | 101988 | Stefano Morozzi | 01/2022 |
6123 | 2^338793-5155 | 101987 | Stefano Morozzi | 02/2022 |
6124 | 2^338793+111107 | 101987 | Stefano Morozzi | 03/2022 |
6125 | 2^338791+112083 | 101987 | Stefano Morozzi | 04/2022 |
6126 | 2^338787+53309 | 101986 | Stefano Morozzi | 01/2022 |
6127 | 2^338787-153817 | 101986 | Stefano Morozzi | 01/2022 |
6128 | 2^338789+56229 | 101986 | Stefano Morozzi | 01/2022 |
6129 | 2^338790+6429 | 101986 | Stefano Morozzi | 01/2022 |
6130 | 2^338788+131701 | 101986 | Stefano Morozzi | 02/2022 |
6131 | 2^338785+104639 | 101985 | Stefano Morozzi | 01/2022 |
6132 | 2^338784+37591 | 101985 | Stefano Morozzi | 04/2022 |
6133 | 2^338786-9831 | 101985 | Stefano Morozzi | 04/2022 |
6134 | 2^338783+109065 | 101984 | Stefano Morozzi | 03/2022 |
6135 | 2^338779+86711 | 101983 | Stefano Morozzi | 04/2022 |
6136 | 2^338778+113589 | 101983 | Stefano Morozzi | 05/2022 |
6137 | 2^338775-30369 | 101982 | Stefano Morozzi | 02/2022 |
6138 | 2^338774+159135 | 101982 | Stefano Morozzi | 03/2022 |
6139 | 2^338776+113001 | 101982 | Stefano Morozzi | 04/2022 |
6140 | 2^338768-181007 | 101980 | Stefano Morozzi | 02/2022 |
6141 | 2^338768+108807 | 101980 | Stefano Morozzi | 03/2022 |
6142 | 2^338764+138013 | 101979 | Stefano Morozzi | 04/2022 |
6145 | lucasU(1373,1,32502)-lucasU(1373,1,32501) | 101978 | Mike Oakes | 05/2009 |
6143 | 2^338761+103671 | 101978 | Stefano Morozzi | 01/2022 |
6144 | 2^338763-7651 | 101978 | Stefano Morozzi | 03/2022 |
6146 | 2^338757-5151 | 101977 | Stefano Morozzi | 02/2022 |
6147 | 2^338760-79037 | 101977 | Stefano Morozzi | 02/2022 |
6148 | 2^338757-82143 | 101977 | Stefano Morozzi | 03/2022 |
6149 | 2^338757+137007 | 101977 | Stefano Morozzi | 04/2022 |
6150 | 2^338755+158531 | 101976 | Stefano Morozzi | 03/2022 |
6151 | 2^338752-153353 | 101975 | Stefano Morozzi | 01/2022 |
6152 | 2^338751+8001 | 101975 | Stefano Morozzi | 02/2022 |
6153 | 2^338752+32977 | 101975 | Stefano Morozzi | 02/2022 |
6154 | 2^338753-79233 | 101975 | Stefano Morozzi | 02/2022 |
6155 | 2^338750-175625 | 101974 | Stefano Morozzi | 12/2021 |
6156 | 2^338747-2731 | 101974 | Stefano Morozzi | 12/2021 |
6157 | 2^338750-29597 | 101974 | Stefano Morozzi | 02/2022 |
6158 | 2^338748+35095 | 101974 | Stefano Morozzi | 03/2022 |
6159 | 2^338747+137475 | 101974 | Stefano Morozzi | 04/2022 |
6160 | 2^338747+162005 | 101974 | Stefano Morozzi | 04/2022 |
6161 | 2^338750+162237 | 101974 | Stefano Morozzi | 04/2022 |
6162 | 2^338747-184365 | 101974 | Stefano Morozzi | 04/2022 |
6163 | 2^338748+64341 | 101974 | Stefano Morozzi | 05/2022 |
6164 | 2^338746+59577 | 101973 | Stefano Morozzi | 03/2022 |
6165 | 2^338746+62055 | 101973 | Stefano Morozzi | 04/2022 |
6166 | 2^338741+25359 | 101972 | Stefano Morozzi | 12/2021 |
6167 | 2^338743+176981 | 101972 | Stefano Morozzi | 12/2021 |
6168 | 2^338741+183029 | 101972 | Stefano Morozzi | 02/2022 |
6169 | 2^338743-130309 | 101972 | Stefano Morozzi | 02/2022 |
6170 | 2^338741+86349 | 101972 | Stefano Morozzi | 04/2022 |
6171 | 2^338741+111561 | 101972 | Stefano Morozzi | 04/2022 |
6172 | 2^338739+76959 | 101971 | Stefano Morozzi | 12/2021 |
6173 | 2^338739-105957 | 101971 | Stefano Morozzi | 02/2022 |
6174 | 2^338739+190149 | 101971 | Stefano Morozzi | 05/2022 |
6175 | 2^338738+64947 | 101971 | Stefano Morozzi | 05/2022 |
6176 | 2^338737+127547 | 101970 | Stefano Morozzi | 12/2021 |
6177 | 2^338737+128591 | 101970 | Stefano Morozzi | 01/2022 |
6178 | 2^338735-153165 | 101970 | Stefano Morozzi | 01/2022 |
6179 | 2^338734+13719 | 101970 | Stefano Morozzi | 05/2022 |
6184 | 25295^10744+10744^25295 | 101969 | Hans Havermann | 01/2019 |
6185 | 25712^9243+9243^25712 | 101969 | Hans Havermann | 01/2019 |
6180 | 2^338731-150895 | 101969 | Stefano Morozzi | 12/2021 |
6181 | 2^338731+54911 | 101969 | Stefano Morozzi | 01/2022 |
6182 | 2^338731+85863 | 101969 | Stefano Morozzi | 03/2022 |
6183 | 2^338732+185047 | 101969 | Stefano Morozzi | 03/2022 |
6186 | 2^338726+128199 | 101967 | Stefano Morozzi | 01/2022 |
6187 | 2^338727+127745 | 101967 | Stefano Morozzi | 01/2022 |
6188 | 2^338724+32971 | 101967 | Stefano Morozzi | 02/2022 |
6189 | 2^338727+189683 | 101967 | Stefano Morozzi | 05/2022 |
6190 | 2^338723-76651 | 101966 | Stefano Morozzi | 12/2021 |
6191 | 2^338721+79037 | 101966 | Stefano Morozzi | 01/2022 |
6192 | 2^338723-132621 | 101966 | Stefano Morozzi | 03/2022 |
6193 | 2^338722+137313 | 101966 | Stefano Morozzi | 04/2022 |
6194 | 2^338722+162915 | 101966 | Stefano Morozzi | 04/2022 |
6195 | 2^338718-126861 | 101965 | Stefano Morozzi | 12/2021 |
6196 | 2^338718-109127 | 101965 | Stefano Morozzi | 04/2022 |
6199 | (71^55079-1)/70 | 101964 | Paul Bourdelais | 08/2017 |
6197 | 2^338714+30835 | 101964 | Stefano Morozzi | 01/2022 |
6198 | 2^338714+156715 | 101964 | Stefano Morozzi | 02/2022 |
6200 | 2^338711+125399 | 101963 | Stefano Morozzi | 12/2021 |
6201 | 2^338713-30895 | 101963 | Stefano Morozzi | 02/2022 |
6202 | 2^338712-132545 | 101963 | Stefano Morozzi | 03/2022 |
6203 | 2^338713+87825 | 101963 | Stefano Morozzi | 04/2022 |
6204 | 2^338709-154429 | 101962 | Stefano Morozzi | 02/2022 |
6205 | 2^338706-102917 | 101961 | Stefano Morozzi | 01/2022 |
6206 | 2^338705+34727 | 101961 | Stefano Morozzi | 03/2022 |
6207 | 2^338698+104083 | 101959 | Stefano Morozzi | 01/2022 |
6208 | 2^338700-184565 | 101959 | Stefano Morozzi | 04/2022 |
6209 | 2^338700+189777 | 101959 | Stefano Morozzi | 05/2022 |
6210 | 2^338696+181671 | 101958 | Stefano Morozzi | 02/2022 |
6211 | 2^338692+106297 | 101957 | Stefano Morozzi | 01/2022 |
6212 | 2^338692+33195 | 101957 | Stefano Morozzi | 02/2022 |
6213 | 2^338692+110505 | 101957 | Stefano Morozzi | 03/2022 |
6214 | 2^338692+190093 | 101957 | Stefano Morozzi | 05/2022 |
6215 | 2^338688+82203 | 101956 | Stefano Morozzi | 02/2022 |
6216 | 2^338689+82365 | 101956 | Stefano Morozzi | 02/2022 |
6217 | 2^338686-81303 | 101955 | Stefano Morozzi | 03/2022 |
6222 | 2^338682-19865 | 101954 | Enzo Doria | 06/2013 |
6223 | (2^(112895*3+1)+243)/7 | 101954 | Kevin Acres | 12/2013 |
6218 | (8*10^101954-269)/9 | 101954 | Robert Price | 09/2021 |
6219 | 2^338683+50303 | 101954 | Stefano Morozzi | 11/2021 |
6220 | 2^338682-107205 | 101954 | Stefano Morozzi | 03/2022 |
6221 | 2^338682+13839 | 101954 | Stefano Morozzi | 05/2022 |
6224 | 2^338678-180005 | 101953 | Stefano Morozzi | 02/2022 |
6225 | 2^338674-175967 | 101952 | Stefano Morozzi | 12/2021 |
6226 | 2^338677-177373 | 101952 | Stefano Morozzi | 12/2021 |
6227 | 2^338677+102999 | 101952 | Stefano Morozzi | 01/2022 |
6228 | 2^338676+33381 | 101952 | Stefano Morozzi | 03/2022 |
6229 | 2^338677-82699 | 101952 | Stefano Morozzi | 03/2022 |
6230 | 2^338676-34299 | 101952 | Stefano Morozzi | 04/2022 |
6231 | 2^338675+188445 | 101952 | Stefano Morozzi | 05/2022 |
6232 | 2^338671-55041 | 101951 | Stefano Morozzi | 02/2022 |
6233 | 2^338673-80203 | 101951 | Stefano Morozzi | 02/2022 |
6234 | 2^338672-182063 | 101951 | Stefano Morozzi | 03/2022 |
6235 | 2^338672+36667 | 101951 | Stefano Morozzi | 04/2022 |
6236 | 2^338668+2583 | 101950 | Stefano Morozzi | 12/2021 |
6237 | 2^338670-157001 | 101950 | Stefano Morozzi | 03/2022 |
6238 | 2^338669-8353 | 101950 | Stefano Morozzi | 04/2022 |
6245 | (2^338666+3154)/2 | 101949 | Stefano Morozzi | 09/2020 |
6239 | 2^338665+1577 | 101949 | Stefano Morozzi | 12/2021 |
6240 | 2^338665-51133 | 101949 | Stefano Morozzi | 12/2021 |
6241 | 2^338664+4345 | 101949 | Stefano Morozzi | 01/2022 |
6242 | 2^338666-128943 | 101949 | Stefano Morozzi | 01/2022 |
6243 | 2^338664+131535 | 101949 | Stefano Morozzi | 01/2022 |
6244 | 2^338667+14943 | 101949 | Stefano Morozzi | 05/2022 |
6246 | 2^338662+31587 | 101948 | Stefano Morozzi | 02/2022 |
6247 | 2^338663-58375 | 101948 | Stefano Morozzi | 04/2022 |
6248 | 2^338663-107869 | 101948 | Stefano Morozzi | 04/2022 |
6249 | 2^338658-159191 | 101947 | Stefano Morozzi | 04/2022 |
6250 | 2^338659-159687 | 101947 | Stefano Morozzi | 04/2022 |