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 ? |
1001 | 2^780408-113453 | 234927 | Enzo Doria | 08/2014 |
1002 | 2^780368-1864829 | 234915 | Enzo Doria | 01/2016 |
1003 | 2^779593-1836559 | 234681 | Enzo Doria | 05/2015 |
1004 | (8713#+(549391#)/(8713#))/360295171 | 234487 | Makoto Morimoto | 11/2017 |
1005 | (5^335429+1)/6 | 234455 | Paul Bourdelais | 08/2010 |
1006 | 2^778395-113617 | 234321 | Enzo Doria | 08/2014 |
1007 | 23*10^234025-7 | 234027 | Robert Price | 10/2022 |
1008 | Phi(78125,5517) | 233857 | Anonymous | 09/2022 |
1009 | 2^776245-2792353 | 233674 | Enzo Doria | 02/2016 |
1010 | 2^776060-114029 | 233618 | Enzo Doria | 11/2014 |
1011 | 2^775987-2789557 | 233596 | Enzo Doria | 12/2015 |
1012 | 2^775672+1866721 | 233501 | Enzo Doria | 03/2016 |
1013 | 2^775238+57 | 233370 | Stefano Morozzi | 05/2021 |
1014 | (11^223999+1)/12 | 233270 | Paul Bourdelais | 02/2010 |
1015 | 2^774118+1885789 | 233033 | Enzo Doria | 04/2017 |
1016 | 21^176191-20^176191 | 232964 | Jean-Louis Charton | 01/2015 |
1017 | 2^773679-113425 | 232901 | Enzo Doria | 08/2014 |
1018 | 10^232599+192489 | 232600 | Patrick De Geest | 12/2013 |
1019 | 10^232599-3 | 232599 | Markus Tervooren | 10/2010 |
1020 | 2^772552-458879 | 232562 | Enzo Doria | 04/2015 |
1021 | 2^772214+1874899 | 232460 | Enzo Doria | 06/2016 |
1022 | 2^771994-1862771 | 232394 | Enzo Doria | 12/2015 |
1023 | 2^771889+1876037 | 232362 | Enzo Doria | 07/2016 |
1024 | 2^771660+1866511 | 232293 | Enzo Doria | 02/2016 |
1025 | 5^332150-18188 | 232163 | Enzo Doria | 06/2014 |
1026 | 3^485977-2^485977 | 231870 | Mike Oakes | 09/2009 |
1027 | 2^770082-114161 | 231818 | Enzo Doria | 01/2015 |
1028 | (20^177967+1)/21 | 231540 | Paul Bourdelais | 05/2013 |
1029 | (4*10^231254+23)/9 | 231254 | Serge Batalov | 11/2022 |
1030 | 2^767622-9221 | 231078 | Lelio R Paula | 01/2016 |
1031 | 2^767344+1880311 | 230994 | Enzo Doria | 09/2016 |
1032 | (3^483611-1)/2 | 230741 | Paul Bourdelais | 02/2010 |
1033 | (10^230706+179)/9 | 230706 | Serge Batalov | 12/2014 |
1034 | 2^766309+1875257 | 230682 | Enzo Doria | 06/2016 |
1035 | 2^765635+1879883 | 230480 | Enzo Doria | 09/2016 |
1036 | 2^764348-113697 | 230092 | Enzo Doria | 09/2014 |
1037 | 2^764131+78863 | 230027 | Enzo Doria | 05/2016 |
1038 | 2^763701+60197 | 229897 | Enzo Doria | 03/2016 |
1039 | 4*10^229836+21 | 229837 | Robert Price | 12/2022 |
1040 | 2^762841-25905 | 229639 | Enzo Doria | 10/2013 |
1041 | 2^761117-113569 | 229120 | Enzo Doria | 08/2014 |
1042 | (98^114859+1)/99 | 228709 | Paul Bourdelais | 12/2018 |
1043 | (2^758231+1)/(3*27146942976539*73236839266867) | 228223 | Gord Palameta | 12/2018 |
1044 | 2^757985-2790013 | 228177 | Enzo Doria | 12/2015 |
1045 | 2^757038-1862081 | 227892 | Enzo Doria | 12/2015 |
1046 | 2^756839+95849 | 227832 | Makoto Morimoto | 10/2013 |
1047 | (2^756839+6989)/756091 | 227826 | Makoto Morimoto | 09/2016 |
1048 | (2^756839-50211)/(137*3203) | 227826 | Makoto Morimoto | 08/2019 |
1049 | 2^756773-112723 | 227812 | Enzo Doria | 07/2014 |
1050 | 524309#+616367 | 227431 | Makoto Morimoto | 02/2016 |
1051 | 2^755097-114193 | 227307 | Enzo Doria | 12/2014 |
1052 | 7*10^227178+39 | 227179 | Robert Price | 01/2023 |
1053 | 2^754473-2791513 | 227120 | Enzo Doria | 01/2016 |
1054 | 2^754376+25 | 227090 | Stefano Morozzi | 05/2021 |
1055 | 2^754038+25 | 226989 | Stefano Morozzi | 05/2021 |
1056 | 2^751426-764321 | 226202 | Enzo Doria | 12/2013 |
1057 | (18^180181-1)/17 | 226176 | Andy Steward | 04/2007 |
1058 | 2^750740-3 | 225996 | Paul Bourdelais | 03/2012 |
1059 | 2^750725+60227 | 225991 | Enzo Doria | 02/2016 |
1060 | 2^750525-113743 | 225931 | Enzo Doria | 09/2014 |
1061 | (2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263) | 225744 | Dario Alpern | 10/2014 |
1062 | 2^749444-1861889 | 225606 | Enzo Doria | 12/2015 |
1063 | tau(311^16452) | 225560 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1064 | 2^749096+1876861 | 225501 | Enzo Doria | 07/2016 |
1065 | (519643#+43033)/(23*1871*2706283) | 225379 | Makoto Morimoto | 08/2019 |
1066 | 2^748657+79607 | 225369 | Enzo Doria | 06/2016 |
1067 | (2^746920-11)/5 | 224845 | Stefano Morozzi | 08/2022 |
1068 | 2^746653-291583 | 224765 | Enzo Doria | 07/2015 |
1069 | 2^746461-114043 | 224708 | Enzo Doria | 11/2014 |
1070 | 2^746302+25 | 224660 | Stefano Morozzi | 05/2021 |
1071 | 2^745098-350471 | 224297 | Enzo Doria | 06/2015 |
1072 | 2^745039-4897 | 224280 | Yves Minet | 03/2021 |
1073 | 23*10^224232-7 | 224234 | Robert Price | 10/2022 |
1074 | (154*10^224061-1)/9 | 224063 | Serge Batalov | 12/2014 |
1075 | 2^744211-1845787 | 224030 | Enzo Doria | 07/2015 |
1076 | 2^743592-134579 | 223844 | Hans Havermann | 10/2018 |
1077 | 2^742452+3 | 223501 | Paul Bourdelais | 06/2019 |
1078 | 234178^9+9^234178 | 223463 | Anatoly F. Selevich | 07/2011 |
1079 | 2^741651-461197 | 223260 | Enzo Doria | 07/2015 |
1080 | 10^223236-1001 | 223236 | Robert Price | 10/2022 |
1081 | 2^741362-1845251 | 223173 | Enzo Doria | 07/2015 |
1082 | 2^740455-1863877 | 222900 | Enzo Doria | 12/2015 |
1083 | (14*10^222718-41)/9 | 222719 | Serge Batalov | 01/2023 |
1084 | 2^739636-2792219 | 222653 | Enzo Doria | 02/2016 |
1085 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
1086 | 2^738957-1859743 | 222449 | Enzo Doria | 11/2015 |
1087 | 4*10^222253-21 | 222254 | Robert Price | 12/2022 |
1088 | 2^737825+57 | 222108 | Stefano Morozzi | 05/2021 |
1089 | (54^128189+1)/55 | 222073 | Paul Bourdelais | 11/2018 |
1090 | (10^221654+179)/9 | 221654 | Serge Batalov | 12/2014 |
1091 | 2^736281+79817 | 221643 | Enzo Doria | 06/2016 |
1092 | 10^221631+247617 | 221632 | Patrick De Geest | 10/2013 |
1093 | 10^221631-9 | 221631 | Alexander Gramolin | 02/2011 |
1094 | 10^221628+7 | 221629 | Alfred Reich | 04/2021 |
1095 | 2^735970-1839821 | 221550 | Enzo Doria | 06/2015 |
1096 | 2^735367+60293 | 221368 | Enzo Doria | 03/2016 |
1097 | (29^151153+1)/30 | 221045 | Paul Bourdelais | 09/2017 |
1098 | 2^733264-2784089 | 220735 | Enzo Doria | 10/2015 |
1099 | 2^733114-24555 | 220690 | Enzo Doria | 09/2013 |
1100 | 2^731891-636259 | 220322 | Enzo Doria | 12/2013 |
1101 | 2^731124-25539 | 220091 | Enzo Doria | 09/2013 |
1102 | 2^730972-462029 | 220045 | Enzo Doria | 07/2015 |
1103 | 2^730833+1868627 | 220003 | Enzo Doria | 04/2016 |
1104 | 2^730645-2787133 | 219947 | Enzo Doria | 11/2015 |
1105 | 2^730547-25581 | 219917 | Enzo Doria | 09/2013 |
1106 | (113*13^197420-5)/12 | 219916 | Anonymous | 11/2022 |
1107 | 2^730460+82291 | 219891 | Enzo Doria | 09/2016 |
1108 | (2^730339+1)/(3*27839062003*7943469324347) | 219831 | Gord Palameta | 12/2018 |
1109 | L(1051849) | 219824 | Renaud Lifchitz | 03/2009 |
1110 | 8*10^219740-3 | 219741 | Serge Batalov | 01/2023 |
1111 | 11^210961-240 | 219694 | Enzo Doria | 01/2013 |
1112 | 2^729611-113437 | 219635 | Enzo Doria | 08/2014 |
1113 | 7^259710-2 | 219481 | Paul Bourdelais | 01/2021 |
1114 | F(1049897) | 219416 | Henri Lifchitz | 10/2008 |
1115 | 2^728604+1879321 | 219332 | Enzo Doria | 10/2016 |
1116 | 33^144412+2 | 219292 | Robert Price | 04/2015 |
1117 | 2^728277-183313 | 219234 | Hans Havermann | 10/2018 |
1118 | 2^727998-1862711 | 219150 | Enzo Doria | 12/2015 |
1119 | (29*10^219124+91)/3 | 219125 | Robert Price | 12/2022 |
1120 | 2^727729-114073 | 219069 | Enzo Doria | 12/2014 |
1121 | 2^727496-1851809 | 218999 | Enzo Doria | 08/2015 |
1122 | 2^726591+2793143 | 218726 | Enzo Doria | 02/2016 |
1123 | 2^725534-2791931 | 218408 | Enzo Doria | 02/2016 |
1124 | Phi(220531,10)/2686456812680882641 | 217774 | Makoto Kamada | 10/2020 |
1125 | 2^722184+1877821 | 217400 | Enzo Doria | 08/2016 |
1126 | (109*10^217360-1)/9 | 217362 | Serge Batalov | 12/2014 |
1127 | 2^721721-4453 | 217260 | Yves Minet | 03/2021 |
1128 | 281*499979#/46410-2702372 | 216849 | Robert Smith | 08/2016 |
1129 | 281*499979#/46410+2400766 | 216849 | Robert Smith | 08/2016 |
1130 | tau(311^15786) | 216429 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1131 | 2^718756-114107 | 216368 | Enzo Doria | 12/2014 |
1132 | 2^717672+121 | 216041 | Stefano Morozzi | 05/2021 |
1133 | 2^717305+80327 | 215931 | Enzo Doria | 07/2016 |
1134 | 2^717069-59773 | 215860 | Enzo Doria | 10/2015 |
1135 | 30^146021-29^146021 | 215691 | Jean-Louis Charton | 09/2018 |
1136 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
1137 | 227^91413-40 | 215372 | Enzo Doria | 04/2015 |
1138 | (2^715008-21)/5 | 215239 | Stefano Morozzi | 08/2022 |
1139 | 2^714717+782897 | 215152 | Enzo Doria | 11/2016 |
1140 | tau(373^15186) | 214796 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1141 | 2^713241+1879157 | 214707 | Enzo Doria | 08/2016 |
1142 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
1143 | 2^712801-69553 | 214575 | Enzo Doria | 01/2016 |
1144 | 2^712603-25357 | 214515 | Enzo Doria | 09/2013 |
1145 | 2^711721-1846723 | 214250 | Enzo Doria | 07/2015 |
1146 | 2^710730-396765 | 213952 | Enzo Doria | 09/2013 |
1147 | 2^708468-114329 | 213271 | Enzo Doria | 02/2015 |
1148 | (163*10^212779-1)/9 | 212781 | Serge Batalov | 12/2014 |
1149 | 2^706838-69041 | 212780 | Enzo Doria | 11/2015 |
1150 | 22*10^212339+7 | 212341 | Robert Price | 10/2022 |
1151 | 2^704577-113871 | 212099 | Enzo Doria | 10/2014 |
1152 | (2^704548-19)/3 | 212090 | Stefano Morozzi | 08/2022 |
1153 | 2^704110-2792441 | 211959 | Enzo Doria | 02/2016 |
1154 | 2^703943-1862947 | 211908 | Enzo Doria | 12/2015 |
1155 | (60^119083+1)/61 | 211746 | Paul Bourdelais | 10/2018 |
1156 | (184*10^211682-1)/3 | 211684 | Robert Price | 12/2022 |
1157 | (10^211610-91)/9 | 211610 | Serge Batalov | 12/2014 |
1158 | 227^89797+2 | 211565 | Lelio R Paula | 08/2012 |
1159 | 2^702194-3 | 211382 | Paul Bourdelais | 03/2012 |
1160 | 2^702064+1874911 | 211343 | Enzo Doria | 07/2016 |
1161 | 2^701968-113873 | 211314 | Enzo Doria | 10/2014 |
1162 | (14*10^211262-41)/9 | 211263 | Serge Batalov | 01/2023 |
1163 | 2^701713-113779 | 211237 | Enzo Doria | 09/2014 |
1164 | 2^701449-25201 | 211158 | Enzo Doria | 09/2013 |
1165 | 2^701403-2786977 | 211144 | Enzo Doria | 11/2015 |
1166 | 2^701189-25423 | 211079 | Enzo Doria | 09/2013 |
1167 | 2^701162-459161 | 211071 | Enzo Doria | 05/2015 |
1168 | (24^152783-1)/23 | 210872 | Paul Bourdelais | 04/2018 |
1169 | 2^700400+9385 | 210842 | Lelio R Paula | 01/2014 |
1170 | 2^700304-17 | 210813 | Stefano Morozzi | 07/2022 |
1171 | 2^700131+1874693 | 210761 | Enzo Doria | 06/2016 |
1172 | (2^700095+225414)/2 | 210750 | Stefano Morozzi | 04/2020 |
1173 | (2^700090+278254)/2 | 210748 | Stefano Morozzi | 04/2020 |
1174 | (2^700075+303666)/2 | 210744 | Stefano Morozzi | 04/2020 |
1175 | (2^700073+75882)/2 | 210743 | Stefano Morozzi | 04/2020 |
1176 | (2^700074+328890)/2 | 210743 | Stefano Morozzi | 04/2020 |
1177 | (2^700052+79162)/2 | 210737 | Stefano Morozzi | 04/2020 |
1178 | (2^700052+304458)/2 | 210737 | Stefano Morozzi | 04/2020 |
1179 | (2^700048+376578)/2 | 210736 | Stefano Morozzi | 04/2020 |
1180 | 11^202357-1140 | 210734 | Enzo Doria | 12/2012 |
1181 | (2^700021+25874)/2 | 210728 | Stefano Morozzi | 04/2020 |
1182 | (2^700018+377518)/2 | 210727 | Stefano Morozzi | 04/2020 |
1183 | 2^699740+25 | 210643 | Stefano Morozzi | 05/2021 |
1184 | 2^698929-2788423 | 210399 | Enzo Doria | 11/2015 |
1185 | (5^300893+4^300893)/9 | 210315 | Jean-Louis Charton | 11/2011 |
1186 | 2^698316+1878601 | 210215 | Enzo Doria | 08/2016 |
1187 | 2^697036+1878751 | 209829 | Enzo Doria | 08/2016 |
1188 | 6^269407+5 | 209640 | Paul Bourdelais | 02/2021 |
1189 | (2^696343-1)/11141489/36009913139329 | 209600 | Tony Prest / Never Odd Or Even | 02/2014 |
1190 | 2^696254-115151 | 209594 | Enzo Doria | 06/2015 |
1191 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
1192 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
1193 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
1194 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
1195 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
1196 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
1197 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
1198 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
1199 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
1200 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
1201 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
1202 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
1203 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
1204 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
1205 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
1206 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
1207 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
1208 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
1209 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
1210 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
1211 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
1212 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
1213 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
1214 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
1215 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
1216 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
1217 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
1218 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
1219 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
1220 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
1221 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
1222 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
1223 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
1224 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
1225 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
1226 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
1227 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
1228 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
1229 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
1230 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
1231 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
1232 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
1233 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
1234 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
1235 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |
1236 | 10247^50678-50678^10247 | 203250 | Norbert Schneider | 03/2022 |
1237 | 2^674627-25161 | 203083 | Enzo Doria | 09/2013 |
1238 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
1239 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
1240 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
1241 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
1242 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
1243 | (2^673184-7)/3 | 202649 | Stefano Morozzi | 08/2022 |
1244 | (467617#+14534)/(2^2*13*43) | 202603 | Makoto Morimoto | 06/2019 |
1245 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
1246 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
1247 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
1248 | (2*10^202059+7)/9 | 202059 | Rytis Slatkevicius | 01/2023 |
1249 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
1250 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |