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
See the Top discoverers
See the Latest PRPs
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 1001 | (50^210319-1)/49 | 357324 | Paul Bourdelais | 08/2020 |
| 1002 | (531^131072+25^131072)/2 | 357184 | Kellen Shenton | 03/2021 |
| 1003 | 2^1186366+226747 | 357132 | Enzo Doria | 09/2024 |
| 1004 | 2^1184565+21227 | 356590 | Enzo Doria | 08/2023 |
| 1005 | 2^1180312+44173 | 355310 | Enzo Doria | 04/2025 |
| 1006 | 2^1180159+22823 | 355264 | Enzo Doria | 11/2023 |
| 1007 | 2^1179836+1885021 | 355167 | Enzo Doria | 02/2017 |
| 1008 | 2^1178942+32269 | 354897 | Enzo Doria | 04/2024 |
| 1009 | 2^1178474+43369 | 354757 | Enzo Doria | 03/2025 |
| 1010 | 2^1177053+28607 | 354329 | Enzo Doria | 02/2024 |
| 1011 | 2^1177027+234863 | 354321 | Enzo Doria | 04/2025 |
| 1012 | (19*10^353884-91)/9 | 353885 | Alfred Reich | 02/2023 |
| 1013 | (10^353884*19-91)/9 | 353885 | Alfred Reich | 10/2023 |
| 1014 | 20^271951+3 | 353817 | Paul Bourdelais | 01/2021 |
| 1015 | 72722^72722+7^7 | 353551 | Serge Batalov | 04/2024 |
| 1016 | 2^1173095+21 | 353137 | Stefano Morozzi | 10/2022 |
| 1017 | 2^1170959+218945 | 352494 | Enzo Doria | 03/2024 |
| 1018 | 2^1170915+382623 | 352481 | Boyan Hu | 08/2024 |
| 1019 | (63^195893-1)/62 | 352477 | Paul Bourdelais | 08/2020 |
| 1020 | 2^1170575+238043 | 352379 | Enzo Doria | 07/2025 |
| 1021 | 2^1170331+27293 | 352305 | Enzo Doria | 01/2024 |
| 1022 | 2^1170326+7 | 352304 | Stefano Morozzi | 10/2022 |
| 1023 | numbpart(100000135540) | 352269 | Serge Batalov | 04/2017 |
| 1024 | (10^352237-1)/9/10567111/950335427 | 352221 | Maksym Voznyy | 01/2015 |
| 1025 | 5*3^737931-2^737931 | 352084 | Jon Grantham | 08/2023 |
| 1026 | 2^1168851+223613 | 351860 | Enzo Doria | 06/2024 |
| 1027 | 2^1168822+236449 | 351851 | Enzo Doria | 06/2025 |
| 1028 | 2^1168554+783529 | 351770 | Enzo Doria | 01/2017 |
| 1029 | (2^1168183-1)/54763676838381762583 | 351639 | Matthias Wurtinger | 01/2011 |
| 1030 | 2^1166950+30409 | 351287 | Enzo Doria | 03/2024 |
| 1031 | 2^1166563+223103 | 351171 | Enzo Doria | 05/2024 |
| 1032 | 2^1166248+38251 | 351076 | Enzo Doria | 11/2024 |
| 1033 | 2^1166152+1882411 | 351047 | Enzo Doria | 12/2016 |
| 1034 | 2^1163972+20971 | 350391 | Enzo Doria | 08/2023 |
| 1035 | 2^1163272+22411 | 350180 | Enzo Doria | 10/2023 |
| 1036 | 10^350071+7 | 350072 | Alfred Reich | 05/2021 |
| 1037 | 2^1162154+1890207 | 349844 | Enzo Doria | 08/2017 |
| 1038 | 2^1161076+25 | 349519 | Henri Lifchitz | 01/2025 |
| 1039 | (7*10^348724-61)/9 | 348724 | Erik Branger | 09/2016 |
| 1040 | (4*10^348453+41)/9 | 348453 | Serge Batalov | 11/2022 |
| 1041 | (127^165601-1)/126 | 348390 | Alexander Zhirkov | 09/2015 |
| 1042 | 2^1155134+43909 | 347730 | Enzo Doria | 04/2025 |
| 1043 | 2^1155085+213377 | 347716 | Enzo Doria | 09/2023 |
| 1044 | 2^1153083+1883693 | 347113 | Enzo Doria | 04/2017 |
| 1045 | 2^1152186+225529 | 346843 | Enzo Doria | 07/2024 |
| 1046 | 2^1151782+42979 | 346721 | Enzo Doria | 02/2025 |
| 1047 | 2^1151754+41599 | 346713 | Enzo Doria | 02/2025 |
| 1048 | (2^1148729+2^574365+1)/5 | 345802 | Borys Jaworski | 03/2007 |
| 1049 | (19*10^345503+53)/9 | 345504 | Rytis Slatkevicius | 12/2024 |
| 1050 | 2^1145882+80779 | 344945 | Enzo Doria | 09/2016 |
| 1051 | 2^1143425+221177 | 344206 | Enzo Doria | 03/2024 |
| 1052 | 2^1141813+27047 | 343720 | Enzo Doria | 12/2023 |
| 1053 | 2^1141114+221869 | 343510 | Enzo Doria | 04/2024 |
| 1054 | 2^1139423+231083 | 343001 | Enzo Doria | 01/2025 |
| 1055 | 2^1138296+27541 | 342662 | Enzo Doria | 01/2024 |
| 1056 | 2^1136462+1887289 | 342110 | Enzo Doria | 05/2017 |
| 1057 | F(1636007) | 341905 | Henri Lifchitz | 03/2009 |
| 1058 | (2^1135567+13)/3 | 341840 | Stefano Morozzi | 09/2022 |
| 1059 | 2^1134873+223637 | 341631 | Enzo Doria | 06/2024 |
| 1060 | 2^1133678+782569 | 341272 | Enzo Doria | 11/2016 |
| 1061 | (11^327001+1)/12 | 340536 | Paul Bourdelais | 09/2013 |
| 1062 | 2^1129965+223667 | 340154 | Enzo Doria | 06/2024 |
| 1063 | 2^1129361+221597 | 339972 | Enzo Doria | 04/2024 |
| 1064 | 2^1128706+225529 | 339775 | Enzo Doria | 07/2024 |
| 1065 | 2^1128621+25919 | 339749 | Enzo Doria | 12/2023 |
| 1066 | 2^1127479+234083 | 339405 | Enzo Doria | 03/2025 |
| 1067 | (2^1127239+2^563620+1)/5 | 339333 | Borys Jaworski | 11/2006 |
| 1068 | Tau(907^20848) | 339132 | Nik Lygeros / Olivier Rozier | 01/2016 |
| 1069 | 2^1126380-3 | 339075 | Paul Bourdelais | 06/2019 |
| 1070 | 2^1125784+24331 | 338895 | Enzo Doria | 10/2023 |
| 1071 | 2^1125446+1885099 | 338794 | Enzo Doria | 08/2017 |
| 1072 | (63^188147+1)/64 | 338539 | Paul Bourdelais | 12/2020 |
| 1073 | 2^1124549+143807 | 338523 | Enzo Doria | 10/2016 |
| 1074 | (4*10^338476+23)/9 | 338476 | Serge Batalov | 11/2022 |
| 1075 | 2^1123083+237413 | 338082 | Enzo Doria | 06/2025 |
| 1076 | 2^1121187+1886783 | 337511 | Enzo Doria | 04/2017 |
| 1077 | (48^200443-1)/47 | 336992 | Paul Bourdelais | 08/2020 |
| 1078 | (2*10^336405+43)/9 | 336405 | Rytis Slatkevicius | 01/2023 |
| 1079 | (94^170371-1)/93 | 336162 | Paul Bourdelais | 09/2020 |
| 1080 | 2^1116184+1883521 | 336005 | Enzo Doria | 02/2017 |
| 1081 | 2^1115727+27683 | 335868 | Enzo Doria | 01/2024 |
| 1082 | 2^1114974+28759 | 335641 | Enzo Doria | 02/2024 |
| 1083 | 2^1114789+46427 | 335585 | Enzo Doria | 05/2025 |
| 1084 | 2^1114517+1880087 | 335504 | Enzo Doria | 10/2016 |
| 1085 | (5*10^335480+31)/9 | 335480 | Serge Batalov | 11/2022 |
| 1086 | 5*3^701688+2^701688 | 334791 | Jon Grantham | 08/2023 |
| 1087 | (101^166849+1)/102 | 334418 | Paul Bourdelais | 12/2020 |
| 1088 | (3^700897+1)/4 | 334413 | Paul Bourdelais | 04/2010 |
| 1089 | 2^1109200+223201 | 333903 | Enzo Doria | 05/2024 |
| 1090 | 2^1108463+32513 | 333681 | Enzo Doria | 05/2024 |
| 1091 | 2^1104500+22411 | 332488 | Enzo Doria | 10/2023 |
| 1092 | 2^1104408-114539 | 332460 | Enzo Doria | 03/2015 |
| 1093 | (3^695701-1)/80701318 | 331926 | Paul Vanderveen | 05/2025 |
| 1094 | 2^1101921+82085 | 331712 | Enzo Doria | 10/2016 |
| 1095 | 2^1101895+29963 | 331704 | Enzo Doria | 03/2024 |
| 1096 | 2^1101167-1101167^2 | 331485 | Henri Lifchitz | 07/2024 |
| 1097 | 2^1101091+224153 | 331462 | Enzo Doria | 06/2024 |
| 1098 | 2^1100655+683513 | 331331 | Enzo Doria | 01/2017 |
| 1099 | (10^330906+71)/9 | 330906 | Serge Batalov | 07/2015 |
| 1100 | 6^425185-425185^6 | 330859 | Henri Lifchitz | 06/2025 |
| 1101 | 2^1098346+482899 | 330636 | Enzo Doria | 11/2016 |
| 1102 | 2^1096976+25 | 330223 | Henri Lifchitz | 11/2024 |
| 1103 | (19*10^330041+53)/9 | 330042 | Rytis Slatkevicius | 12/2024 |
| 1104 | (2^1096212+19)/5 | 329992 | Stefano Morozzi | 09/2022 |
| 1105 | 2^1095976+44701 | 329922 | Enzo Doria | 05/2025 |
| 1106 | 2^1095679+1878713 | 329833 | Enzo Doria | 09/2016 |
| 1107 | 2^1094874+27499 | 329590 | Enzo Doria | 01/2024 |
| 1108 | 2^1094740-1851539 | 329550 | Enzo Doria | 08/2015 |
| 1109 | 2^1092242+19 | 328798 | Stefano Morozzi | 10/2022 |
| 1110 | (19*10^328590+53)/9 | 328591 | Rytis Slatkevicius | 12/2024 |
| 1111 | 2^1091469-379369 | 328565 | Enzo Doria | 03/2014 |
| 1112 | 2^1090801+24227 | 328364 | Enzo Doria | 10/2023 |
| 1113 | 2^1088416+237661 | 327646 | Enzo Doria | 06/2025 |
| 1114 | 2^1087944+39091 | 327504 | Enzo Doria | 11/2024 |
| 1115 | (69^178093-1)/68 | 327485 | Paul Bourdelais | 08/2020 |
| 1116 | 2^1086662+43909 | 327118 | Enzo Doria | 04/2025 |
| 1117 | (10^326884+7)/421 | 326882 | Alfred Reich | 12/2021 |
| 1118 | 2^1085876+48151 | 326882 | Enzo Doria | 06/2025 |
| 1119 | 2^1085750+582349 | 326844 | Enzo Doria | 11/2016 |
| 1120 | (54308^69169-1)/(54308^263-1) | 326261 | Ryan Propper | 11/2023 |
| 1121 | 2^1083596+483061 | 326195 | Enzo Doria | 12/2016 |
| 1122 | (2^541456-1)*10^162995+2^541455-1 | 325990 | paolo galliani | 01/2019 |
| 1123 | 2^1082908+583561 | 325988 | Enzo Doria | 05/2017 |
| 1124 | 30^220411-29^220411 | 325574 | Jean-Louis Charton | 10/2018 |
| 1125 | 2^1081308+7 | 325507 | Stefano Morozzi | 10/2022 |
| 1126 | 2^1080151+225413 | 325158 | Enzo Doria | 08/2024 |
| 1127 | 2^1080032+25171 | 325123 | Enzo Doria | 11/2023 |
| 1128 | 2^1078242+1881649 | 324584 | Enzo Doria | 11/2016 |
| 1129 | 2^1077737+1880117 | 324432 | Enzo Doria | 10/2016 |
| 1130 | 2^1076996+45631 | 324209 | Enzo Doria | 05/2025 |
| 1131 | 3^679017-5*2^679017 | 323974 | Jon Grantham | 08/2023 |
| 1132 | 2^1076006+29539 | 323911 | Enzo Doria | 03/2024 |
| 1133 | 2^1075573+32417 | 323780 | Enzo Doria | 05/2024 |
| 1134 | 2^1075425+1880117 | 323736 | Enzo Doria | 10/2016 |
| 1135 | (28^223381+1)/29 | 323267 | Paul Bourdelais | 12/2020 |
| 1136 | 10^322999+187071 | 323000 | Stefano Morozzi | 03/2019 |
| 1137 | 10^322999-143151 | 322999 | Patrick De Geest | 05/2020 |
| 1138 | 2^1072744+32641 | 322929 | Enzo Doria | 05/2024 |
| 1139 | 2^1072146+1886869 | 322749 | Enzo Doria | 04/2017 |
| 1140 | 2^1072118-7321953 | 322740 | Enzo Doria | 02/2015 |
| 1141 | 2025^97561-2024^97561 | 322579 | Henri Lifchitz | 01/2025 |
| 1142 | 2^1071026+1886869 | 322411 | Enzo Doria | 04/2017 |
| 1143 | 2^1070539+1880633 | 322265 | Enzo Doria | 10/2016 |
| 1144 | 2^1069894+235399 | 322071 | Enzo Doria | 05/2025 |
| 1145 | 2^1069788+26587 | 322039 | Enzo Doria | 12/2023 |
| 1146 | 2^1069293-1147195 | 321890 | Enzo Doria | 05/2015 |
| 1147 | 2^1065968+1880941 | 320889 | Enzo Doria | 10/2016 |
| 1148 | 2^1065897-1147195 | 320867 | Enzo Doria | 05/2015 |
| 1149 | 2^1063427+1882103 | 320124 | Enzo Doria | 12/2016 |
| 1150 | 2^1061095-1061095 | 319422 | Henri Lifchitz | 10/2013 |
| 1151 | 2^1060950+653119 | 319378 | Enzo Doria | 12/2016 |
| 1152 | 2^1060363+782753 | 319202 | Enzo Doria | 11/2016 |
| 1153 | 2^1060028+31771 | 319101 | Enzo Doria | 04/2024 |
| 1154 | (71^172259-1)/70 | 318895 | Paul Bourdelais | 08/2020 |
| 1155 | 2^1058425+38507 | 318618 | Enzo Doria | 11/2024 |
| 1156 | -30*Bern(85996)/236037521 | 318354 | Sergey Batalov | 10/2023 |
| 1157 | (13^285707-1)/870834948 | 318253 | Paul Vanderveen | 05/2025 |
| 1158 | 2^1055665+30407 | 317787 | Enzo Doria | 03/2024 |
| 1159 | 2^1054736+483061 | 317508 | Enzo Doria | 12/2016 |
| 1160 | 2^1053965+1879667 | 317276 | Enzo Doria | 10/2016 |
| 1161 | (43^194119-1)/42 | 317086 | Paul Bourdelais | 08/2020 |
| 1162 | 2^1052899+225413 | 316955 | Enzo Doria | 08/2024 |
| 1163 | 2^1052186-458165 | 316740 | Enzo Doria | 03/2015 |
| 1164 | 11^303909+2 | 316489 | Paul Bourdelais | 08/2023 |
| 1165 | 2^1049026+214609 | 315789 | Enzo Doria | 11/2023 |
| 1166 | 2^1048576+69661 | 315653 | Boyan Hu | 08/2024 |
| 1167 | 2^1046613-114685 | 315062 | Enzo Doria | 04/2015 |
| 1168 | 2^1045625-459373 | 314765 | Enzo Doria | 06/2015 |
| 1169 | 10^(2*157363+1)-8*10^157363-1 | 314727 | Robert Price | 07/2023 |
| 1170 | (7*10^314564-61)/9 | 314564 | Erik Branger | 09/2016 |
| 1171 | 2^1044771+228023 | 314508 | Enzo Doria | 11/2024 |
| 1172 | 2^1044206+7 | 314338 | Stefano Morozzi | 10/2022 |
| 1173 | (7^371669-1)/6 | 314096 | Paul Bourdelais | 02/2010 |
| 1174 | (53^181981-1)/52 | 313784 | Paul Bourdelais | 08/2020 |
| 1175 | (8^347437-5^347437)/3 | 313767 | Jon Grantham | 08/2023 |
| 1176 | (10^313741+1)/11/11294677 | 313733 | Alfred Reich | 04/2024 |
| 1177 | 2^1041944+283051 | 313657 | Enzo Doria | 12/2016 |
| 1178 | (1624^97969-1)/(1624^313-1) | 313533 | Sergey Batalov | 11/2023 |
| 1179 | 2^1041153-114391 | 313419 | Enzo Doria | 02/2015 |
| 1180 | (2^1039700+9)/5 | 312981 | Stefano Morozzi | 09/2022 |
| 1181 | (74^167311+1)/75 | 312742 | Paul Bourdelais | 12/2020 |
| 1182 | 2^1038871+1866983 | 312732 | Enzo Doria | 04/2016 |
| 1183 | 2^1038545+71657 | 312634 | Enzo Doria | 08/2023 |
| 1184 | (55^179573-1)/54 | 312521 | Paul Bourdelais | 08/2020 |
| 1185 | 2^1037647+1881263 | 312363 | Enzo Doria | 11/2016 |
| 1186 | 2^1037226+1879699 | 312237 | Enzo Doria | 10/2016 |
| 1187 | 2^1036867+1865843 | 312129 | Enzo Doria | 02/2016 |
| 1188 | (76^165947+1)/77 | 312114 | Paul Bourdelais | 01/2021 |
| 1189 | 2^1036324+39091 | 311965 | Enzo Doria | 11/2024 |
| 1190 | 2^1036020-114539 | 311874 | Enzo Doria | 02/2015 |
| 1191 | (90^159463-1)/89 | 311628 | Paul Bourdelais | 08/2020 |
| 1192 | 2^1034546+28819 | 311430 | Enzo Doria | 02/2024 |
| 1193 | 2^1032240+1883431 | 310736 | Enzo Doria | 01/2017 |
| 1194 | 64211^64588+64588^64211 | 310514 | Norbert Schneider | 11/2023 |
| 1195 | 2^1031450+29629 | 310498 | Enzo Doria | 03/2024 |
| 1196 | 2^1030352+1870021 | 310167 | Enzo Doria | 06/2016 |
| 1197 | 2^1030046+1882843 | 310075 | Enzo Doria | 11/2016 |
| 1198 | 2^1029120+227971 | 309796 | Enzo Doria | 11/2024 |
| 1199 | 3^648872+16 | 309591 | Robert Price | 04/2020 |
| 1200 | (16976^73441-1)/(16976^271-1) | 309498 | Ryan Propper | 11/2023 |
| 1201 | 64221^64366+64366^64221 | 309451 | Norbert Schneider | 06/2023 |
| 1202 | (11121^76729-1)/(11121^277-1) | 309336 | Ryan Propper | 11/2023 |
| 1203 | 2^1027478+219259 | 309302 | Enzo Doria | 02/2024 |
| 1204 | 2^1026999+20513 | 309158 | Enzo Doria | 07/2023 |
| 1205 | 5^442281+2 | 309142 | Paul Bourdelais | 01/2021 |
| 1206 | 2^1026204+22741 | 308919 | Enzo Doria | 09/2023 |
| 1207 | 2^1026190+15 | 308914 | Stefano Morozzi | 10/2022 |
| 1208 | 2^1025108+20851 | 308589 | Enzo Doria | 08/2023 |
| 1209 | 2^1022860+234121 | 307912 | Enzo Doria | 03/2025 |
| 1210 | A352736(16) | 306985 | Kellen Shenton | 05/2022 |
| 1211 | 2^1019777+213947 | 306984 | Enzo Doria | 10/2023 |
| 1212 | 2^1018820+236731 | 306696 | Enzo Doria | 05/2025 |
| 1213 | (11^293831-1)/10 | 305993 | Paul Bourdelais | 03/2010 |
| 1214 | (67^167449-1)/66 | 305773 | Paul Bourdelais | 08/2020 |
| 1215 | (62^170539+1)/63 | 305671 | Paul Bourdelais | 12/2020 |
| 1216 | 2^1015321-1015321 | 305643 | Henri Lifchitz | 08/2013 |
| 1217 | 2^1014775+27113 | 305478 | Enzo Doria | 12/2023 |
| 1218 | 2^1014450+7 | 305380 | Stefano Morozzi | 10/2022 |
| 1219 | 2^1014404+46171 | 305367 | Enzo Doria | 05/2025 |
| 1220 | 2^1014336+215731 | 305346 | Enzo Doria | 12/2023 |
| 1221 | 2^1014224-2791229 | 305312 | Enzo Doria | 01/2016 |
| 1222 | (10^304986+7)/673 | 304984 | Alfred Reich | 11/2021 |
| 1223 | 65473^45250+45250^65473 | 304818 | Hans Havermann | 02/2022 |
| 1224 | 66012^41423+41423^66012 | 304794 | Hans Havermann | 03/2022 |
| 1225 | 65073^48202+48202^65073 | 304742 | Hans Havermann | 04/2022 |
| 1226 | 2^1012054+31669 | 304659 | Enzo Doria | 06/2024 |
| 1227 | 238176^19+19^238176 | 304569 | Hans Havermann | 03/2022 |
| 1228 | 73122^14615+14615^73122 | 304539 | Hans Havermann | 05/2022 |
| 1229 | 64492^52639+52639^64492 | 304487 | Hans Havermann | 03/2022 |
| 1230 | 65955^41288+41288^65955 | 304437 | Hans Havermann | 04/2022 |
| 1231 | 71729^17530+17530^71729 | 304403 | Hans Havermann | 03/2022 |
| 1232 | 70170^21733+21733^70170 | 304336 | Hans Havermann | 03/2022 |
| 1233 | 2^1010751-107709 | 304267 | Enzo Doria | 03/2014 |
| 1234 | 84473^3994+3994^84473 | 304222 | Hans Havermann | 03/2022 |
| 1235 | (2^1010623-1)/12602017578957977 | 304212 | Tony Prest / Never Odd Or Even | 02/2014 |
| 1236 | 74442^12125+12125^74442 | 303998 | Hans Havermann | 02/2022 |
| 1237 | 77842^8039+8039^77842 | 303989 | Hans Havermann | 01/2022 |
| 1238 | 64209^54140+54140^64209 | 303935 | Hans Havermann | 02/2022 |
| 1239 | 2^1009577+1869587 | 303913 | Enzo Doria | 06/2016 |
| 1240 | 67389^32338+32338^67389 | 303906 | Hans Havermann | 02/2022 |
| 1241 | 8^336419-7^336419 | 303817 | Jean-Louis Charton | 01/2008 |
| 1242 | 2^1009168+15 | 303790 | Stefano Morozzi | 10/2022 |
| 1243 | 80766^5771+5771^80766 | 303782 | Hans Havermann | 01/2022 |
| 1244 | 66094^39385+39385^66094 | 303724 | Hans Havermann | 01/2022 |
| 1245 | 69147^24574+24574^69147 | 303589 | Hans Havermann | 02/2022 |
| 1246 | 78390^7459+7459^78390 | 303580 | Hans Havermann | 01/2022 |
| 1247 | 2^1008301+1869377 | 303529 | Enzo Doria | 06/2016 |
| 1248 | 65008^46615+46615^65008 | 303492 | Hans Havermann | 02/2022 |
| 1249 | (2^1007838+5)/3 | 303389 | Serge Batalov | 08/2015 |
| 1250 | 65018^46293+46293^65018 | 303343 | Hans Havermann | 01/2022 |
