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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 1001 | 2^1303102+1866409 | 392273 | Enzo Doria | 09/2017 |
| 1002 | 2^1302818+283429 | 392188 | Enzo Doria | 01/2017 |
| 1003 | 2^1301430+22669 | 391770 | Enzo Doria | 10/2023 |
| 1004 | 2^1301229+222467 | 391709 | Enzo Doria | 04/2024 |
| 1005 | 2^1300835+232523 | 391591 | Enzo Doria | 03/2025 |
| 1006 | (934422^81920+1)/(934422^16384+1) | 391286 | Serge Batalov | 01/2017 |
| 1007 | 2^1299181+1886867 | 391093 | Enzo Doria | 04/2017 |
| 1008 | (37^249341-1)/36 | 391016 | Paul Bourdelais | 08/2020 |
| 1009 | 2^1298304+1882891 | 390829 | Enzo Doria | 01/2017 |
| 1010 | 2^1297732+228721 | 390657 | Enzo Doria | 11/2024 |
| 1011 | Phi(87181,13#) | 390354 | Henri Lifchitz | 02/2026 |
| 1012 | 2^1295728+240751 | 390053 | Enzo Doria | 09/2025 |
| 1013 | 95196^12497+12497^95196 | 390000 | Hans Havermann | 12/2021 |
| 1014 | 2^1295539+35633 | 389997 | Enzo Doria | 08/2024 |
| 1015 | 86206^33381+33381^86206 | 389953 | Hans Havermann | 05/2023 |
| 1016 | 2^1294976+236731 | 389827 | Enzo Doria | 06/2025 |
| 1017 | 2^1294324+25171 | 389631 | Enzo Doria | 12/2023 |
| 1018 | 2^1294298+243649 | 389623 | Enzo Doria | 01/2026 |
| 1019 | (874207^81920+1)/(874207^16384+1) | 389390 | Serge Batalov | 01/2017 |
| 1020 | 2^1292338+229249 | 389033 | Enzo Doria | 11/2024 |
| 1021 | 2^1289624+32551 | 388216 | Enzo Doria | 05/2024 |
| 1022 | 2^1286857+37967 | 387383 | Enzo Doria | 10/2024 |
| 1023 | 2^1285458+46159 | 386962 | Enzo Doria | 06/2025 |
| 1024 | 2^1285456+230611 | 386961 | Enzo Doria | 01/2025 |
| 1025 | (7^457871-5^457871)/2 | 386946 | Jon Grantham | 08/2023 |
| 1026 | 79455^73828+73828^79455 | 386805 | Hans Havermann | 03/2023 |
| 1027 | 81650^54369+54369^81650 | 386642 | Yusuf AttarBashi | 06/2021 |
| 1028 | 80565^62824+62824^80565 | 386561 | Hans Havermann | 08/2021 |
| 1029 | 83747^41272+41272^83747 | 386548 | Hans Havermann | 08/2021 |
| 1030 | 15^328574+328574^15 | 386434 | Serge Batalov | 05/2014 |
| 1031 | 2^1283304+53551 | 386313 | Enzo Doria | 01/2026 |
| 1032 | 2^1283147+54833 | 386266 | Enzo Doria | 02/2026 |
| 1033 | 2^1282676+30493 | 386124 | Enzo Doria | 12/2024 |
| 1034 | 2^1280078+1885099 | 385342 | Enzo Doria | 08/2017 |
| 1035 | 2^1279921+17 | 385295 | Stefano Morozzi | 10/2022 |
| 1036 | 2^1279245+224087 | 385092 | Enzo Doria | 07/2024 |
| 1037 | 2^1278091+47963 | 384744 | Enzo Doria | 07/2025 |
| 1038 | 2^1277980+231391 | 384711 | Enzo Doria | 01/2025 |
| 1039 | 2^1277688+231241 | 384623 | Enzo Doria | 01/2025 |
| 1040 | 2^1277142+234979 | 384459 | Enzo Doria | 04/2025 |
| 1041 | 2^1276977+71657 | 384409 | Enzo Doria | 08/2023 |
| 1042 | (76803^78961-1)/(76803^281-1) | 384382 | Ryan Propper | 11/2023 |
| 1043 | 2^1276571+26213 | 384287 | Enzo Doria | 12/2023 |
| 1044 | MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832,26908) | 384166 | Sergey Batalov | 05/2024 |
| 1045 | 2^1274941+1880717 | 383796 | Enzo Doria | 10/2016 |
| 1046 | 2^1272632+383431 | 383101 | Enzo Doria | 01/2017 |
| 1047 | 2^1271346+1889839 | 382714 | Enzo Doria | 08/2017 |
| 1048 | 2^1271173+219587 | 382662 | Enzo Doria | 03/2024 |
| 1049 | 2^1266263+239783 | 381184 | Enzo Doria | 09/2025 |
| 1050 | 5*3^798534-2^798534 | 380999 | Jon Grantham | 08/2023 |
| 1051 | (10^380976-7)/3 | 380976 | Leonid Durman | 01/2012 |
| 1052 | 2^1264748+23221 | 380728 | Enzo Doria | 11/2023 |
| 1053 | 2^1262877+56897 | 380164 | Enzo Doria | 04/2026 |
| 1054 | (4*10^380056+11)/3 | 380057 | Tyler Busby | 03/2023 |
| 1055 | 2^1262504+242821 | 380052 | Enzo Doria | 12/2025 |
| 1056 | 2^1262431+228353 | 380030 | Enzo Doria | 11/2024 |
| 1057 | 2^1260859+222683 | 379557 | Enzo Doria | 06/2024 |
| 1058 | 2^1258313+43727 | 378790 | Enzo Doria | 03/2025 |
| 1059 | 2^1257787+1447761 | 378632 | Makoto Morimoto | 10/2013 |
| 1060 | (2^1257787+32270)/(2*233*281*2207*3011) | 378620 | Makoto Morimoto | 12/2016 |
| 1061 | 2^1257728+20851 | 378614 | Enzo Doria | 08/2023 |
| 1062 | (77^200657-1)/76 | 378536 | Paul Bourdelais | 08/2020 |
| 1063 | 2^1257107+45413 | 378427 | Enzo Doria | 05/2025 |
| 1064 | 2^1254797+229487 | 377732 | Enzo Doria | 11/2024 |
| 1065 | (98^189619+1)/99 | 377573 | Paul Bourdelais | 02/2021 |
| 1066 | Phi(17#,12492) | 377546 | Henri Lifchitz | 10/2025 |
| 1067 | F(1803059) | 376817 | Henri Lifchitz | 06/2009 |
| 1068 | 2^1250590+29389 | 376466 | Enzo Doria | 03/2024 |
| 1069 | (10^376417-3^376417)/7 | 376417 | Jon Grantham | 08/2023 |
| 1070 | 2^1250116+34951 | 376323 | Enzo Doria | 08/2024 |
| 1071 | 2^1248318+51859 | 375782 | Enzo Doria | 11/2025 |
| 1072 | 2^1248184-57329 | 375741 | Enzo Doria | 05/2026 |
| 1073 | 2^1246724+213961 | 375302 | Enzo Doria | 10/2023 |
| 1074 | 2^1246340+54961 | 375186 | Enzo Doria | 02/2026 |
| 1075 | 2^1245610+237919 | 374966 | Enzo Doria | 06/2025 |
| 1076 | 2^1245230+19 | 374852 | Stefano Morozzi | 10/2022 |
| 1077 | 2^1244480+52021 | 374626 | Enzo Doria | 11/2025 |
| 1078 | 2^1244368+247771 | 374593 | Enzo Doria | 04/2026 |
| 1079 | 2^1244263+230033 | 374561 | Enzo Doria | 01/2025 |
| 1080 | 7^442674+4 | 374103 | Paul Bourdelais | 02/2021 |
| 1081 | 2^1242374+240919 | 373992 | Enzo Doria | 09/2025 |
| 1082 | 2^1242268+239641 | 373960 | Enzo Doria | 08/2025 |
| 1083 | 2^1239939+242513 | 373259 | Enzo Doria | 12/2025 |
| 1084 | 2^1239151+35633 | 373022 | Enzo Doria | 08/2024 |
| 1085 | 2^1238732+39181 | 372896 | Enzo Doria | 11/2024 |
| 1086 | 2^1237699+34703 | 372585 | Enzo Doria | 07/2024 |
| 1087 | (97^187393-1)/96 | 372306 | Paul Bourdelais | 09/2020 |
| 1088 | 2^1235070+46219 | 371794 | Enzo Doria | 05/2025 |
| 1089 | 10^371696+7 | 371697 | Alfred Reich | 05/2021 |
| 1090 | 2^1234709+883127 | 371685 | Enzo Doria | 12/2016 |
| 1091 | 2^1234688+237151 | 371679 | Enzo Doria | 08/2025 |
| 1092 | 2^1234119+21803 | 371507 | Enzo Doria | 09/2023 |
| 1093 | (67^203431+1)/68 | 371479 | Paul Bourdelais | 09/2021 |
| 1094 | 2^1233971+216593 | 371463 | Enzo Doria | 12/2023 |
| 1095 | 2^1233212+27301 | 371234 | Enzo Doria | 12/2023 |
| 1096 | 2^1231847+244103 | 370823 | Enzo Doria | 01/2026 |
| 1097 | 2^1231529+237557 | 370728 | Enzo Doria | 06/2025 |
| 1098 | 2^1231466+283819 | 370709 | Enzo Doria | 07/2017 |
| 1099 | 2^1229766+26659 | 370197 | Enzo Doria | 12/2023 |
| 1100 | 2^1228899+30713 | 369936 | Enzo Doria | 03/2024 |
| 1101 | 2^1228892+223831 | 369934 | Enzo Doria | 06/2024 |
| 1102 | 2^1227635+45413 | 369555 | Enzo Doria | 05/2025 |
| 1103 | (49627^78961-1)/(49627^281-1) | 369460 | Ryan Propper | 11/2023 |
| 1104 | 2^1227060+226663 | 369382 | Enzo Doria | 09/2024 |
| 1105 | 2^1226987+28163 | 369360 | Enzo Doria | 02/2024 |
| 1106 | 2^1226725+234887 | 369282 | Enzo Doria | 04/2025 |
| 1107 | 2^1226569+30857 | 369235 | Enzo Doria | 03/2024 |
| 1108 | 2^1225268+46591 | 368843 | Enzo Doria | 05/2025 |
| 1109 | 73^197880+197880 | 368715 | Kellen Shenton | 06/2023 |
| 1110 | 2^1223601+242357 | 368341 | Enzo Doria | 11/2025 |
| 1111 | 5*3^771723-2^771723 | 368207 | Jon Grantham | 08/2023 |
| 1112 | 2^1222741+231707 | 368082 | Enzo Doria | 02/2025 |
| 1113 | 2^1222473+221597 | 368002 | Enzo Doria | 04/2024 |
| 1114 | 2^1222211+22703 | 367923 | Enzo Doria | 11/2023 |
| 1115 | (2^1222097+19)/3 | 367888 | Stefano Morozzi | 09/2022 |
| 1116 | 2^1220335+1881263 | 367358 | Enzo Doria | 11/2016 |
| 1117 | 2^1219565+49967 | 367126 | Enzo Doria | 03/2026 |
| 1118 | 2^1219561+47897 | 367125 | Enzo Doria | 09/2025 |
| 1119 | 2^1219351+240773 | 367062 | Enzo Doria | 09/2025 |
| 1120 | 2^1219016+53041 | 366961 | Enzo Doria | 12/2025 |
| 1121 | 2^1218344+215641 | 366759 | Enzo Doria | 12/2023 |
| 1122 | 2^1217510+220039 | 366508 | Enzo Doria | 03/2024 |
| 1123 | 2^1217500+226321 | 366505 | Enzo Doria | 09/2024 |
| 1124 | (233^154787-1)/232 | 366434 | Anonymous | 05/2024 |
| 1125 | 2^1216694+1884769 | 366262 | Enzo Doria | 02/2017 |
| 1126 | 2^1216267+45143 | 366133 | Enzo Doria | 05/2025 |
| 1127 | 2^1215889-3 | 366020 | Paul Bourdelais | 06/2019 |
| 1128 | 2^1215296+1885441 | 365841 | Enzo Doria | 03/2017 |
| 1129 | (80^192133+1)/81 | 365645 | Paul Bourdelais | 01/2021 |
| 1130 | 2^1214307+1888115 | 365543 | Enzo Doria | 05/2017 |
| 1131 | 2^1213815+3 | 365395 | Paul Bourdelais | 06/2019 |
| 1132 | (80^191953+1)/81 | 365302 | Paul Bourdelais | 01/2021 |
| 1133 | 2^1213313+215837 | 365244 | Enzo Doria | 11/2023 |
| 1134 | 2^1208816+55081 | 363890 | Enzo Doria | 02/2026 |
| 1135 | 2^1208276+22201 | 363728 | Enzo Doria | 09/2023 |
| 1136 | 2^1207345+1882577 | 363448 | Enzo Doria | 12/2016 |
| 1137 | 2^1207336+217801 | 363445 | Enzo Doria | 03/2024 |
| 1138 | 2^1207073+883727 | 363366 | Enzo Doria | 03/2017 |
| 1139 | 3^761457-2 | 363308 | Ryan Propper | 07/2015 |
| 1140 | (10^363030+7)/337/443 | 363025 | Alfred Reich | 12/2021 |
| 1141 | 2^1204869+224885 | 362702 | Enzo Doria | 07/2024 |
| 1142 | 2^1204540+237541 | 362603 | Enzo Doria | 07/2025 |
| 1143 | 2^1203721+44117 | 362357 | Enzo Doria | 04/2025 |
| 1144 | 2^1203309+54857 | 362233 | Enzo Doria | 02/2026 |
| 1145 | 2^1200972+141811 | 361529 | Stefano Morozzi | 10/2022 |
| 1146 | (2^1200924+324730)/2 | 361514 | Stefano Morozzi | 06/2021 |
| 1147 | (2^1200912+274110)/2 | 361511 | Stefano Morozzi | 01/2021 |
| 1148 | 2^1200906+165249 | 361509 | Stefano Morozzi | 07/2022 |
| 1149 | 2^1200890+166339 | 361504 | Stefano Morozzi | 01/2023 |
| 1150 | (2^1200887+344126)/2 | 361503 | Stefano Morozzi | 10/2020 |
| 1151 | 2^1200877+186755 | 361500 | Stefano Morozzi | 09/2022 |
| 1152 | 2^1200861+198521 | 361496 | Stefano Morozzi | 11/2021 |
| 1153 | (2^1200856+305790)/2 | 361494 | Stefano Morozzi | 10/2020 |
| 1154 | (2^1200853+372822)/2 | 361493 | Stefano Morozzi | 06/2021 |
| 1155 | 2^1200812+324178)/2 | 361481 | Stefano Morozzi | 06/2021 |
| 1156 | (2^1200768+380458)/2 | 361467 | Stefano Morozzi | 01/2021 |
| 1157 | 2^1200756+140917 | 361464 | Stefano Morozzi | 05/2022 |
| 1158 | 2^1200741+184781 | 361460 | Stefano Morozzi | 09/2022 |
| 1159 | (2^1200741+293402)/2 | 361459 | Stefano Morozzi | 07/2021 |
| 1160 | 2^1200734+142653 | 361457 | Stefano Morozzi | 02/2023 |
| 1162 | 2^1200672+1880881 | 361439 | Enzo Doria | 10/2016 |
| 1161 | 2^1200672+141535 | 361439 | Stefano Morozzi | 09/2022 |
| 1163 | 2^1200669+178805 | 361438 | Stefano Morozzi | 11/2022 |
| 1164 | 2^1200660+198555 | 361435 | Stefano Morozzi | 12/2021 |
| 1165 | 2^1200657+164837 | 361434 | Stefano Morozzi | 05/2022 |
| 1166 | 2^1200631+166431 | 361426 | Stefano Morozzi | 02/2023 |
| 1167 | 2^1200627+150669 | 361425 | Stefano Morozzi | 02/2023 |
| 1168 | (2^1200603+356030)/2 | 361418 | Stefano Morozzi | 10/2020 |
| 1169 | (2^1200590+275854)/2 | 361414 | Stefano Morozzi | 03/2021 |
| 1170 | 2^1200550+139297 | 361402 | Stefano Morozzi | 10/2021 |
| 1171 | 2^1200486+172855 | 361383 | Stefano Morozzi | 01/2023 |
| 1172 | (2^1200456+320526)/2 | 361373 | Stefano Morozzi | 10/2020 |
| 1173 | 2^1200443+142121 | 361370 | Stefano Morozzi | 01/2023 |
| 1174 | 2^1200416+164065 | 361362 | Stefano Morozzi | 01/2022 |
| 1175 | 2^1200331+155429 | 361336 | Stefano Morozzi | 10/2021 |
| 1177 | (2^1200289+348366)/2 | 361323 | Stefano Morozzi | 10/2020 |
| 1176 | 2^1200289+141885 | 361323 | Stefano Morozzi | 11/2022 |
| 1178 | (2^1200284+273162)/2 | 361322 | Stefano Morozzi | 10/2020 |
| 1179 | 2^1200252+194535 | 361312 | Stefano Morozzi | 11/2021 |
| 1180 | (2^1200250+364230)/2 | 361311 | Stefano Morozzi | 10/2020 |
| 1181 | 2^1200227+156881 | 361305 | Stefano Morozzi | 05/2022 |
| 1182 | (2^1200209+305990)/2 | 361299 | Stefano Morozzi | 10/2020 |
| 1183 | (2^1200210+376278)/2 | 361299 | Stefano Morozzi | 10/2020 |
| 1184 | 2^1200202+216499 | 361297 | Enzo Doria | 12/2023 |
| 1185 | (2^1200182+274462)/2 | 361291 | Stefano Morozzi | 01/2021 |
| 1186 | 2^1200178+149193 | 361290 | Stefano Morozzi | 07/2022 |
| 1187 | 2^1200168+140403 | 361287 | Stefano Morozzi | 03/2022 |
| 1188 | (2^1200162+275910)/2 | 361285 | Stefano Morozzi | 03/2021 |
| 1189 | 2^1200157+168927 | 361284 | Stefano Morozzi | 02/2023 |
| 1190 | 2^1200134+141385 | 361277 | Stefano Morozzi | 08/2022 |
| 1191 | (2^1200131+360150)/2 | 361276 | Stefano Morozzi | 10/2020 |
| 1192 | (2^1200118+290718)/2 | 361272 | Stefano Morozzi | 01/2021 |
| 1193 | 2^1200022+192777 | 361243 | Stefano Morozzi | 09/2022 |
| 1194 | 2^1200021+149777 | 361243 | Stefano Morozzi | 10/2022 |
| 1195 | Phi(451125,2^5) | 361236 | Henri Lifchitz | 12/2025 |
| 1196 | (64*10^360173-1)/243 | 360173 | Serge Batalov | 09/2014 |
| 1197 | (59^203309+1)/60 | 360029 | Paul Bourdelais | 09/2021 |
| 1198 | (2*10^359860-11)/9 | 359860 | Rytis Slatkevicius | 01/2023 |
| 1199 | 2^1195093+1882577 | 359759 | Enzo Doria | 12/2016 |
| 1200 | 3^753451+5*2^753451 | 359488 | Jon Grantham | 08/2023 |
| 1201 | 2^1193505+238397 | 359281 | Enzo Doria | 07/2025 |
| 1202 | 2^1192258+36739 | 358906 | Enzo Doria | 09/2024 |
| 1203 | 2^1192251+47183 | 358904 | Enzo Doria | 06/2025 |
| 1204 | (6^461108-11)/5 | 358812 | Paul Bourdelais | 04/2019 |
| 1205 | 2^1191375+8543 | 358640 | Phil Moore | 06/2008 |
| 1206 | 2^1191335+50783 | 358628 | Enzo Doria | 10/2025 |
| 1207 | 2^1190972+1880191 | 358519 | Enzo Doria | 11/2016 |
| 1208 | 2^1190752+245041 | 358453 | Enzo Doria | 02/2026 |
| 1209 | 2^1189930+28549 | 358205 | Enzo Doria | 03/2024 |
| 1210 | (45^216551-1)/44 | 358004 | Paul Bourdelais | 08/2020 |
| 1211 | 2^1187473+237257 | 357465 | Enzo Doria | 06/2025 |
| 1212 | 2^1187356+44641 | 357430 | Enzo Doria | 06/2025 |
| 1213 | 2^1187005+230807 | 357325 | Enzo Doria | 01/2025 |
| 1214 | (50^210319-1)/49 | 357324 | Paul Bourdelais | 08/2020 |
| 1215 | (531^131072+25^131072)/2 | 357184 | Kellen Shenton | 03/2021 |
| 1216 | 2^1186366+226747 | 357132 | Enzo Doria | 09/2024 |
| 1217 | 2^1185014+241039 | 356725 | Enzo Doria | 09/2025 |
| 1218 | 2^1184565+21227 | 356590 | Enzo Doria | 08/2023 |
| 1219 | 2^1180312+44173 | 355310 | Enzo Doria | 04/2025 |
| 1220 | 2^1180159+22823 | 355264 | Enzo Doria | 11/2023 |
| 1221 | 2^1179944+238741 | 355199 | Enzo Doria | 07/2025 |
| 1222 | 2^1179836+1885021 | 355167 | Enzo Doria | 02/2017 |
| 1223 | 2^1178942+32269 | 354897 | Enzo Doria | 04/2024 |
| 1224 | 2^1178474+43369 | 354757 | Enzo Doria | 03/2025 |
| 1225 | 2^1177053+28607 | 354329 | Enzo Doria | 02/2024 |
| 1226 | 2^1177027+234863 | 354321 | Enzo Doria | 04/2025 |
| 1227 | (19*10^353884-91)/9 | 353885 | Alfred Reich | 02/2023 |
| 1228 | (10^353884*19-91)/9 | 353885 | Alfred Reich | 10/2023 |
| 1229 | 20^271951+3 | 353817 | Paul Bourdelais | 01/2021 |
| 1230 | 72722^72722+7^7 | 353551 | Serge Batalov | 04/2024 |
| 1231 | 2^1173095+21 | 353137 | Stefano Morozzi | 10/2022 |
| 1232 | 2^1170959+218945 | 352494 | Enzo Doria | 03/2024 |
| 1233 | 2^1170915+382623 | 352481 | Boyan Hu | 08/2024 |
| 1234 | (63^195893-1)/62 | 352477 | Paul Bourdelais | 08/2020 |
| 1235 | 2^1170575+238043 | 352379 | Enzo Doria | 07/2025 |
| 1236 | 2^1170331+27293 | 352305 | Enzo Doria | 01/2024 |
| 1237 | 2^1170326+7 | 352304 | Stefano Morozzi | 10/2022 |
| 1238 | numbpart(100000135540) | 352269 | Serge Batalov | 04/2017 |
| 1239 | (10^352237-1)/9/10567111/950335427 | 352221 | Maksym Voznyy | 01/2015 |
| 1240 | 5*3^737931-2^737931 | 352084 | Jon Grantham | 08/2023 |
| 1241 | 2^1168851+223613 | 351860 | Enzo Doria | 06/2024 |
| 1242 | 2^1168822+236449 | 351851 | Enzo Doria | 06/2025 |
| 1243 | 2^1168554+783529 | 351770 | Enzo Doria | 01/2017 |
| 1244 | (2^1168183-1)/54763676838381762583 | 351639 | Matthias Wurtinger | 01/2011 |
| 1245 | 2^1166950+30409 | 351287 | Enzo Doria | 03/2024 |
| 1246 | 2^1166563+223103 | 351171 | Enzo Doria | 05/2024 |
| 1247 | 2^1166248+38251 | 351076 | Enzo Doria | 11/2024 |
| 1248 | 2^1166152+1882411 | 351047 | Enzo Doria | 12/2016 |
| 1249 | 2^1163972+20971 | 350391 | Enzo Doria | 08/2023 |
| 1250 | 2^1163272+22411 | 350180 | Enzo Doria | 10/2023 |
