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 ? |
| 1251 | 10^350071+7 | 350072 | Alfred Reich | 05/2021 |
| 1252 | 2^1162154+1890207 | 349844 | Enzo Doria | 08/2017 |
| 1253 | 2^1161076+25 | 349519 | Henri Lifchitz | 01/2025 |
| 1254 | 2^1158543+239573 | 348757 | Enzo Doria | 08/2025 |
| 1255 | (7*10^348724-61)/9 | 348724 | Erik Branger | 09/2016 |
| 1256 | 2^1158213+52817 | 348657 | Enzo Doria | 11/2025 |
| 1257 | (4*10^348453+41)/9 | 348453 | Serge Batalov | 11/2022 |
| 1258 | (127^165601-1)/126 | 348390 | Alexander Zhirkov | 09/2015 |
| 1259 | 2^1156938+51289 | 348274 | Enzo Doria | 10/2025 |
| 1260 | 2^1155134+43909 | 347730 | Enzo Doria | 04/2025 |
| 1261 | 2^1155085+213377 | 347716 | Enzo Doria | 09/2023 |
| 1262 | 2^1153083+1883693 | 347113 | Enzo Doria | 04/2017 |
| 1263 | 2^1152186+225529 | 346843 | Enzo Doria | 07/2024 |
| 1264 | 2^1151973+52817 | 346779 | Enzo Doria | 11/2025 |
| 1265 | 2^1151782+42979 | 346721 | Enzo Doria | 02/2025 |
| 1266 | 2^1151754+41599 | 346713 | Enzo Doria | 02/2025 |
| 1267 | 2^1149592+49801 | 346062 | Enzo Doria | 09/2025 |
| 1268 | 2^1148995+50693 | 345882 | Enzo Doria | 09/2025 |
| 1269 | (2^1148729+2^574365+1)/5 | 345802 | Borys Jaworski | 03/2007 |
| 1270 | (19*10^345503+53)/9 | 345504 | Rytis Slatkevicius | 12/2024 |
| 1271 | 2^1145882+80779 | 344945 | Enzo Doria | 09/2016 |
| 1272 | 2^1145327+51893 | 344778 | Enzo Doria | 10/2025 |
| 1273 | 2^1143425+221177 | 344206 | Enzo Doria | 03/2024 |
| 1274 | 2^1141813+27047 | 343720 | Enzo Doria | 12/2023 |
| 1275 | 2^1141114+221869 | 343510 | Enzo Doria | 04/2024 |
| 1276 | 2^1139423+231083 | 343001 | Enzo Doria | 01/2025 |
| 1277 | 2^1138296+27541 | 342662 | Enzo Doria | 01/2024 |
| 1278 | 2^1136462+1887289 | 342110 | Enzo Doria | 05/2017 |
| 1279 | F(1636007) | 341905 | Henri Lifchitz | 03/2009 |
| 1280 | (2^1135567+13)/3 | 341840 | Stefano Morozzi | 09/2022 |
| 1281 | 2^1134873+223637 | 341631 | Enzo Doria | 06/2024 |
| 1282 | 2^1133678+782569 | 341272 | Enzo Doria | 11/2016 |
| 1283 | (11^327001+1)/12 | 340536 | Paul Bourdelais | 09/2013 |
| 1284 | 2^1130530+51799 | 340324 | Enzo Doria | 10/2025 |
| 1285 | 2^1129965+223667 | 340154 | Enzo Doria | 06/2024 |
| 1286 | 2^1129361+221597 | 339972 | Enzo Doria | 04/2024 |
| 1287 | 2^1128706+225529 | 339775 | Enzo Doria | 07/2024 |
| 1288 | 2^1128621+25919 | 339749 | Enzo Doria | 12/2023 |
| 1289 | 2^1127479+234083 | 339405 | Enzo Doria | 03/2025 |
| 1290 | (2^1127239+2^563620+1)/5 | 339333 | Borys Jaworski | 11/2006 |
| 1291 | Tau(907^20848) | 339132 | Nik Lygeros / Olivier Rozier | 01/2016 |
| 1292 | 2^1126380-3 | 339075 | Paul Bourdelais | 06/2019 |
| 1293 | 2^1125784+24331 | 338895 | Enzo Doria | 10/2023 |
| 1294 | 2^1125446+1885099 | 338794 | Enzo Doria | 08/2017 |
| 1295 | (63^188147+1)/64 | 338539 | Paul Bourdelais | 12/2020 |
| 1296 | 2^1124549+143807 | 338523 | Enzo Doria | 10/2016 |
| 1297 | (4*10^338476+23)/9 | 338476 | Serge Batalov | 11/2022 |
| 1298 | 2^1123484+50251 | 338203 | Enzo Doria | 08/2025 |
| 1299 | 2^1123295+240773 | 338146 | Enzo Doria | 09/2025 |
| 1300 | 2^1123083+237413 | 338082 | Enzo Doria | 06/2025 |
| 1301 | 2^1121187+1886783 | 337511 | Enzo Doria | 04/2017 |
| 1302 | (48^200443-1)/47 | 336992 | Paul Bourdelais | 08/2020 |
| 1303 | (2*10^336405+43)/9 | 336405 | Rytis Slatkevicius | 01/2023 |
| 1304 | (94^170371-1)/93 | 336162 | Paul Bourdelais | 09/2020 |
| 1305 | 2^1116184+1883521 | 336005 | Enzo Doria | 02/2017 |
| 1306 | 2^1115727+27683 | 335868 | Enzo Doria | 01/2024 |
| 1307 | 2^1114974+28759 | 335641 | Enzo Doria | 02/2024 |
| 1308 | 2^1114789+46427 | 335585 | Enzo Doria | 05/2025 |
| 1309 | 2^1114517+1880087 | 335504 | Enzo Doria | 10/2016 |
| 1310 | (5*10^335480+31)/9 | 335480 | Serge Batalov | 11/2022 |
| 1311 | 5*3^701688+2^701688 | 334791 | Jon Grantham | 08/2023 |
| 1312 | (101^166849+1)/102 | 334418 | Paul Bourdelais | 12/2020 |
| 1313 | (3^700897+1)/4 | 334413 | Paul Bourdelais | 04/2010 |
| 1314 | 2^1109520+48331 | 333999 | Enzo Doria | 07/2025 |
| 1315 | 2^1109200+223201 | 333903 | Enzo Doria | 05/2024 |
| 1316 | 2^1108463+32513 | 333681 | Enzo Doria | 05/2024 |
| 1317 | 2^1107871+240233 | 333503 | Enzo Doria | 08/2025 |
| 1318 | 2^1104500+22411 | 332488 | Enzo Doria | 10/2023 |
| 1319 | 2^1104408-114539 | 332460 | Enzo Doria | 03/2015 |
| 1320 | (3^695701-1)/80701318 | 331926 | Paul Vanderveen | 05/2025 |
| 1321 | 2^1101921+82085 | 331712 | Enzo Doria | 10/2016 |
| 1322 | 2^1101895+29963 | 331704 | Enzo Doria | 03/2024 |
| 1323 | 2^1101167-1101167^2 | 331485 | Henri Lifchitz | 07/2024 |
| 1324 | 2^1101091+224153 | 331462 | Enzo Doria | 06/2024 |
| 1325 | 2^1100655+683513 | 331331 | Enzo Doria | 01/2017 |
| 1326 | 2^1100590+50809 | 331311 | Enzo Doria | 09/2025 |
| 1327 | 2^1100373+48527 | 331246 | Enzo Doria | 07/2025 |
| 1328 | (10^330906+71)/9 | 330906 | Serge Batalov | 07/2015 |
| 1329 | 6^425185-425185^6 | 330859 | Henri Lifchitz | 06/2025 |
| 1330 | 2^1098346+482899 | 330636 | Enzo Doria | 11/2016 |
| 1331 | 2^1096976+25 | 330223 | Henri Lifchitz | 11/2024 |
| 1332 | (19*10^330041+53)/9 | 330042 | Rytis Slatkevicius | 12/2024 |
| 1333 | (2^1096212+19)/5 | 329992 | Stefano Morozzi | 09/2022 |
| 1334 | 2^1095976+44701 | 329922 | Enzo Doria | 05/2025 |
| 1335 | 2^1095820+239581 | 329875 | Enzo Doria | 08/2025 |
| 1336 | 2^1095679+1878713 | 329833 | Enzo Doria | 09/2016 |
| 1337 | 2^1094874+27499 | 329590 | Enzo Doria | 01/2024 |
| 1338 | 2^1094740-1851539 | 329550 | Enzo Doria | 08/2015 |
| 1339 | 2^1092242+19 | 328798 | Stefano Morozzi | 10/2022 |
| 1340 | (19*10^328590+53)/9 | 328591 | Rytis Slatkevicius | 12/2024 |
| 1341 | 2^1091469-379369 | 328565 | Enzo Doria | 03/2014 |
| 1342 | 2^1090801+24227 | 328364 | Enzo Doria | 10/2023 |
| 1343 | 2^1088416+237661 | 327646 | Enzo Doria | 06/2025 |
| 1344 | 2^1087944+39091 | 327504 | Enzo Doria | 11/2024 |
| 1345 | (69^178093-1)/68 | 327485 | Paul Bourdelais | 08/2020 |
| 1346 | 2^1086662+43909 | 327118 | Enzo Doria | 04/2025 |
| 1347 | (10^326884+7)/421 | 326882 | Alfred Reich | 12/2021 |
| 1348 | 2^1085876+48151 | 326882 | Enzo Doria | 06/2025 |
| 1349 | 2^1085750+582349 | 326844 | Enzo Doria | 11/2016 |
| 1350 | (54308^69169-1)/(54308^263-1) | 326261 | Ryan Propper | 11/2023 |
| 1351 | 2^1083596+483061 | 326195 | Enzo Doria | 12/2016 |
| 1352 | (2^541456-1)*10^162995+2^541455-1 | 325990 | paolo galliani | 01/2019 |
| 1353 | 2^1082908+583561 | 325988 | Enzo Doria | 05/2017 |
| 1354 | 30^220411-29^220411 | 325574 | Jean-Louis Charton | 10/2018 |
| 1355 | 2^1081308+7 | 325507 | Stefano Morozzi | 10/2022 |
| 1356 | 2^1080151+225413 | 325158 | Enzo Doria | 08/2024 |
| 1357 | 2^1080032+25171 | 325123 | Enzo Doria | 11/2023 |
| 1358 | 2^1078242+1881649 | 324584 | Enzo Doria | 11/2016 |
| 1359 | 2^1077737+1880117 | 324432 | Enzo Doria | 10/2016 |
| 1360 | 2^1076996+45631 | 324209 | Enzo Doria | 05/2025 |
| 1361 | 3^679017-5*2^679017 | 323974 | Jon Grantham | 08/2023 |
| 1362 | 2^1076006+29539 | 323911 | Enzo Doria | 03/2024 |
| 1363 | 2^1075573+32417 | 323780 | Enzo Doria | 05/2024 |
| 1364 | 2^1075425+1880117 | 323736 | Enzo Doria | 10/2016 |
| 1365 | (28^223381+1)/29 | 323267 | Paul Bourdelais | 12/2020 |
| 1366 | 10^322999+187071 | 323000 | Stefano Morozzi | 03/2019 |
| 1367 | 10^322999-143151 | 322999 | Patrick De Geest | 05/2020 |
| 1368 | 2^1072744+32641 | 322929 | Enzo Doria | 05/2024 |
| 1369 | 2^1072146+1886869 | 322749 | Enzo Doria | 04/2017 |
| 1370 | 2^1072118-7321953 | 322740 | Enzo Doria | 02/2015 |
| 1371 | 2025^97561-2024^97561 | 322579 | Henri Lifchitz | 01/2025 |
| 1372 | 2^1071026+1886869 | 322411 | Enzo Doria | 04/2017 |
| 1373 | 2^1070539+1880633 | 322265 | Enzo Doria | 10/2016 |
| 1374 | 2^1069894+235399 | 322071 | Enzo Doria | 05/2025 |
| 1375 | 2^1069788+26587 | 322039 | Enzo Doria | 12/2023 |
| 1376 | 2^1069293-1147195 | 321890 | Enzo Doria | 05/2015 |
| 1377 | 2^1065968+1880941 | 320889 | Enzo Doria | 10/2016 |
| 1378 | 2^1065897-1147195 | 320867 | Enzo Doria | 05/2015 |
| 1379 | 2^1063427+1882103 | 320124 | Enzo Doria | 12/2016 |
| 1380 | 2^1061095-1061095 | 319422 | Henri Lifchitz | 10/2013 |
| 1381 | 2^1060950+653119 | 319378 | Enzo Doria | 12/2016 |
| 1382 | 2^1060363+782753 | 319202 | Enzo Doria | 11/2016 |
| 1383 | 2^1060028+31771 | 319101 | Enzo Doria | 04/2024 |
| 1384 | (71^172259-1)/70 | 318895 | Paul Bourdelais | 08/2020 |
| 1385 | 2^1058425+38507 | 318618 | Enzo Doria | 11/2024 |
| 1386 | -30*Bern(85996)/236037521 | 318354 | Sergey Batalov | 10/2023 |
| 1387 | (13^285707-1)/870834948 | 318253 | Paul Vanderveen | 05/2025 |
| 1388 | 2^1055665+30407 | 317787 | Enzo Doria | 03/2024 |
| 1389 | 2^1054736+483061 | 317508 | Enzo Doria | 12/2016 |
| 1390 | 2^1053965+1879667 | 317276 | Enzo Doria | 10/2016 |
| 1391 | (43^194119-1)/42 | 317086 | Paul Bourdelais | 08/2020 |
| 1392 | 2^1052899+225413 | 316955 | Enzo Doria | 08/2024 |
| 1393 | 2^1052186-458165 | 316740 | Enzo Doria | 03/2015 |
| 1394 | 11^303909+2 | 316489 | Paul Bourdelais | 08/2023 |
| 1395 | 2^1049026+214609 | 315789 | Enzo Doria | 11/2023 |
| 1396 | 2^1048576+69661 | 315653 | Boyan Hu | 08/2024 |
| 1397 | 2^1046613-114685 | 315062 | Enzo Doria | 04/2015 |
| 1398 | 2^1045625-459373 | 314765 | Enzo Doria | 06/2015 |
| 1399 | 10^(2*157363+1)-8*10^157363-1 | 314727 | Robert Price | 07/2023 |
| 1400 | (7*10^314564-61)/9 | 314564 | Erik Branger | 09/2016 |
| 1401 | 2^1044771+228023 | 314508 | Enzo Doria | 11/2024 |
| 1402 | 2^1044206+7 | 314338 | Stefano Morozzi | 10/2022 |
| 1403 | (7^371669-1)/6 | 314096 | Paul Bourdelais | 02/2010 |
| 1404 | (53^181981-1)/52 | 313784 | Paul Bourdelais | 08/2020 |
| 1405 | (8^347437-5^347437)/3 | 313767 | Jon Grantham | 08/2023 |
| 1406 | (10^313741+1)/11/11294677 | 313733 | Alfred Reich | 04/2024 |
| 1407 | 2^1041944+283051 | 313657 | Enzo Doria | 12/2016 |
| 1408 | (1624^97969-1)/(1624^313-1) | 313533 | Sergey Batalov | 11/2023 |
| 1409 | 2^1041153-114391 | 313419 | Enzo Doria | 02/2015 |
| 1410 | (2^1039700+9)/5 | 312981 | Stefano Morozzi | 09/2022 |
| 1411 | (74^167311+1)/75 | 312742 | Paul Bourdelais | 12/2020 |
| 1412 | 2^1038871+1866983 | 312732 | Enzo Doria | 04/2016 |
| 1413 | 2^1038545+71657 | 312634 | Enzo Doria | 08/2023 |
| 1414 | (55^179573-1)/54 | 312521 | Paul Bourdelais | 08/2020 |
| 1415 | 2^1037647+1881263 | 312363 | Enzo Doria | 11/2016 |
| 1416 | 2^1037226+1879699 | 312237 | Enzo Doria | 10/2016 |
| 1417 | 2^1036867+1865843 | 312129 | Enzo Doria | 02/2016 |
| 1418 | (76^165947+1)/77 | 312114 | Paul Bourdelais | 01/2021 |
| 1419 | 2^1036324+39091 | 311965 | Enzo Doria | 11/2024 |
| 1420 | 2^1036020-114539 | 311874 | Enzo Doria | 02/2015 |
| 1421 | (90^159463-1)/89 | 311628 | Paul Bourdelais | 08/2020 |
| 1422 | 2^1034546+28819 | 311430 | Enzo Doria | 02/2024 |
| 1423 | 2^1032240+1883431 | 310736 | Enzo Doria | 01/2017 |
| 1424 | 64211^64588+64588^64211 | 310514 | Norbert Schneider | 11/2023 |
| 1425 | 2^1031450+29629 | 310498 | Enzo Doria | 03/2024 |
| 1426 | 2^1030352+1870021 | 310167 | Enzo Doria | 06/2016 |
| 1427 | 2^1030046+1882843 | 310075 | Enzo Doria | 11/2016 |
| 1428 | 2^1029120+227971 | 309796 | Enzo Doria | 11/2024 |
| 1429 | 3^648872+16 | 309591 | Robert Price | 04/2020 |
| 1430 | (16976^73441-1)/(16976^271-1) | 309498 | Ryan Propper | 11/2023 |
| 1431 | 64221^64366+64366^64221 | 309451 | Norbert Schneider | 06/2023 |
| 1432 | (11121^76729-1)/(11121^277-1) | 309336 | Ryan Propper | 11/2023 |
| 1433 | 2^1027478+219259 | 309302 | Enzo Doria | 02/2024 |
| 1434 | 2^1026999+20513 | 309158 | Enzo Doria | 07/2023 |
| 1435 | 5^442281+2 | 309142 | Paul Bourdelais | 01/2021 |
| 1436 | 2^1026204+22741 | 308919 | Enzo Doria | 09/2023 |
| 1437 | 2^1026190+15 | 308914 | Stefano Morozzi | 10/2022 |
| 1438 | 2^1025108+20851 | 308589 | Enzo Doria | 08/2023 |
| 1439 | 2^1022860+234121 | 307912 | Enzo Doria | 03/2025 |
| 1440 | A352736(16) | 306985 | Kellen Shenton | 05/2022 |
| 1441 | 2^1019777+213947 | 306984 | Enzo Doria | 10/2023 |
| 1442 | 2^1018820+236731 | 306696 | Enzo Doria | 05/2025 |
| 1443 | (11^293831-1)/10 | 305993 | Paul Bourdelais | 03/2010 |
| 1444 | (67^167449-1)/66 | 305773 | Paul Bourdelais | 08/2020 |
| 1445 | (62^170539+1)/63 | 305671 | Paul Bourdelais | 12/2020 |
| 1446 | 2^1015321-1015321 | 305643 | Henri Lifchitz | 08/2013 |
| 1447 | 2^1014775+27113 | 305478 | Enzo Doria | 12/2023 |
| 1448 | 2^1014450+7 | 305380 | Stefano Morozzi | 10/2022 |
| 1449 | 2^1014404+46171 | 305367 | Enzo Doria | 05/2025 |
| 1450 | 2^1014336+215731 | 305346 | Enzo Doria | 12/2023 |
| 1451 | 2^1014224-2791229 | 305312 | Enzo Doria | 01/2016 |
| 1452 | (10^304986+7)/673 | 304984 | Alfred Reich | 11/2021 |
| 1453 | 65473^45250+45250^65473 | 304818 | Hans Havermann | 02/2022 |
| 1454 | 66012^41423+41423^66012 | 304794 | Hans Havermann | 03/2022 |
| 1455 | 65073^48202+48202^65073 | 304742 | Hans Havermann | 04/2022 |
| 1456 | 2^1012054+31669 | 304659 | Enzo Doria | 06/2024 |
| 1457 | 238176^19+19^238176 | 304569 | Hans Havermann | 03/2022 |
| 1458 | 73122^14615+14615^73122 | 304539 | Hans Havermann | 05/2022 |
| 1459 | 64492^52639+52639^64492 | 304487 | Hans Havermann | 03/2022 |
| 1460 | 65955^41288+41288^65955 | 304437 | Hans Havermann | 04/2022 |
| 1461 | 71729^17530+17530^71729 | 304403 | Hans Havermann | 03/2022 |
| 1462 | 70170^21733+21733^70170 | 304336 | Hans Havermann | 03/2022 |
| 1463 | 2^1010751-107709 | 304267 | Enzo Doria | 03/2014 |
| 1464 | 84473^3994+3994^84473 | 304222 | Hans Havermann | 03/2022 |
| 1465 | (2^1010623-1)/12602017578957977 | 304212 | Tony Prest / Never Odd Or Even | 02/2014 |
| 1466 | 74442^12125+12125^74442 | 303998 | Hans Havermann | 02/2022 |
| 1467 | 77842^8039+8039^77842 | 303989 | Hans Havermann | 01/2022 |
| 1468 | 64209^54140+54140^64209 | 303935 | Hans Havermann | 02/2022 |
| 1469 | 2^1009577+1869587 | 303913 | Enzo Doria | 06/2016 |
| 1470 | 67389^32338+32338^67389 | 303906 | Hans Havermann | 02/2022 |
| 1471 | 8^336419-7^336419 | 303817 | Jean-Louis Charton | 01/2008 |
| 1472 | 2^1009168+15 | 303790 | Stefano Morozzi | 10/2022 |
| 1473 | 80766^5771+5771^80766 | 303782 | Hans Havermann | 01/2022 |
| 1474 | 66094^39385+39385^66094 | 303724 | Hans Havermann | 01/2022 |
| 1475 | 69147^24574+24574^69147 | 303589 | Hans Havermann | 02/2022 |
| 1476 | 78390^7459+7459^78390 | 303580 | Hans Havermann | 01/2022 |
| 1477 | 2^1008301+1869377 | 303529 | Enzo Doria | 06/2016 |
| 1478 | 65008^46615+46615^65008 | 303492 | Hans Havermann | 02/2022 |
| 1479 | (2^1007838+5)/3 | 303389 | Serge Batalov | 08/2015 |
| 1480 | 65018^46293+46293^65018 | 303343 | Hans Havermann | 01/2022 |
| 1481 | 6^389756+5 | 303290 | Paul Bourdelais | 02/2021 |
| 1482 | 71016^18649+18649^71016 | 303285 | Hans Havermann | 01/2022 |
| 1483 | 2^1007065+29231 | 303157 | Enzo Doria | 03/2024 |
| 1484 | 80160^6047+6047^80160 | 303129 | Hans Havermann | 01/2022 |
| 1485 | 67434^31237+31237^67434 | 303094 | Hans Havermann | 03/2022 |
| 1486 | 65537^42102+42102^65537 | 303063 | Hans Havermann | 02/2022 |
| 1487 | 71790^16553+16553^71790 | 302874 | Hans Havermann | 11/2021 |
| 1488 | 65208^44129+44129^65208 | 302874 | Hans Havermann | 11/2021 |
| 1489 | 84181^3960+3960^84181 | 302858 | Hans Havermann | 11/2021 |
| 1490 | (13703^73441-1)/(13703^271-1) | 302691 | Ryan Propper | 11/2023 |
| 1491 | 71956^16087+16087^71956 | 302682 | Hans Havermann | 11/2021 |
| 1492 | 2^1005326+383059 | 302634 | Enzo Doria | 12/2016 |
| 1493 | 2^1004929+1877567 | 302514 | Enzo Doria | 08/2016 |
| 1494 | 69341^22978+22978^69341 | 302418 | Hans Havermann | 12/2021 |
| 1495 | 111443^516+516^111443 | 302306 | Hans Havermann | 12/2021 |
| 1496 | 67638^29387+29387^67638 | 302218 | Hans Havermann | 11/2021 |
| 1497 | 2^1003494+1874899 | 302082 | Enzo Doria | 06/2016 |
| 1498 | 75189^10400+10400^75189 | 302037 | Hans Havermann | 12/2021 |
| 1499 | 67237^31042+31042^67237 | 302026 | Hans Havermann | 12/2021 |
| 1500 | 64540^47791+47791^64540 | 302005 | Hans Havermann | 11/2021 |
