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 ? |
1251 | 3*10^182614-11 | 182615 | Robert Price | 07/2018 |
1252 | 2^606560-357 | 182593 | Enzo Doria | 05/2014 |
1253 | 66*10^182420+7 | 182422 | Robert Price | 07/2020 |
1254 | 2^605687+1866983 | 182330 | Enzo Doria | 03/2016 |
1255 | 2^605655-114445 | 182321 | Enzo Doria | 02/2015 |
1256 | 94*10^182291-3 | 182293 | Robert Price | 05/2020 |
1257 | (20^140053+1)/21 | 182212 | Paul Bourdelais | 04/2010 |
1258 | (14*10^182177-221)/9 | 182178 | Robert Price | 04/2018 |
1259 | 2^605174-112751 | 182176 | Enzo Doria | 06/2014 |
1260 | 2^604761+1874507 | 182052 | Enzo Doria | 06/2016 |
1261 | 2^604705+1871957 | 182035 | Enzo Doria | 05/2016 |
1262 | (14*10^182000+229)/9 | 182001 | Robert Price | 03/2018 |
1263 | (10^181996+41)/3 | 181996 | Robert Price | 12/2017 |
1264 | (5*10^181950-101)/3 | 181951 | Robert Price | 04/2018 |
1265 | 2^603915+75233 | 181797 | Enzo Doria | 04/2016 |
1266 | 7*10^181594-57 | 181595 | Robert Price | 06/2020 |
1267 | (194*10^181369-11)/3 | 181371 | Robert Price | 09/2020 |
1268 | 11^174145-360 | 181354 | Enzo Doria | 10/2012 |
1269 | 2^602351-396765 | 181326 | Enzo Doria | 08/2013 |
1270 | 6*10^181306+17 | 181307 | Robert Price | 04/2019 |
1271 | (286*10^181220-1)/3 | 181222 | Robert Price | 11/2020 |
1272 | 2^601957-113833 | 181208 | Enzo Doria | 09/2014 |
1273 | 66^99581-65^99581 | 181193 | Robert Price | 09/2013 |
1274 | 10^181182+383973 | 181183 | Patrick De Geest | 04/2016 |
1275 | 10^181182-21 | 181182 | Serge Batalov | 12/2014 |
1276 | (5*10^181127-29)/3 | 181128 | Robert Price | 03/2018 |
1277 | 2^601521-29143 | 181076 | Enzo Doria | 07/2015 |
1278 | 2^601442-2797811 | 181053 | Enzo Doria | 04/2016 |
1279 | 44*10^181029+3 | 181031 | Robert Price | 04/2020 |
1280 | 5*10^180992-9 | 180993 | Robert Price | 05/2015 |
1281 | 10^180979+79477 | 180980 | Patrick De Geest | 04/2016 |
1282 | 10^180979+107739 | 180980 | Patrick De Geest | 04/2016 |
1283 | 10^180979-11 | 180979 | Serge Batalov | 12/2014 |
1284 | 2^601023-113851 | 180926 | Enzo Doria | 10/2014 |
1285 | (23*10^180862-143)/3 | 180863 | Robert Price | 12/2019 |
1286 | 3*10^180852+29 | 180853 | Robert Price | 05/2018 |
1287 | (79*10^180710-1)/3 | 180712 | Robert Price | 02/2020 |
1288 | 2^600300-1852559 | 180709 | Enzo Doria | 08/2015 |
1289 | (10^180689+71)/9 | 180689 | Serge Batalov | 07/2015 |
1290 | 2^600209+76487 | 180681 | Enzo Doria | 05/2016 |
1291 | 2^599702-369885 | 180529 | Enzo Doria | 11/2013 |
1292 | Tau(643^11688) | 180524 | Nik Lygeros / Olivier Rozier | 05/2015 |
1293 | (2951*29^123418-3)/4 | 180490 | Curtis Bright | 05/2015 |
1294 | (29*10^180432-17)/3 | 180433 | Robert Price | 09/2019 |
1295 | 4*10^180360+93 | 180361 | Robert Price | 08/2018 |
1296 | 2^598942+80779 | 180300 | Enzo Doria | 07/2016 |
1297 | (38*10^180296+403)/9 | 180297 | Robert Price | 10/2018 |
1298 | 2^598591-1844797 | 180194 | Enzo Doria | 06/2015 |
1299 | (100^90089+1)/101 | 180176 | Paul Bourdelais | 08/2017 |
1300 | 6*10^179970+91 | 179971 | Robert Price | 05/2019 |
1301 | (4*10^179963-79)/3 | 179964 | Robert Price | 02/2018 |
1302 | Gamma-Prime(179849) | 179849 | Eric W. Weisstein | 06/2011 |
1303 | 2^597424-1859729 | 179843 | Enzo Doria | 11/2015 |
1304 | Phi(180683,10) | 179760 | Maksym Voznyy | 09/2015 |
1305 | (10^180683-1)*9/(10^643-1)/(10^281-1) | 179760 | Robert Price | 07/2016 |
1306 | (3^376657-2^376657)/22301107657 | 179701 | Mike Oakes | 04/2017 |
1307 | (29*10^179697+223)/9 | 179698 | Robert Price | 09/2018 |
1308 | (68*10^179656+7)/3 | 179658 | Robert Price | 01/2020 |
1309 | 2^596690-461261 | 179622 | Enzo Doria | 07/2015 |
1310 | 2^596684-113939 | 179620 | Enzo Doria | 10/2014 |
1311 | 2*10^179602+63 | 179603 | Robert Price | 05/2018 |
1312 | (25*10^179488-403)/9 | 179489 | Robert Price | 01/2021 |
1313 | 3^375887-112696 | 179344 | Enzo Doria | 07/2014 |
1314 | 4*10^179265-71 | 179266 | Robert Price | 12/2018 |
1315 | 2^595144-1850429 | 179157 | Enzo Doria | 08/2015 |
1316 | 3*10^179138+89 | 179139 | Robert Price | 10/2018 |
1317 | 2^594531+82253 | 178972 | Enzo Doria | 09/2016 |
1318 | 2^594260-2787899 | 178891 | Enzo Doria | 11/2015 |
1319 | 2^593631+101381 | 178701 | Jorge Menendez | 04/2018 |
1320 | 10^178695+136719 | 178696 | Patrick De Geest | 05/2016 |
1321 | 10^178695-71 | 178695 | Serge Batalov | 12/2014 |
1322 | (2*10^178649-161)/3 | 178649 | Robert Price | 12/2020 |
1323 | (691^62903-1)/690 | 178609 | Michael Stocker | 05/2020 |
1324 | (2^148330+1)^4-2 | 178608 | Cletus Emmanuel | 12/2003 |
1325 | 2^593222-14145 | 178578 | Jorge Menendez | 10/2017 |
1326 | 7*10^178566+33 | 178567 | Robert Price | 06/2020 |
1327 | 2^593178+1867219 | 178565 | Enzo Doria | 03/2016 |
1328 | (302*10^178369+13)/9 | 178371 | Robert Price | 02/2020 |
1329 | (26*10^178296-113)/3 | 178297 | Robert Price | 06/2020 |
1330 | (18^142031-1)/17 | 178287 | Paul Bourdelais | 03/2010 |
1331 | (5*10^178206+91)/3 | 178207 | Robert Price | 04/2018 |
1332 | 2^591872-291929 | 178172 | Enzo Doria | 07/2015 |
1333 | 2^591682-286871 | 178115 | Enzo Doria | 07/2015 |
1334 | 4*10^178091+9 | 178092 | Robert Price | 05/2015 |
1335 | 410747#+478483 | 178007 | Makoto Morimoto | 02/2016 |
1336 | 3*10^177872+73 | 177873 | Robert Price | 08/2018 |
1337 | 2^590762-396765 | 177838 | Enzo Doria | 08/2013 |
1338 | (136*10^177754-1)/9 | 177756 | Serge Batalov | 12/2014 |
1339 | ReverseConsecutiveIntegerPrime(37765) | 177719 | Eric W. Weisstein | 04/2010 |
1340 | (266*10^177577-11)/3 | 177579 | Robert Price | 04/2020 |
1341 | (11*10^177466-113)/3 | 177467 | Robert Price | 10/2018 |
1342 | 3*10^177373-97 | 177374 | Robert Price | 07/2018 |
1343 | 2^589204+1881151 | 177369 | Enzo Doria | 11/2016 |
1344 | 2^589132-69479 | 177347 | Enzo Doria | 01/2016 |
1345 | (101*10^177302-17)/3 | 177304 | Robert Price | 02/2020 |
1346 | 2^588912-113519 | 177281 | Enzo Doria | 08/2014 |
1347 | 15^150706+2 | 177245 | Robert Price | 06/2015 |
1348 | 2^588194-1861001 | 177065 | Enzo Doria | 11/2015 |
1349 | (23*10^176964-47)/3 | 176965 | Robert Price | 09/2019 |
1350 | (19*10^176932+521)/9 | 176933 | Robert Price | 05/2018 |
1351 | (8*10^176908+43)/3 | 176909 | Robert Price | 06/2018 |
1352 | (85*10^176900+203)/9 | 176901 | Robert Price | 09/2020 |
1353 | 2^587560-113699 | 176874 | Enzo Doria | 09/2014 |
1354 | (101*10^176815-17)/3 | 176817 | Robert Price | 02/2020 |
1355 | (25*10^176715-37)/3 | 176716 | Robert Price | 10/2019 |
1356 | 5^252763-12862 | 176674 | Enzo Doria | 05/2014 |
1357 | 2^586804+81721 | 176646 | Enzo Doria | 08/2016 |
1358 | (10^176584+77)/3 | 176584 | Robert Price | 01/2018 |
1359 | 2^586570+1874419 | 176576 | Enzo Doria | 06/2016 |
1360 | 2^585994-3311 | 176402 | Yves Minet | 12/2014 |
1361 | 2^585832-112799 | 176354 | Enzo Doria | 07/2014 |
1362 | 2^585336-461039 | 176204 | Enzo Doria | 06/2015 |
1363 | (25*10^176164+143)/3 | 176165 | Robert Price | 08/2020 |
1364 | 2^585095-1848127 | 176132 | Enzo Doria | 08/2015 |
1365 | 6*10^176092+77 | 176093 | Robert Price | 06/2020 |
1366 | 2^584950-115451 | 176088 | Enzo Doria | 07/2015 |
1367 | 2^584671-3697 | 176004 | Yves Minet | 03/2017 |
1368 | (13*10^175965-37)/3 | 175966 | Robert Price | 01/2019 |
1369 | 2*10^175860-87 | 175861 | Robert Price | 04/2018 |
1370 | (86*10^175774-221)/9 | 175775 | Robert Price | 09/2019 |
1371 | 10^175608+2971 | 175609 | Mike Oakes | 05/2010 |
1372 | 10^175608-55829 | 175608 | Patrick De Geest | 09/2013 |
1373 | 2^583051+1879793 | 175516 | Enzo Doria | 09/2016 |
1374 | 2^582860-23829 | 175459 | Enzo Doria | 08/2013 |
1375 | (28*10^175417-67)/3 | 175418 | Robert Price | 10/2020 |
1376 | 2^582670-23913 | 175402 | Enzo Doria | 08/2013 |
1377 | 2^582573-29563 | 175372 | Enzo Doria | 08/2015 |
1378 | 2^582435-1862767 | 175331 | Enzo Doria | 12/2015 |
1379 | (11*10^175250-149)/3 | 175251 | Robert Price | 09/2018 |
1380 | 2^582072-1848599 | 175222 | Enzo Doria | 08/2015 |
1381 | (404267#+465)/(3^4*5^2*31) | 175208 | Makoto Morimoto | 06/2019 |
1382 | (220221^32768+1)/2 | 175075 | Serge Batalov | 03/2018 |
1383 | 2^581560+1874911 | 175068 | Enzo Doria | 06/2016 |
1384 | (75^93307-1)/74 | 174955 | Paul Bourdelais | 09/2017 |
1385 | (47*10^174790+493)/9 | 174791 | Robert Price | 03/2019 |
1386 | 2^580528-114035 | 174757 | Enzo Doria | 11/2014 |
1387 | (19*10^174754+737)/9 | 174755 | Robert Price | 07/2018 |
1388 | (35*10^174704-377)/9 | 174705 | Robert Price | 07/2018 |
1389 | 3*10^174665-97 | 174666 | Robert Price | 07/2018 |
1390 | 2^580046-459161 | 174612 | Enzo Doria | 05/2015 |
1391 | 2^579992-39779 | 174595 | Enzo Doria | 09/2015 |
1392 | (2*10^174301-71)/3 | 174301 | Robert Price | 12/2017 |
1393 | 14^152048+3 | 174267 | Paul Bourdelais | 12/2020 |
1394 | (2^578696+1)/257 | 174203 | Lelio R Paula | 09/2015 |
1395 | 2^578656-1851809 | 174193 | Enzo Doria | 08/2015 |
1396 | 2^578583-113917 | 174171 | Enzo Doria | 10/2014 |
1397 | 2^578434-83 | 174126 | Yves Minet | 07/2017 |
1398 | 15^148048-2 | 174118 | Robert Price | 06/2015 |
1399 | 5*10^174101+81 | 174102 | Robert Price | 03/2019 |
1400 | 2^578346+2794249 | 174100 | Enzo Doria | 03/2016 |
1401 | 10^173947-500000001 | 173947 | Robert Price | 12/2020 |
1402 | 5*10^173904-13 | 173905 | Robert Price | 01/2019 |
1403 | (71*10^173854-287)/9 | 173855 | Robert Price | 09/2019 |
1404 | (43*10^173826+101)/9 | 173827 | Robert Price | 11/2018 |
1405 | 2*10^173809-87 | 173810 | Robert Price | 04/2018 |
1406 | (L!41532)/2 | 173772 | Serge Batalov | 07/2017 |
1407 | 2^577146-49877 | 173739 | Enzo Doria | 10/2015 |
1408 | 2^576889+49727 | 173661 | Enzo Doria | 09/2016 |
1409 | (167*10^173571-17)/3 | 173573 | Robert Price | 03/2020 |
1410 | 5*10^173534+29 | 173535 | Robert Price | 12/2020 |
1411 | (2^576551-1)/4612409/64758208321/242584327930759 | 173528 | Dario Alpern | 06/2014 |
1412 | 4*10^173509+99 | 173510 | Robert Price | 12/2020 |
1413 | (13*10^173467-37)/3 | 173468 | Robert Price | 01/2019 |
1414 | 2^576016-113919 | 173399 | Enzo Doria | 11/2014 |
1415 | 2^575911-1849387 | 173367 | Enzo Doria | 08/2015 |
1416 | (16*10^173251+107)/3 | 173252 | Robert Price | 03/2019 |
1417 | 2^575196-114053 | 173152 | Enzo Doria | 11/2014 |
1418 | 7*10^173135-53 | 173136 | Robert Price | 06/2020 |
1419 | 2^574591-115387 | 172970 | Enzo Doria | 07/2015 |
1420 | (202*10^172940-13)/9 | 172942 | Robert Price | 01/2020 |
1421 | 2^574328+81121 | 172890 | Enzo Doria | 07/2016 |
1422 | (115*10^172862-1)/3 | 172864 | Serge Batalov | 12/2014 |
1423 | 3*10^172812+13 | 172813 | Robert Price | 07/2018 |
1424 | 4*5^247217-9 | 172798 | Lelio R Paula | 10/2015 |
1425 | 6*10^172772-31 | 172773 | Robert Price | 07/2020 |
1426 | 69061#+(467617#)/(69061#) | 172766 | Makoto Morimoto | 10/2017 |
1427 | 5*10^172692+57 | 172693 | Robert Price | 12/2018 |
1428 | 2^573668-2782319 | 172692 | Enzo Doria | 09/2015 |
1429 | 2^573444-1855109 | 172624 | Enzo Doria | 09/2015 |
1430 | 3^361608+2 | 172531 | Robert Price | 08/2014 |
1431 | (54^99563+1)/55 | 172481 | Paul Bourdelais | 11/2017 |
1432 | 2^572592-114893 | 172368 | Enzo Doria | 05/2015 |
1433 | 4*10^172354-39 | 172355 | Robert Price | 09/2020 |
1434 | 5^246497-4^246497 | 172295 | Jean-Louis Charton | 11/2008 |
1435 | (38^109037-1)/37 | 172254 | Paul Bourdelais | 10/2017 |
1436 | 3*10^172219+73 | 172220 | Robert Price | 08/2018 |
1437 | (36^110503+1)/37 | 171975 | Lelio R Paula | 04/2017 |
1438 | (22*10^171929-73)/3 | 171930 | Robert Price | 04/2019 |
1439 | 4*10^171891-63 | 171892 | Robert Price | 10/2018 |
1440 | 2^570980-2782289 | 171883 | Enzo Doria | 09/2015 |
1441 | (25*10^171849-37)/3 | 171850 | Robert Price | 10/2019 |
1442 | (2^(12*47563+13)-9)/7 | 171818 | Kevin Acres | 11/2013 |
1443 | (536*10^171601-23)/9 | 171603 | Robert Price | 02/2020 |
1444 | 7*10^171535-99 | 171536 | Robert Price | 06/2019 |
1445 | (28*10^171534+101)/3 | 171535 | Robert Price | 09/2020 |
1446 | 2^569563-1854607 | 171456 | Enzo Doria | 09/2015 |
1447 | 3*10^171391+59 | 171392 | Robert Price | 08/2018 |
1448 | (13*10^171306-37)/3 | 171307 | Robert Price | 01/2019 |
1449 | 8*10^171296+87 | 171297 | Robert Price | 10/2019 |
1450 | (55^98419-1)/54 | 171284 | Paul Bourdelais | 12/2017 |
1451 | (29*10^171275+67)/3 | 171276 | Robert Price | 12/2019 |
1452 | 2^568642+1876129 | 171179 | Enzo Doria | 07/2016 |
1453 | (19*10^170970+131)/3 | 170971 | Robert Price | 06/2020 |
1454 | (46*10^170932+143)/9 | 170933 | Robert Price | 01/2019 |
1455 | (79*10^170901-1)/3 | 170903 | Robert Price | 02/2020 |
1456 | (58*10^170842+221)/9 | 170843 | Robert Price | 02/2017 |
1457 | 3*10^170800+73 | 170801 | Robert Price | 08/2018 |
1458 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
1459 | 2*10^170767+41 | 170768 | Robert Price | 05/2018 |
1460 | 3^357706-112358 | 170670 | Enzo Doria | 07/2014 |
1461 | TheodorusPrime(170657) | 170657 | Eric W. Weisstein | 08/2013 |
1462 | 2^566871+1876163 | 170646 | Enzo Doria | 07/2016 |
1463 | (10657#+(404267#)/(10657#))/(1675379) | 170624 | Makoto Morimoto | 10/2017 |
1464 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
1465 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
1466 | 7*10^170348+33 | 170349 | Robert Price | 06/2020 |
1467 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
1468 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
1469 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
1470 | (7*10^169944+23)/3 | 169945 | Robert Price | 06/2020 |
1471 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
1472 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
1473 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
1474 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
1475 | (194*10^169461-17)/3 | 169463 | Robert Price | 09/2020 |
1476 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
1477 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
1478 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
1479 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
1480 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
1481 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
1482 | 2^560405-39943 | 168699 | Enzo Doria | 09/2015 |
1483 | 89*10^168614-7 | 168616 | Robert Price | 04/2020 |
1484 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
1485 | (94*10^168541+11)/3 | 168543 | Robert Price | 04/2020 |
1486 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
1487 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
1488 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
1489 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
1490 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
1491 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
1492 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
1493 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
1494 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
1495 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
1496 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
1497 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
1498 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
1499 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
1500 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |