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 ? |
1251 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
1252 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
1253 | 2^670133+89 | 201731 | Stefano Morozzi | 05/2021 |
1254 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
1255 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
1256 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
1257 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
1258 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
1259 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
1260 | 10194^50161-50161^10194 | 201063 | Norbert Schneider | 09/2020 |
1261 | 2^667894+1875589 | 201057 | Enzo Doria | 06/2016 |
1262 | 2^667569-1836559 | 200959 | Enzo Doria | 05/2015 |
1263 | (172*10^200746-1)/9 | 200748 | Serge Batalov | 12/2014 |
1264 | 2^666430+782569 | 200616 | Enzo Doria | 10/2016 |
1265 | (86^103471+1)/87 | 200163 | Paul Bourdelais | 05/2018 |
1266 | 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 | 200003 | Robert Price | 05/2017 |
1267 | 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 | 200003 | Robert Price | 01/2018 |
1268 | numbpart(32235776596) | 200002 | Serge Batalov | 04/2017 |
1269 | (10^200001+149)/3 | 200001 | Serge Batalov | 12/2014 |
1270 | 10^200000+571791 | 200001 | Patrick De Geest | 08/2019 |
1271 | (3^419180-621444)/3 | 200000 | Stefano Morozzi | 06/2019 |
1272 | (3^419180-1941384)/3 | 200000 | Stefano Morozzi | 08/2019 |
1273 | 10^200000-45557 | 200000 | Patrick De Geest | 08/2019 |
1274 | (10^200000-1)/9-10^58838 | 200000 | Akihiko Yoshida | 04/2020 |
1275 | 2593604092947240127723272^8192+2593604092947240127722755^8192 | 200000 | Youcef Lemsafer | 01/2023 |
1276 | (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 | 199999 | Youcef Lemsafer | 01/2023 |
1277 | (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 | 199994 | Youcef Lemsafer | 01/2023 |
1278 | (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 | 199989 | Youcef Lemsafer | 01/2023 |
1279 | (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 | 199986 | Youcef Lemsafer | 01/2023 |
1280 | 92*10^199980-9 | 199982 | Robert Price | 12/2021 |
1281 | (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 | 199977 | Youcef Lemsafer | 01/2023 |
1282 | (85*10^199951-139)/9 | 199952 | Robert Price | 08/2021 |
1283 | (10^199926+7)/29/373/2339 | 199919 | Alfred Reich | 08/2021 |
1284 | 23*10^199833-9 | 199835 | Robert Price | 10/2021 |
1285 | (299*10^199801-17)/3 | 199803 | Robert Price | 04/2020 |
1286 | 6*10^199788+77 | 199789 | Robert Price | 06/2020 |
1287 | (23*10^199615+37)/3 | 199616 | Robert Price | 02/2022 |
1288 | (17*10^199607-167)/3 | 199608 | Robert Price | 05/2022 |
1289 | 2^663020-933075 | 199589 | Paul Bourdelais | 06/2021 |
1290 | (14*10^199447+73)/3 | 199448 | Robert Price | 12/2018 |
1291 | (2^662424-15)/7 | 199409 | Stefano Morozzi | 08/2022 |
1292 | 2^662103-29287 | 199313 | Enzo Doria | 08/2015 |
1293 | (2*10^199283+457)/9 | 199283 | Robert Price | 01/2018 |
1294 | (10^199248-19)/9 | 199248 | Robert Price | 01/2018 |
1295 | (83*10^199213+529)/9 | 199214 | Robert Price | 12/2021 |
1296 | (194*10^199146-17)/3 | 199148 | Robert Price | 09/2020 |
1297 | (151*10^199003-1)/3 | 199005 | Robert Price | 03/2020 |
1298 | 9*10^198946-73 | 198947 | Robert Price | 01/2021 |
1299 | 45*10^198931-7 | 198933 | Robert Price | 07/2020 |
1300 | 2^660482-2891 | 198825 | Yves Minet | 05/2016 |
1301 | 2^659589-21 | 198557 | Stefano Morozzi | 07/2022 |
1302 | 2^659583+1879223 | 198555 | Enzo Doria | 08/2016 |
1303 | (53*10^198529+1)/9 | 198530 | Serge Batalov | 07/2010 |
1304 | (49*10^198403+311)/9 | 198404 | Robert Price | 06/2019 |
1305 | 96*10^198376-7 | 198378 | Robert Price | 03/2021 |
1306 | (10^198375+7)/59/1201/87589 | 198366 | Alfred Reich | 08/2021 |
1307 | 2^658828-29819 | 198327 | Enzo Doria | 08/2015 |
1308 | 2^658776-2791229 | 198312 | Enzo Doria | 01/2016 |
1309 | (35*10^198294-377)/9 | 198295 | Robert Price | 07/2018 |
1310 | (4*10^198268+137)/3 | 198269 | Robert Price | 03/2018 |
1311 | 2^658544-1854029 | 198242 | Enzo Doria | 09/2015 |
1312 | (62*10^198229-233)/9 | 198230 | Robert Price | 02/2022 |
1313 | (26*10^198200-41)/3 | 198201 | Robert Price | 02/2022 |
1314 | (157^90239-1)/156 | 198154 | Alexander Zhirkov | 06/2016 |
1315 | 2*10^197959-37 | 197960 | Robert Price | 11/2021 |
1316 | (232*10^197897+17)/3 | 197899 | Robert Price | 04/2021 |
1317 | (4*10^197778+173)/3 | 197779 | Robert Price | 02/2018 |
1318 | 78*10^197702-7 | 197704 | Robert Price | 10/2020 |
1319 | (17*10^197640-23)/3 | 197641 | Robert Price | 03/2021 |
1320 | (29*10^197629-77)/3 | 197630 | Robert Price | 02/2020 |
1321 | 2^656462+1874419 | 197615 | Enzo Doria | 06/2016 |
1322 | (89^101363+1)/90 | 197595 | Paul Bourdelais | 11/2017 |
1323 | 2^655893-344563 | 197444 | Enzo Doria | 07/2015 |
1324 | 2^655875+71333 | 197439 | Enzo Doria | 04/2016 |
1325 | 2^655845-9 | 197430 | Robert Price | 01/2017 |
1326 | (299*10^197426+1)/3 | 197428 | Robert Price | 04/2020 |
1327 | 2^655682-1849121 | 197380 | Enzo Doria | 08/2015 |
1328 | 4*10^197268-89 | 197269 | Robert Price | 11/2018 |
1329 | (11*10^197198-89)/3 | 197199 | Robert Price | 05/2021 |
1330 | 2^655045-49603 | 197189 | Enzo Doria | 10/2015 |
1331 | 2^655000-2784089 | 197175 | Enzo Doria | 10/2015 |
1332 | (18^157051-1)/17 | 197141 | Paul Bourdelais | 03/2010 |
1333 | (4*10^197061+41)/9 | 197061 | Serge Batalov | 11/2022 |
1334 | (154*10^197005+17)/9 | 197007 | Robert Price | 06/2022 |
1335 | 2^654400-39719 | 196995 | Enzo Doria | 09/2015 |
1336 | (14*10^196965-221)/9 | 196966 | Robert Price | 04/2018 |
1337 | 2^654216-459995 | 196939 | Enzo Doria | 06/2015 |
1338 | (17*10^196921+31)/3 | 196922 | Robert Price | 01/2019 |
1339 | (14*10^196885-89)/3 | 196886 | Robert Price | 05/2020 |
1340 | 3*10^196881-59 | 196882 | Robert Price | 09/2018 |
1341 | 2^653851+82295 | 196829 | Enzo Doria | 09/2016 |
1342 | (38*10^196792+691)/9 | 196793 | Robert Price | 10/2018 |
1343 | (65*10^196768+493)/9 | 196769 | Robert Price | 08/2021 |
1345 | 2^653636-29429 | 196765 | Enzo Doria | 08/2015 |
1344 | 2^653638-11 | 196765 | Stefano Morozzi | 07/2022 |
1346 | 2^653601-69673 | 196754 | Enzo Doria | 02/2016 |
1347 | (44*10^196684+1)/9 | 196685 | Serge Batalov | 07/2010 |
1348 | 2^652786-1852571 | 196509 | Enzo Doria | 08/2015 |
1349 | 2^652752-1325 | 196498 | Yves Minet | 07/2015 |
1350 | 2^652470-1859141 | 196414 | Enzo Doria | 10/2015 |
1351 | 2^652307+1877483 | 196364 | Enzo Doria | 08/2016 |
1352 | 2^652293-115273 | 196360 | Enzo Doria | 06/2015 |
1353 | (47*10^196281+403)/9 | 196282 | Robert Price | 03/2019 |
1354 | (7*10^196125-31)/3 | 196126 | Robert Price | 12/2021 |
1355 | 33^129128+129128^33 | 196083 | Norbert Schneider | 06/2022 |
1356 | 6*10^196070+73 | 196071 | Robert Price | 04/2019 |
1357 | 2^651218-1868201 | 196037 | Enzo Doria | 04/2016 |
1358 | 2^651047-49687 | 195985 | Enzo Doria | 10/2015 |
1359 | 10^195968-700001 | 195968 | Robert Price | 08/2021 |
1360 | (29*10^195875-197)/3 | 195876 | Robert Price | 08/2021 |
1361 | (25*10^195808-97)/9 | 195809 | Robert Price | 01/2022 |
1362 | 2^650285-2785333 | 195756 | Enzo Doria | 10/2015 |
1363 | (10^195732+7)/18089/49605893 | 195721 | Alfred Reich | 08/2021 |
1364 | (69^106397-1)/68 | 195647 | Paul Bourdelais | 10/2017 |
1365 | 2^649811+1877573 | 195613 | Enzo Doria | 08/2016 |
1366 | 2^649662-170531 | 195568 | Hans Havermann | 10/2018 |
1367 | 2^649586+182839 | 195545 | Enzo Doria | 11/2016 |
1368 | 2^649537-1867363 | 195531 | Enzo Doria | 04/2016 |
1369 | 2^649536-1861499 | 195530 | Enzo Doria | 12/2015 |
1370 | (103*10^195478-1)/3 | 195480 | Serge Batalov | 12/2014 |
1371 | 2^649102-59351 | 195400 | Enzo Doria | 10/2015 |
1372 | (2*10^195399+529)/9 | 195399 | Robert Price | 01/2018 |
1373 | (202*10^195383-13)/9 | 195385 | Robert Price | 01/2020 |
1374 | 2^648988+1178971 | 195365 | Enzo Doria | 06/2016 |
1375 | 2^648975-114319 | 195361 | Enzo Doria | 02/2015 |
1376 | (11*10^195350-137)/9 | 195351 | Robert Price | 01/2018 |
1377 | 2^648619-24835 | 195254 | Enzo Doria | 09/2013 |
1378 | 5*10^195250-21 | 195251 | Robert Price | 12/2021 |
1379 | (14*10^195234-83)/3 | 195235 | Robert Price | 12/2018 |
1380 | 5*10^195221+81 | 195222 | Robert Price | 03/2019 |
1381 | 10^195143-5001 | 195143 | Robert Price | 12/2021 |
1382 | 2^648190-24737 | 195125 | Enzo Doria | 09/2013 |
1383 | (57^111119+1)/58 | 195110 | Paul Bourdelais | 10/2017 |
1384 | (29*10^195098-197)/3 | 195099 | Robert Price | 08/2021 |
1385 | 10^195060+89701 | 195061 | Patrick De Geest | 02/2021 |
1387 | 10^195060-40000000001 | 195060 | Robert Price | 09/2020 |
1386 | 10^195060-110337 | 195060 | Patrick De Geest | 02/2021 |
1388 | 56*10^195032-3 | 195034 | Robert Price | 03/2020 |
1389 | 11^187185-90 | 194934 | Enzo Doria | 09/2012 |
1390 | (86*10^194818-437)/9 | 194819 | Robert Price | 03/2021 |
1391 | 2^647068+77281 | 194787 | Enzo Doria | 05/2016 |
1392 | 2*10^194716-93 | 194717 | Robert Price | 12/2021 |
1393 | 15^165559-14^165559 | 194713 | Jean-Louis Charton | 03/2011 |
1394 | F(931517) | 194676 | Henri Lifchitz | 09/2008 |
1395 | 4*10^194668+49 | 194669 | Robert Price | 01/2019 |
1396 | 2^646589+1179407 | 194643 | Enzo Doria | 06/2016 |
1397 | 2^646289-114621 | 194553 | Enzo Doria | 05/2015 |
1398 | 2^646236-39659 | 194537 | Enzo Doria | 09/2015 |
1399 | (16*10^194536+53)/3 | 194537 | Robert Price | 03/2019 |
1400 | 2^646161-59833 | 194514 | Enzo Doria | 11/2015 |
1401 | (17*10^194502+31)/3 | 194503 | Robert Price | 01/2019 |
1402 | (19*10^194428+287)/9 | 194429 | Robert Price | 10/2021 |
1403 | 2*10^194413+3 | 194414 | Robert Price | 07/2015 |
1404 | 2^645360-1848599 | 194273 | Enzo Doria | 08/2015 |
1405 | (112*10^194150-1)/3 | 194152 | Serge Batalov | 12/2014 |
1406 | 2*10^193981-43 | 193982 | Robert Price | 04/2018 |
1407 | 2^644382+75169 | 193979 | Enzo Doria | 04/2016 |
1408 | 2^644304-1861409 | 193955 | Enzo Doria | 11/2015 |
1409 | (29*10^193950-23)/3 | 193951 | Robert Price | 03/2022 |
1410 | 5*10^193907-9 | 193908 | Robert Price | 05/2015 |
1411 | 2^644043+1876703 | 193877 | Enzo Doria | 07/2016 |
1412 | 2*10^193841-63 | 193842 | Robert Price | 01/2022 |
1413 | 2^643735+1879733 | 193784 | Enzo Doria | 09/2016 |
1414 | (5^277183+1)/6 | 193742 | Paul Bourdelais | 07/2010 |
1415 | 9*10^193712+71 | 193713 | Robert Price | 08/2020 |
1416 | 2^643216-286565 | 193628 | Enzo Doria | 07/2015 |
1417 | 10^193566+1126339 | 193567 | Patrick De Geest | 09/2022 |
1419 | 10^193566-10000000001 | 193566 | Robert Price | 04/2021 |
1418 | 10^193566-454041 | 193566 | Patrick De Geest | 08/2021 |
1420 | 2^642888-24965 | 193529 | Enzo Doria | 09/2013 |
1421 | 2^642448-114825 | 193397 | Enzo Doria | 05/2015 |
1422 | 2^642437-1856623 | 193393 | Enzo Doria | 10/2015 |
1423 | 2^642039-59797 | 193273 | Enzo Doria | 11/2015 |
1424 | 10^193230+513861 | 193231 | Patrick De Geest | 07/2018 |
1425 | 10^193230-8001 | 193230 | Robert Price | 03/2018 |
1426 | (62*10^193225-233)/9 | 193226 | Robert Price | 02/2022 |
1427 | 2^641692-286349 | 193169 | Enzo Doria | 07/2015 |
1428 | 2^641690-24737 | 193168 | Enzo Doria | 09/2013 |
1429 | 2^641514+1876549 | 193115 | Enzo Doria | 07/2016 |
1430 | 2^640888-2785619 | 192927 | Enzo Doria | 10/2015 |
1431 | 2^640874-2783741 | 192923 | Enzo Doria | 09/2015 |
1432 | 10^192922+192207 | 192923 | Patrick De Geest | 08/2021 |
1433 | 10^192922-7001 | 192922 | Robert Price | 04/2021 |
1434 | 2^640854+25 | 192917 | Stefano Morozzi | 05/2021 |
1435 | 34*10^192868-9 | 192870 | Robert Price | 06/2020 |
1436 | (46*10^192841+683)/9 | 192842 | Robert Price | 03/2019 |
1437 | 2^640181+467 | 192714 | Lelio R Paula | 08/2013 |
1438 | 2^639536-1850249 | 192520 | Enzo Doria | 08/2015 |
1439 | 40714<>40712<>...<>1086421357911<>...<>40711<>40713 | 192464 | Hans Havermann | 12/2019 |
1440 | 5*10^192422-43 | 192423 | Robert Price | 01/2019 |
1441 | 2^639110-2792441 | 192392 | Enzo Doria | 02/2016 |
1442 | 2^638955-29827 | 192345 | Enzo Doria | 08/2015 |
1443 | 2^638713-2784223 | 192272 | Enzo Doria | 10/2015 |
1444 | (10^192216+7)/149 | 192214 | Alfred Reich | 07/2021 |
1445 | 2^638490-113507 | 192205 | Enzo Doria | 08/2014 |
1446 | 2^638189-39943 | 192115 | Enzo Doria | 09/2015 |
1447 | 2^638110+1877119 | 192091 | Enzo Doria | 07/2016 |
1448 | 2^638066-2785211 | 192078 | Enzo Doria | 10/2015 |
1449 | (35*10^191973-341)/9 | 191974 | Robert Price | 08/2021 |
1450 | (112*10^191900+17)/3 | 191902 | Robert Price | 03/2020 |
1451 | 2^637475-115309 | 191900 | Enzo Doria | 07/2015 |
1452 | (68*10^191754-113)/9 | 191755 | Robert Price | 03/2021 |
1453 | 2^636930-11 | 191736 | Stefano Morozzi | 07/2022 |
1454 | (47*10^191732+259)/9 | 191733 | Robert Price | 03/2022 |
1455 | 2^636661+1876577 | 191655 | Enzo Doria | 07/2016 |
1456 | (34^125101-1)/33 | 191589 | Paul Bourdelais | 11/2017 |
1457 | 2^636177-1855123 | 191509 | Enzo Doria | 09/2015 |
1458 | 2^636158-113627 | 191503 | Enzo Doria | 08/2014 |
1459 | (37*25^136966+63)/4 | 191472 | Curtis Bright | 05/2015 |
1460 | 2^636035+79823 | 191466 | Enzo Doria | 06/2016 |
1461 | 2^636011-1860847 | 191459 | Enzo Doria | 11/2015 |
1462 | 2^635926-1860611 | 191433 | Enzo Doria | 11/2015 |
1463 | 3*10^191152-7 | 191153 | Robert Price | 08/2015 |
1464 | 2^634883-1865677 | 191119 | Enzo Doria | 02/2016 |
1465 | 2^634801+1871957 | 191095 | Enzo Doria | 05/2016 |
1466 | (77*10^191080+157)/9 | 191081 | Robert Price | 05/2022 |
1467 | (35*10^191073+1)/9 | 191074 | Serge Batalov | 07/2010 |
1468 | 9*10^191018-41 | 191019 | Robert Price | 08/2020 |
1469 | 2^634470-59861 | 190995 | Enzo Doria | 11/2015 |
1470 | 2^634368-29519 | 190964 | Enzo Doria | 08/2015 |
1471 | 2^634188-350609 | 190910 | Enzo Doria | 06/2015 |
1472 | (65*10^190899+493)/9 | 190900 | Robert Price | 08/2021 |
1473 | (62*10^190795-413)/9 | 190796 | Robert Price | 09/2021 |
1474 | (26*10^190789-131)/3 | 190790 | Robert Price | 10/2019 |
1475 | (13*10^190732-61)/3 | 190733 | Robert Price | 11/2018 |
1476 | (7*10^190683+143)/3 | 190684 | Robert Price | 03/2018 |
1477 | 2^633088-113879 | 190579 | Enzo Doria | 10/2014 |
1478 | 2^633064+1874911 | 190572 | Enzo Doria | 06/2016 |
1479 | (43*10^190547+83)/9 | 190548 | Robert Price | 11/2018 |
1480 | 99*10^190543+7 | 190545 | Robert Price | 05/2021 |
1481 | (299*10^190533+1)/3 | 190535 | Robert Price | 04/2020 |
1482 | (1744*10^190519-1747)/3 | 190522 | Robert Price | 12/2020 |
1483 | 2^632815-15 | 190497 | Stefano Morozzi | 07/2022 |
1484 | 2^632795-351205 | 190491 | Enzo Doria | 06/2015 |
1485 | (16*10^190420-19)/3 | 190421 | Robert Price | 02/2019 |
1486 | (43*10^190351+101)/9 | 190352 | Robert Price | 11/2018 |
1487 | 2^632156+78391 | 190298 | Enzo Doria | 06/2016 |
1488 | 97*10^190295-3 | 190297 | Robert Price | 05/2020 |
1489 | 2^632082-1851971 | 190276 | Enzo Doria | 08/2015 |
1490 | 2^632020+1880311 | 190257 | Enzo Doria | 09/2016 |
1491 | (5*10^190242-77)/9 | 190242 | Robert Price | 04/2021 |
1492 | 7*10^190210+13 | 190211 | Robert Price | 03/2021 |
1493 | 2^631637-462373 | 190142 | Enzo Doria | 08/2015 |
1494 | 2*10^190126-21 | 190127 | Robert Price | 09/2020 |
1495 | (28*10^190105+191)/3 | 190106 | Robert Price | 02/2020 |
1496 | 2*10^190093+33 | 190094 | Robert Price | 11/2021 |
1497 | (68*10^190053-113)/9 | 190054 | Robert Price | 03/2021 |
1498 | 2^631122-39251 | 189987 | Enzo Doria | 08/2015 |
1499 | (26*10^189928-89)/9 | 189929 | Robert Price | 06/2018 |
1500 | 2^630839-97 | 189902 | Yves Minet | 07/2017 |