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 | (2^700048+376578)/2 | 210736 | Stefano Morozzi | 04/2020 |
1252 | 11^202357-1140 | 210734 | Enzo Doria | 12/2012 |
1253 | (2^700021+25874)/2 | 210728 | Stefano Morozzi | 04/2020 |
1254 | (2^700018+377518)/2 | 210727 | Stefano Morozzi | 04/2020 |
1255 | 2^699740+25 | 210643 | Stefano Morozzi | 05/2021 |
1256 | 2^698929-2788423 | 210399 | Enzo Doria | 11/2015 |
1257 | (5^300893+4^300893)/9 | 210315 | Jean-Louis Charton | 11/2011 |
1258 | 2^698316+1878601 | 210215 | Enzo Doria | 08/2016 |
1259 | 34*10^210097-9 | 210099 | Robert Price | 05/2023 |
1260 | 6*10^209846-91 | 209847 | Robert Price | 05/2023 |
1261 | 2^697036+1878751 | 209829 | Enzo Doria | 08/2016 |
1262 | 6^269407+5 | 209640 | Paul Bourdelais | 02/2021 |
1263 | (2^696343-1)/11141489/36009913139329 | 209600 | Tony Prest / Never Odd Or Even | 02/2014 |
1264 | 2^696254-115151 | 209594 | Enzo Doria | 06/2015 |
1265 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
1266 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
1267 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
1268 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
1269 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
1270 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
1271 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
1272 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
1273 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
1274 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
1275 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
1276 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
1277 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
1278 | 9*10^207254-89 | 207255 | Robert Price | 02/2023 |
1279 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
1280 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
1281 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
1282 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
1283 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
1284 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
1285 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
1286 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
1287 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
1288 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
1289 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
1290 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
1291 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
1292 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
1293 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
1294 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
1295 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
1296 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
1297 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
1298 | 10^204764-8001 | 204764 | Robert Price | 03/2023 |
1299 | (26*10^204730-77)/3 | 204731 | Robert Price | 03/2023 |
1300 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
1301 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
1302 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
1303 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
1304 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
1305 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
1306 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
1307 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
1308 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
1309 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
1310 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
1311 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
1312 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |
1313 | 10247^50678-50678^10247 | 203250 | Norbert Schneider | 03/2022 |
1314 | 2^674627-25161 | 203083 | Enzo Doria | 09/2013 |
1315 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
1316 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
1317 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
1318 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
1319 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
1320 | (2^673184-7)/3 | 202649 | Stefano Morozzi | 08/2022 |
1321 | (467617#+14534)/(2^2*13*43) | 202603 | Makoto Morimoto | 06/2019 |
1322 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
1323 | (7*10^202267+179)/3 | 202268 | Robert Price | 02/2023 |
1324 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
1325 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
1326 | (2*10^202059+7)/9 | 202059 | Rytis Slatkevicius | 01/2023 |
1327 | 98*10^202021-9 | 202023 | Robert Price | 05/2023 |
1328 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
1329 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |
1330 | 10^201801-93 | 201801 | Robert Price | 02/2023 |
1331 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
1332 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
1333 | 2^670133+89 | 201731 | Stefano Morozzi | 05/2021 |
1334 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
1335 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
1336 | (299*10^201547-17)/3 | 201549 | Robert Price | 02/2023 |
1337 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
1338 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
1339 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
1340 | 7*10^201140-87 | 201141 | Robert Price | 03/2023 |
1341 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
1342 | 10194^50161-50161^10194 | 201063 | Norbert Schneider | 09/2020 |
1343 | 2^667894+1875589 | 201057 | Enzo Doria | 06/2016 |
1344 | 2^667569-1836559 | 200959 | Enzo Doria | 05/2015 |
1345 | (172*10^200746-1)/9 | 200748 | Serge Batalov | 12/2014 |
1346 | 2^666430+782569 | 200616 | Enzo Doria | 10/2016 |
1347 | (86^103471+1)/87 | 200163 | Paul Bourdelais | 05/2018 |
1348 | 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 | 200003 | Robert Price | 05/2017 |
1349 | 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 | 200003 | Robert Price | 01/2018 |
1350 | numbpart(32235776596) | 200002 | Serge Batalov | 04/2017 |
1351 | (10^200001+149)/3 | 200001 | Serge Batalov | 12/2014 |
1352 | 10^200000+571791 | 200001 | Patrick De Geest | 08/2019 |
1353 | (3^419180-621444)/3 | 200000 | Stefano Morozzi | 06/2019 |
1354 | (3^419180-1941384)/3 | 200000 | Stefano Morozzi | 08/2019 |
1355 | 10^200000-45557 | 200000 | Patrick De Geest | 08/2019 |
1357 | (10^200000-1)/9-10^58838 | 200000 | Akihiko Yoshida | 04/2020 |
1356 | 2593604092947240127723272^8192+2593604092947240127722755^8192 | 200000 | Youcef Lemsafer | 01/2023 |
1358 | (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 | 199999 | Youcef Lemsafer | 01/2023 |
1359 | (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 | 199994 | Youcef Lemsafer | 01/2023 |
1360 | (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 | 199989 | Youcef Lemsafer | 01/2023 |
1361 | (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 | 199986 | Youcef Lemsafer | 01/2023 |
1362 | 92*10^199980-9 | 199982 | Robert Price | 12/2021 |
1363 | (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 | 199977 | Youcef Lemsafer | 01/2023 |
1364 | (85*10^199951-139)/9 | 199952 | Robert Price | 08/2021 |
1365 | (10^199926+7)/29/373/2339 | 199919 | Alfred Reich | 08/2021 |
1366 | 23*10^199833-9 | 199835 | Robert Price | 10/2021 |
1367 | (299*10^199801-17)/3 | 199803 | Robert Price | 04/2020 |
1368 | 6*10^199788+77 | 199789 | Robert Price | 06/2020 |
1369 | (23*10^199615+37)/3 | 199616 | Robert Price | 02/2022 |
1370 | (17*10^199607-167)/3 | 199608 | Robert Price | 05/2022 |
1371 | 2^663020-933075 | 199589 | Paul Bourdelais | 06/2021 |
1372 | (14*10^199447+73)/3 | 199448 | Robert Price | 12/2018 |
1373 | (2^662424-15)/7 | 199409 | Stefano Morozzi | 08/2022 |
1374 | 2^662103-29287 | 199313 | Enzo Doria | 08/2015 |
1375 | (2*10^199283+457)/9 | 199283 | Robert Price | 01/2018 |
1376 | (10^199248-19)/9 | 199248 | Robert Price | 01/2018 |
1377 | (83*10^199213+529)/9 | 199214 | Robert Price | 12/2021 |
1378 | (194*10^199146-17)/3 | 199148 | Robert Price | 09/2020 |
1379 | (151*10^199003-1)/3 | 199005 | Robert Price | 03/2020 |
1380 | 9*10^198946-73 | 198947 | Robert Price | 01/2021 |
1381 | 45*10^198931-7 | 198933 | Robert Price | 07/2020 |
1382 | 2^660482-2891 | 198825 | Yves Minet | 05/2016 |
1383 | 2^659589-21 | 198557 | Stefano Morozzi | 07/2022 |
1384 | 2^659583+1879223 | 198555 | Enzo Doria | 08/2016 |
1385 | (53*10^198529+1)/9 | 198530 | Serge Batalov | 07/2010 |
1386 | (49*10^198403+311)/9 | 198404 | Robert Price | 06/2019 |
1387 | 96*10^198376-7 | 198378 | Robert Price | 03/2021 |
1388 | (10^198375+7)/59/1201/87589 | 198366 | Alfred Reich | 08/2021 |
1389 | 2^658828-29819 | 198327 | Enzo Doria | 08/2015 |
1390 | 2^658776-2791229 | 198312 | Enzo Doria | 01/2016 |
1391 | (35*10^198294-377)/9 | 198295 | Robert Price | 07/2018 |
1392 | (4*10^198268+137)/3 | 198269 | Robert Price | 03/2018 |
1393 | 2^658544-1854029 | 198242 | Enzo Doria | 09/2015 |
1394 | (62*10^198229-233)/9 | 198230 | Robert Price | 02/2022 |
1395 | (26*10^198200-41)/3 | 198201 | Robert Price | 02/2022 |
1396 | (157^90239-1)/156 | 198154 | Alexander Zhirkov | 06/2016 |
1397 | 2*10^197959-37 | 197960 | Robert Price | 11/2021 |
1398 | (232*10^197897+17)/3 | 197899 | Robert Price | 04/2021 |
1399 | (4*10^197778+173)/3 | 197779 | Robert Price | 02/2018 |
1400 | 78*10^197702-7 | 197704 | Robert Price | 10/2020 |
1401 | (17*10^197640-23)/3 | 197641 | Robert Price | 03/2021 |
1402 | (29*10^197629-77)/3 | 197630 | Robert Price | 02/2020 |
1403 | 2^656462+1874419 | 197615 | Enzo Doria | 06/2016 |
1404 | (89^101363+1)/90 | 197595 | Paul Bourdelais | 11/2017 |
1405 | 2^655893-344563 | 197444 | Enzo Doria | 07/2015 |
1406 | 2^655875+71333 | 197439 | Enzo Doria | 04/2016 |
1407 | 2^655845-9 | 197430 | Robert Price | 01/2017 |
1408 | (299*10^197426+1)/3 | 197428 | Robert Price | 04/2020 |
1409 | 2^655682-1849121 | 197380 | Enzo Doria | 08/2015 |
1410 | 4*10^197268-89 | 197269 | Robert Price | 11/2018 |
1411 | (11*10^197198-89)/3 | 197199 | Robert Price | 05/2021 |
1412 | 2^655045-49603 | 197189 | Enzo Doria | 10/2015 |
1413 | 2^655000-2784089 | 197175 | Enzo Doria | 10/2015 |
1414 | (18^157051-1)/17 | 197141 | Paul Bourdelais | 03/2010 |
1415 | (4*10^197061+41)/9 | 197061 | Serge Batalov | 11/2022 |
1416 | (154*10^197005+17)/9 | 197007 | Robert Price | 06/2022 |
1417 | 2^654400-39719 | 196995 | Enzo Doria | 09/2015 |
1418 | (14*10^196965-221)/9 | 196966 | Robert Price | 04/2018 |
1419 | 2^654216-459995 | 196939 | Enzo Doria | 06/2015 |
1420 | (17*10^196921+31)/3 | 196922 | Robert Price | 01/2019 |
1421 | (14*10^196885-89)/3 | 196886 | Robert Price | 05/2020 |
1422 | 3*10^196881-59 | 196882 | Robert Price | 09/2018 |
1423 | 2^653851+82295 | 196829 | Enzo Doria | 09/2016 |
1424 | (38*10^196792+691)/9 | 196793 | Robert Price | 10/2018 |
1425 | (65*10^196768+493)/9 | 196769 | Robert Price | 08/2021 |
1427 | 2^653636-29429 | 196765 | Enzo Doria | 08/2015 |
1426 | 2^653638-11 | 196765 | Stefano Morozzi | 07/2022 |
1428 | 2^653601-69673 | 196754 | Enzo Doria | 02/2016 |
1429 | (44*10^196684+1)/9 | 196685 | Serge Batalov | 07/2010 |
1430 | 2^652786-1852571 | 196509 | Enzo Doria | 08/2015 |
1431 | 2^652752-1325 | 196498 | Yves Minet | 07/2015 |
1432 | 2^652470-1859141 | 196414 | Enzo Doria | 10/2015 |
1433 | 2^652307+1877483 | 196364 | Enzo Doria | 08/2016 |
1434 | 2^652293-115273 | 196360 | Enzo Doria | 06/2015 |
1435 | (47*10^196281+403)/9 | 196282 | Robert Price | 03/2019 |
1436 | (7*10^196125-31)/3 | 196126 | Robert Price | 12/2021 |
1437 | 33^129128+129128^33 | 196083 | Norbert Schneider | 06/2022 |
1438 | 6*10^196070+73 | 196071 | Robert Price | 04/2019 |
1439 | 2^651218-1868201 | 196037 | Enzo Doria | 04/2016 |
1440 | 2^651047-49687 | 195985 | Enzo Doria | 10/2015 |
1441 | 10^195968-700001 | 195968 | Robert Price | 08/2021 |
1442 | (29*10^195875-197)/3 | 195876 | Robert Price | 08/2021 |
1443 | (25*10^195808-97)/9 | 195809 | Robert Price | 01/2022 |
1444 | 2^650285-2785333 | 195756 | Enzo Doria | 10/2015 |
1445 | (10^195732+7)/18089/49605893 | 195721 | Alfred Reich | 08/2021 |
1446 | (69^106397-1)/68 | 195647 | Paul Bourdelais | 10/2017 |
1447 | 2^649811+1877573 | 195613 | Enzo Doria | 08/2016 |
1448 | 2^649662-170531 | 195568 | Hans Havermann | 10/2018 |
1449 | 2^649586+182839 | 195545 | Enzo Doria | 11/2016 |
1450 | 2^649537-1867363 | 195531 | Enzo Doria | 04/2016 |
1451 | 2^649536-1861499 | 195530 | Enzo Doria | 12/2015 |
1452 | (103*10^195478-1)/3 | 195480 | Serge Batalov | 12/2014 |
1453 | 2^649102-59351 | 195400 | Enzo Doria | 10/2015 |
1454 | (2*10^195399+529)/9 | 195399 | Robert Price | 01/2018 |
1455 | (202*10^195383-13)/9 | 195385 | Robert Price | 01/2020 |
1456 | 2^648988+1178971 | 195365 | Enzo Doria | 06/2016 |
1457 | 2^648975-114319 | 195361 | Enzo Doria | 02/2015 |
1458 | (11*10^195350-137)/9 | 195351 | Robert Price | 01/2018 |
1459 | 2^648619-24835 | 195254 | Enzo Doria | 09/2013 |
1460 | 5*10^195250-21 | 195251 | Robert Price | 12/2021 |
1461 | (14*10^195234-83)/3 | 195235 | Robert Price | 12/2018 |
1462 | 5*10^195221+81 | 195222 | Robert Price | 03/2019 |
1463 | 10^195143-5001 | 195143 | Robert Price | 12/2021 |
1464 | 2^648190-24737 | 195125 | Enzo Doria | 09/2013 |
1465 | (57^111119+1)/58 | 195110 | Paul Bourdelais | 10/2017 |
1466 | (29*10^195098-197)/3 | 195099 | Robert Price | 08/2021 |
1467 | 10^195060+89701 | 195061 | Patrick De Geest | 02/2021 |
1469 | 10^195060-40000000001 | 195060 | Robert Price | 09/2020 |
1468 | 10^195060-110337 | 195060 | Patrick De Geest | 02/2021 |
1470 | 56*10^195032-3 | 195034 | Robert Price | 03/2020 |
1471 | 11^187185-90 | 194934 | Enzo Doria | 09/2012 |
1472 | (86*10^194818-437)/9 | 194819 | Robert Price | 03/2021 |
1473 | 2^647068+77281 | 194787 | Enzo Doria | 05/2016 |
1474 | 2*10^194716-93 | 194717 | Robert Price | 12/2021 |
1475 | 15^165559-14^165559 | 194713 | Jean-Louis Charton | 03/2011 |
1476 | F(931517) | 194676 | Henri Lifchitz | 09/2008 |
1477 | 4*10^194668+49 | 194669 | Robert Price | 01/2019 |
1478 | 2^646589+1179407 | 194643 | Enzo Doria | 06/2016 |
1479 | 2^646289-114621 | 194553 | Enzo Doria | 05/2015 |
1480 | 2^646236-39659 | 194537 | Enzo Doria | 09/2015 |
1481 | (16*10^194536+53)/3 | 194537 | Robert Price | 03/2019 |
1482 | 2^646161-59833 | 194514 | Enzo Doria | 11/2015 |
1483 | (17*10^194502+31)/3 | 194503 | Robert Price | 01/2019 |
1484 | (19*10^194428+287)/9 | 194429 | Robert Price | 10/2021 |
1485 | 2*10^194413+3 | 194414 | Robert Price | 07/2015 |
1486 | 2^645360-1848599 | 194273 | Enzo Doria | 08/2015 |
1487 | (112*10^194150-1)/3 | 194152 | Serge Batalov | 12/2014 |
1488 | 2*10^193981-43 | 193982 | Robert Price | 04/2018 |
1489 | 2^644382+75169 | 193979 | Enzo Doria | 04/2016 |
1490 | 2^644304-1861409 | 193955 | Enzo Doria | 11/2015 |
1491 | (29*10^193950-23)/3 | 193951 | Robert Price | 03/2022 |
1492 | 5*10^193907-9 | 193908 | Robert Price | 05/2015 |
1493 | 2^644043+1876703 | 193877 | Enzo Doria | 07/2016 |
1494 | 2*10^193841-63 | 193842 | Robert Price | 01/2022 |
1495 | 2^643735+1879733 | 193784 | Enzo Doria | 09/2016 |
1496 | (5^277183+1)/6 | 193742 | Paul Bourdelais | 07/2010 |
1497 | 9*10^193712+71 | 193713 | Robert Price | 08/2020 |
1498 | 2^643216-286565 | 193628 | Enzo Doria | 07/2015 |
1499 | 10^193566+1126339 | 193567 | Patrick De Geest | 09/2022 |
1500 | 10^193566-454041 | 193566 | Patrick De Geest | 08/2021 |