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
Search by form
Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
1251 | 2^802025-25999 | 241434 | Enzo Doria | 10/2013 |
1252 | (3^505823+3^252912+1)/7 | 241339 | Serge Batalov | 03/2014 |
1253 | 2^801575+25073 | 241299 | Enzo Doria | 11/2023 |
1254 | 2^801303+1872923 | 241217 | Enzo Doria | 05/2016 |
1255 | (23*10^241048-143)/3 | 241049 | Robert Price | 12/2023 |
1256 | 2^800579-1862947 | 240999 | Enzo Doria | 12/2015 |
1257 | 2^799999+16205 | 240824 | Norman Luhn | 09/2023 |
1258 | 3^504206+2 | 240568 | Luke W. Richards | 03/2018 |
1259 | 2^798973-26283 | 240515 | Enzo Doria | 10/2013 |
1260 | 2^798671-69487 | 240424 | Enzo Doria | 12/2015 |
1261 | 2^797220+79831 | 239988 | Enzo Doria | 06/2016 |
1262 | 2^796910-26001 | 239894 | Enzo Doria | 10/2013 |
1263 | 2^796598+653119 | 239800 | Enzo Doria | 12/2016 |
1264 | 2^796432-1859729 | 239750 | Enzo Doria | 11/2015 |
1265 | 2^796002-1852211 | 239621 | Enzo Doria | 08/2015 |
1266 | 2^795884+214081 | 239585 | Enzo Doria | 10/2023 |
1267 | 2^795709+75767 | 239533 | Enzo Doria | 04/2016 |
1268 | 2^795708+81721 | 239532 | Enzo Doria | 08/2016 |
1269 | 2^795468-2786249 | 239460 | Enzo Doria | 10/2015 |
1270 | 2^795442+80779 | 239452 | Enzo Doria | 07/2016 |
1271 | 2^795075-1852057 | 239342 | Enzo Doria | 08/2015 |
1272 | (86^123677+1)/87 | 239252 | Paul Bourdelais | 01/2019 |
1273 | 2^794043+1875023 | 239031 | Enzo Doria | 06/2016 |
1274 | 2^793347-69577 | 238822 | Enzo Doria | 01/2016 |
1275 | 5*2^793288+3 | 238805 | Jon Grantham | 07/2023 |
1276 | 2^792988-344429 | 238714 | Enzo Doria | 08/2015 |
1277 | 2^792700-2786369 | 238627 | Enzo Doria | 11/2015 |
1278 | 2^792663-1844797 | 238616 | Enzo Doria | 06/2015 |
1279 | 2^792605-291943 | 238598 | Enzo Doria | 07/2015 |
1280 | (2^792061-2^396031+1)/5 | 238434 | Thomas Ritschel | 03/2014 |
1281 | 4*10^238163+21 | 238164 | Robert Price | 12/2022 |
1282 | (26*10^238157-77)/3 | 238158 | Robert Price | 03/2023 |
1283 | 10^237670+9 | 237671 | Robert Price | 08/2023 |
1284 | 2^789373+1869377 | 237625 | Enzo Doria | 05/2016 |
1285 | ((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961 | 237544 | Serge Batalov | 04/2015 |
1286 | 2^788942+1866409 | 237496 | Enzo Doria | 02/2016 |
1287 | 2^788844-114329 | 237466 | Enzo Doria | 01/2015 |
1288 | 2^788705-1859713 | 237424 | Enzo Doria | 11/2015 |
1289 | 15^201475+14 | 236953 | Alfred Reich | 10/2023 |
1290 | 2^786180+1871971 | 236664 | Enzo Doria | 05/2016 |
1291 | 11^227092-90 | 236492 | Enzo Doria | 11/2012 |
1292 | 2^785260+1866361 | 236387 | Enzo Doria | 02/2016 |
1293 | 2^785220+1880611 | 236375 | Enzo Doria | 10/2016 |
1294 | (2^784689-15)/7 | 236215 | Stefano Morozzi | 08/2022 |
1295 | 19^184650-2 | 236122 | Robert Price | 10/2014 |
1296 | 10^236059+216513 | 236060 | Patrick De Geest | 04/2016 |
1297 | 10^236059-20909 | 236059 | Robert Price | 09/2015 |
1298 | 2^783893-21 | 235976 | Stefano Morozzi | 07/2022 |
1299 | (87^121487-1)/86 | 235625 | Paul Bourdelais | 12/2018 |
1300 | 2^782634-113981 | 235597 | Enzo Doria | 11/2014 |
1301 | 2^782423+1879733 | 235533 | Enzo Doria | 09/2016 |
1302 | (10^(2*117707+1)+12*10^117707-1)/3 | 235415 | Robert Price | 10/2023 |
1303 | 2^781682-2789543 | 235310 | Enzo Doria | 12/2015 |
1304 | 2^780408-113453 | 234927 | Enzo Doria | 08/2014 |
1305 | 7*10^234915+9 | 234916 | Robert Price | 04/2023 |
1306 | 2^780368-1864829 | 234915 | Enzo Doria | 01/2016 |
1307 | 2^780284+7 | 234889 | Jon Grantham | 08/2023 |
1308 | 2^779593-1836559 | 234681 | Enzo Doria | 05/2015 |
1309 | (8713#+(549391#)/(8713#))/360295171 | 234487 | Makoto Morimoto | 11/2017 |
1310 | (5^335429+1)/6 | 234455 | Paul Bourdelais | 08/2010 |
1311 | 2^778788+22201 | 234439 | Enzo Doria | 09/2023 |
1312 | 2^778395-113617 | 234321 | Enzo Doria | 08/2014 |
1313 | 5*2^778090+3 | 234230 | Jon Grantham | 07/2023 |
1314 | (21430^54289-1)/(21430^233-1) | 234118 | Ryan Propper | 11/2023 |
1315 | (5*10^234054-101)/3 | 234055 | Robert Price | 08/2023 |
1316 | 23*10^234025-7 | 234027 | Robert Price | 10/2022 |
1317 | Phi(78125,5517) | 233857 | Anonymous | 09/2022 |
1318 | 5^334359-3^334359-1 | 233707 | Jon Grantham | 08/2023 |
1319 | 2^776245-2792353 | 233674 | Enzo Doria | 02/2016 |
1320 | 2^776060-114029 | 233618 | Enzo Doria | 11/2014 |
1321 | 2^775987-2789557 | 233596 | Enzo Doria | 12/2015 |
1322 | 2*10^233564-91 | 233565 | Robert Price | 02/2023 |
1323 | 2^775672+1866721 | 233501 | Enzo Doria | 03/2016 |
1324 | 2^775238+57 | 233370 | Stefano Morozzi | 05/2021 |
1325 | (11^223999+1)/12 | 233270 | Paul Bourdelais | 02/2010 |
1326 | 2^774118+1885789 | 233033 | Enzo Doria | 04/2017 |
1327 | 21^176191-20^176191 | 232964 | Jean-Louis Charton | 01/2015 |
1328 | 2^773679-113425 | 232901 | Enzo Doria | 08/2014 |
1329 | (7*10^232620+23)/3 | 232621 | Robert Price | 05/2023 |
1330 | 10^232599+192489 | 232600 | Patrick De Geest | 12/2013 |
1331 | 10^232599-3 | 232599 | Markus Tervooren | 10/2010 |
1332 | 2^772552-458879 | 232562 | Enzo Doria | 04/2015 |
1333 | 2^772214+1874899 | 232460 | Enzo Doria | 06/2016 |
1334 | 2^771994-1862771 | 232394 | Enzo Doria | 12/2015 |
1335 | 2^771889+1876037 | 232362 | Enzo Doria | 07/2016 |
1336 | 2^771660+1866511 | 232293 | Enzo Doria | 02/2016 |
1337 | 5^332150-18188 | 232163 | Enzo Doria | 06/2014 |
1338 | 2^770623+212543 | 231981 | Enzo Doria | 09/2023 |
1339 | 3^485977-2^485977 | 231870 | Mike Oakes | 09/2009 |
1340 | 2^770082-114161 | 231818 | Enzo Doria | 01/2015 |
1341 | 2^769791+25523 | 231731 | Enzo Doria | 11/2023 |
1342 | 7^274120-2 | 231659 | Paul Bourdelais | 08/2023 |
1343 | (20^177967+1)/21 | 231540 | Paul Bourdelais | 05/2013 |
1344 | (4*10^231254+23)/9 | 231254 | Serge Batalov | 11/2022 |
1345 | 2^768205+22217 | 231253 | Enzo Doria | 09/2023 |
1346 | 2^767622-9221 | 231078 | Lelio R Paula | 01/2016 |
1347 | 2^767344+1880311 | 230994 | Enzo Doria | 09/2016 |
1348 | 8*10^230921-13 | 230922 | Robert Price | 08/2023 |
1349 | (3^483611-1)/2 | 230741 | Paul Bourdelais | 02/2010 |
1350 | (10^230706+179)/9 | 230706 | Serge Batalov | 12/2014 |
1351 | 2^766309+1875257 | 230682 | Enzo Doria | 06/2016 |
1352 | (26131^52441-1)/(26131^229-1) | 230629 | Ryan Propper | 11/2023 |
1353 | 2^765635+1879883 | 230480 | Enzo Doria | 09/2016 |
1354 | 43^141090+141090 | 230467 | Kellen Shenton | 06/2023 |
1355 | (26*10^230394-119)/3 | 230395 | Robert Price | 07/2023 |
1356 | 2^764348-113697 | 230092 | Enzo Doria | 09/2014 |
1357 | 2^764131+78863 | 230027 | Enzo Doria | 05/2016 |
1358 | 2^763701+60197 | 229897 | Enzo Doria | 03/2016 |
1359 | 4*10^229836+21 | 229837 | Robert Price | 12/2022 |
1360 | 2^762841-25905 | 229639 | Enzo Doria | 10/2013 |
1361 | 2^762659+212633 | 229584 | Enzo Doria | 09/2023 |
1362 | 77*10^229211+3 | 229213 | Robert Price | 11/2023 |
1363 | 2^761117-113569 | 229120 | Enzo Doria | 08/2014 |
1364 | (29022^51529-1)/(29022^227-1) | 228947 | Ryan Propper | 11/2023 |
1365 | (98^114859+1)/99 | 228709 | Paul Bourdelais | 12/2018 |
1366 | 5*3^479067-2^479067 | 228574 | Jon Grantham | 08/2023 |
1367 | (2^758231+1)/(3*27146942976539*73236839266867) | 228223 | Gord Palameta | 12/2018 |
1368 | (298*10^228177-7)/3 | 228179 | Robert Price | 02/2023 |
1369 | 2^757985-2790013 | 228177 | Enzo Doria | 12/2015 |
1370 | 34*10^228129-9 | 228131 | Robert Price | 05/2023 |
1371 | 2^757038-1862081 | 227892 | Enzo Doria | 12/2015 |
1372 | 2^756839+95849 | 227832 | Makoto Morimoto | 10/2013 |
1374 | (2^756839+6989)/756091 | 227826 | Makoto Morimoto | 09/2016 |
1373 | (2^756839-50211)/(137*3203) | 227826 | Makoto Morimoto | 08/2019 |
1375 | 2^756773-112723 | 227812 | Enzo Doria | 07/2014 |
1376 | 524309#+616367 | 227431 | Makoto Morimoto | 02/2016 |
1377 | 2^755097-114193 | 227307 | Enzo Doria | 12/2014 |
1378 | 7*10^227178+39 | 227179 | Robert Price | 01/2023 |
1379 | 9*10^227153-89 | 227154 | Robert Price | 02/2023 |
1380 | 2^754473-2791513 | 227120 | Enzo Doria | 01/2016 |
1381 | 2^754376+25 | 227090 | Stefano Morozzi | 05/2021 |
1382 | 2^754138+213289 | 227019 | Enzo Doria | 09/2023 |
1383 | 2^754038+25 | 226989 | Stefano Morozzi | 05/2021 |
1384 | 7*10^226479-9 | 226480 | Robert Price | 02/2023 |
1385 | 2^751426-764321 | 226202 | Enzo Doria | 12/2013 |
1386 | (18^180181-1)/17 | 226176 | Andy Steward | 04/2007 |
1387 | 2^750740-3 | 225996 | Paul Bourdelais | 03/2012 |
1388 | 2^750725+60227 | 225991 | Enzo Doria | 02/2016 |
1389 | 2^750525-113743 | 225931 | Enzo Doria | 09/2014 |
1390 | (2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263) | 225744 | Dario Alpern | 10/2014 |
1391 | 2^749444-1861889 | 225606 | Enzo Doria | 12/2015 |
1392 | tau(311^16452) | 225560 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1393 | 2^749096+1876861 | 225501 | Enzo Doria | 07/2016 |
1394 | (519643#+43033)/(23*1871*2706283) | 225379 | Makoto Morimoto | 08/2019 |
1395 | 2^748657+79607 | 225369 | Enzo Doria | 06/2016 |
1396 | (2^746920-11)/5 | 224845 | Stefano Morozzi | 08/2022 |
1397 | 2^746653-291583 | 224765 | Enzo Doria | 07/2015 |
1398 | 2^746461-114043 | 224708 | Enzo Doria | 11/2014 |
1399 | 2^746302+25 | 224660 | Stefano Morozzi | 05/2021 |
1400 | (202*10^224545-1)/3 | 224547 | Robert Price | 06/2023 |
1401 | 2^745674+213949 | 224471 | Enzo Doria | 10/2023 |
1402 | 2^745098-350471 | 224297 | Enzo Doria | 06/2015 |
1403 | 2^745039-4897 | 224280 | Yves Minet | 03/2021 |
1404 | 23*10^224232-7 | 224234 | Robert Price | 10/2022 |
1405 | (154*10^224061-1)/9 | 224063 | Serge Batalov | 12/2014 |
1406 | 2^744211-1845787 | 224030 | Enzo Doria | 07/2015 |
1407 | 2^743592-134579 | 223844 | Hans Havermann | 10/2018 |
1408 | 2^742452+3 | 223501 | Paul Bourdelais | 06/2019 |
1409 | 234178^9+9^234178 | 223463 | Anatoly F. Selevich | 07/2011 |
1410 | 2^741651-461197 | 223260 | Enzo Doria | 07/2015 |
1411 | 10^223236-1001 | 223236 | Robert Price | 10/2022 |
1412 | 2^741362-1845251 | 223173 | Enzo Doria | 07/2015 |
1413 | 3^467546-5*2^467546 | 223077 | Jon Grantham | 08/2023 |
1414 | 2^740455-1863877 | 222900 | Enzo Doria | 12/2015 |
1415 | (14*10^222718-41)/9 | 222719 | Serge Batalov | 01/2023 |
1416 | 2^739636-2792219 | 222653 | Enzo Doria | 02/2016 |
1417 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
1418 | 2^738957-1859743 | 222449 | Enzo Doria | 11/2015 |
1419 | 4*10^222253-21 | 222254 | Robert Price | 12/2022 |
1420 | 2^737825+57 | 222108 | Stefano Morozzi | 05/2021 |
1421 | (54^128189+1)/55 | 222073 | Paul Bourdelais | 11/2018 |
1422 | (10^221654+179)/9 | 221654 | Serge Batalov | 12/2014 |
1423 | 2^736281+79817 | 221643 | Enzo Doria | 06/2016 |
1424 | 10^221631+247617 | 221632 | Patrick De Geest | 10/2013 |
1425 | 10^221631-9 | 221631 | Alexander Gramolin | 02/2011 |
1426 | 10^221628+7 | 221629 | Alfred Reich | 04/2021 |
1427 | 2^735970-1839821 | 221550 | Enzo Doria | 06/2015 |
1428 | 2^735367+60293 | 221368 | Enzo Doria | 03/2016 |
1429 | 77*10^221343+3 | 221345 | Robert Price | 11/2023 |
1430 | (202*10^221092-1)/3 | 221094 | Robert Price | 06/2023 |
1431 | (29^151153+1)/30 | 221045 | Paul Bourdelais | 09/2017 |
1432 | 2^734228+24751 | 221025 | Enzo Doria | 10/2023 |
1433 | 2^733264-2784089 | 220735 | Enzo Doria | 10/2015 |
1434 | 2^733114-24555 | 220690 | Enzo Doria | 09/2013 |
1435 | 2^731891-636259 | 220322 | Enzo Doria | 12/2013 |
1436 | 98*10^220185-9 | 220187 | Robert Price | 05/2023 |
1437 | 418319^39164+418318 | 220161 | Alfred Reich | 11/2023 |
1438 | 2^731124-25539 | 220091 | Enzo Doria | 09/2013 |
1439 | 2^730972-462029 | 220045 | Enzo Doria | 07/2015 |
1440 | 2^730833+1868627 | 220003 | Enzo Doria | 04/2016 |
1441 | 2^730645-2787133 | 219947 | Enzo Doria | 11/2015 |
1442 | 2^730547-25581 | 219917 | Enzo Doria | 09/2013 |
1443 | (113*13^197420-5)/12 | 219916 | Anonymous | 11/2022 |
1444 | (13^197420*113-5)/12 | 219916 | Eric Chen | 10/2023 |
1445 | 2^730460+82291 | 219891 | Enzo Doria | 09/2016 |
1446 | (5*10^219847-101)/3 | 219848 | Robert Price | 08/2023 |
1447 | (2^730339+1)/(3*27839062003*7943469324347) | 219831 | Gord Palameta | 12/2018 |
1448 | L(1051849) | 219824 | Renaud Lifchitz | 03/2009 |
1449 | 3*2^730149+5 | 219798 | Jon Grantham | 07/2023 |
1450 | 8*10^219740-3 | 219741 | Serge Batalov | 01/2023 |
1451 | 11^210961-240 | 219694 | Enzo Doria | 01/2013 |
1452 | (26*10^219639-77)/3 | 219640 | Robert Price | 03/2023 |
1453 | 2^729611-113437 | 219635 | Enzo Doria | 08/2014 |
1454 | 7^259710-2 | 219481 | Paul Bourdelais | 01/2021 |
1455 | F(1049897) | 219416 | Henri Lifchitz | 10/2008 |
1456 | (1488^69151-1)/1487 | 219386 | Alexander Zhirkov | 02/2023 |
1457 | 2^728604+1879321 | 219332 | Enzo Doria | 10/2016 |
1458 | 33^144412+2 | 219292 | Robert Price | 04/2015 |
1459 | 2^728277-183313 | 219234 | Hans Havermann | 10/2018 |
1460 | 2^727998-1862711 | 219150 | Enzo Doria | 12/2015 |
1461 | (29*10^219124+91)/3 | 219125 | Robert Price | 12/2022 |
1462 | 2^727729-114073 | 219069 | Enzo Doria | 12/2014 |
1463 | 2^727496-1851809 | 218999 | Enzo Doria | 08/2015 |
1464 | 2^726591+2793143 | 218726 | Enzo Doria | 02/2016 |
1465 | (7*10^218644+17)/3 | 218645 | Robert Price | 06/2023 |
1466 | 2^725534-2791931 | 218408 | Enzo Doria | 02/2016 |
1467 | Phi(220531,10)/2686456812680882641 | 217774 | Makoto Kamada | 10/2020 |
1468 | 2^722184+1877821 | 217400 | Enzo Doria | 08/2016 |
1469 | (109*10^217360-1)/9 | 217362 | Serge Batalov | 12/2014 |
1470 | 2^721721-4453 | 217260 | Yves Minet | 03/2021 |
1471 | 10^216950+49 | 216951 | Robert Price | 02/2023 |
1472 | 281*499979#/46410-2702372 | 216849 | Robert Smith | 08/2016 |
1473 | 281*499979#/46410+2400766 | 216849 | Robert Smith | 08/2016 |
1474 | tau(311^15786) | 216429 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1475 | 2^718756-114107 | 216368 | Enzo Doria | 12/2014 |
1476 | 2^717672+121 | 216041 | Stefano Morozzi | 05/2021 |
1477 | 2^717305+80327 | 215931 | Enzo Doria | 07/2016 |
1478 | 2^717069-59773 | 215860 | Enzo Doria | 10/2015 |
1479 | 10^215802+33 | 215803 | Robert Price | 08/2023 |
1480 | 30^146021-29^146021 | 215691 | Jean-Louis Charton | 09/2018 |
1481 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
1482 | 2^716428+215011 | 215667 | Enzo Doria | 11/2023 |
1483 | (13*10^215592-43)/3 | 215593 | Robert Price | 08/2023 |
1484 | 227^91413-40 | 215372 | Enzo Doria | 04/2015 |
1485 | (2^715008-21)/5 | 215239 | Stefano Morozzi | 08/2022 |
1486 | 2^714717+782897 | 215152 | Enzo Doria | 11/2016 |
1487 | tau(373^15186) | 214796 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1488 | 2^713241+1879157 | 214707 | Enzo Doria | 08/2016 |
1489 | (23*10^214633+91)/3 | 214634 | Robert Price | 03/2023 |
1490 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
1491 | 2^712801-69553 | 214575 | Enzo Doria | 01/2016 |
1492 | 2^712603-25357 | 214515 | Enzo Doria | 09/2013 |
1493 | 2^711721-1846723 | 214250 | Enzo Doria | 07/2015 |
1494 | 2^710730-396765 | 213952 | Enzo Doria | 09/2013 |
1495 | (713^74897-1)/712 | 213685 | Jinyuan Wang | 08/2023 |
1496 | 2^708468-114329 | 213271 | Enzo Doria | 02/2015 |
1497 | (163*10^212779-1)/9 | 212781 | Serge Batalov | 12/2014 |
1498 | 2^706838-69041 | 212780 | Enzo Doria | 11/2015 |
1499 | 22*10^212339+7 | 212341 | Robert Price | 10/2022 |
1500 | 2^704577-113871 | 212099 | Enzo Doria | 10/2014 |