## PRP Records

### Probable Primes Top 10000

#### (294113 PRPs in the top)

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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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 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

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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