## PRP Records

### Probable Primes Top 10000

#### (295148 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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 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 2^865048+1882411 260406 Enzo Doria 12/2016 1252 2^864899-113871 260361 Enzo Doria 10/2014 1253 (16*10^260256-91)/3 260257 Robert Price 11/2022 1254 (7*10^260198-61)/9 260198 Erik Branger 11/2011 1255 2^864298-2788421 260180 Enzo Doria 12/2015 1256 2^864039-2791357 260102 Enzo Doria 01/2016 1257 2^863621-113833 259976 Enzo Doria 10/2014 1258 10^259945-11 259945 Mischa Rodermond 04/2023 1259 (28*10^259897+113)/3 259898 Robert Price 06/2023 1260 2^862837+75767 259740 Enzo Doria 05/2016 1261 2^862637-31 259680 Jorge Menendez 05/2019 1262 2^862088+1874941 259515 Enzo Doria 06/2016 1263 2^861987-134557 259484 Hans Havermann 10/2018 1264 (14*10^259431-143)/3 259432 Robert Price 05/2023 1265 2^861516-1854029 259343 Enzo Doria 09/2015 1266 2^860975-1853977 259180 Enzo Doria 09/2015 1267 3^543128+16 259138 Robert Price 04/2020 1268 2^860625-1858843 259074 Enzo Doria 10/2015 1269 2^860110+77689 258919 Enzo Doria 05/2016 1270 2^859600+1880371 258766 Enzo Doria 10/2016 1271 2^859433+494711 258716 Makoto Morimoto 10/2013 1273 (2^859433-44)/(2^2*3) 258715 Makoto Morimoto 08/2019 1272 (2^859431-11)/3 258715 Stefano Morozzi 08/2022 1274 (13*10^258710-43)/3 258711 Robert Price 08/2023 1275 (2^859433+39899)/(73*3907*46301) 258705 Makoto Morimoto 10/2016 1276 2^859240+1875271 258658 Enzo Doria 06/2016 1277 Tau(971^15738) 258571 Nik Lygeros / Olivier Rozier 05/2015 1278 2^858812+30421 258529 Enzo Doria 03/2024 1279 (23*10^258494-47)/3 258495 Robert Price 09/2023 1280 (144^119671+1)/145 258292 Paul Bourdelais 08/2019 1281 2^857608+105 258166 Stefano Morozzi 05/2021 1282 (11*2^857159-13)/15 258031 Renaud Lifchitz 08/2011 1283 2^857016-633113 257988 Enzo Doria 12/2013 1284 2^855732-113969 257602 Enzo Doria 10/2014 1285 (5*10^257431+91)/3 257432 Robert Price 08/2023 1286 2^853682-3911 256984 Enzo Doria 05/2014 1287 11^246668-90 256879 Enzo Doria 12/2012 1288 2^853181+30287 256834 Enzo Doria 03/2024 1289 5*2^852698+3 256689 Jon Grantham 07/2023 1290 (23*10^256654+7)/3 256655 Robert Price 05/2023 1291 2^851904-113939 256449 Enzo Doria 10/2014 1292 2^851725-851725^2 256395 Henri Lifchitz 03/2019 1293 11^246167-90 256357 Enzo Doria 12/2012 1294 (85*10^256301-1)/3 256303 Robert Price 12/2022 1295 (10^256187+7)/63443/148782853 256175 Alfred Reich 10/2021 1296 2^850700-569049 256087 Enzo Doria 11/2013 1297 2^850675+153 256079 Stefano Morozzi 05/2021 1298 21^193601-20^193601 255983 Jean-Louis Charton 02/2015 1299 (37^163193+1)/38 255918 Paul Bourdelais 07/2019 1300 (14*10^255805-83)/3 255806 Robert Price 11/2022 1301 2^849316+25861 255670 Enzo Doria 12/2023 1302 2^849177-114025 255628 Enzo Doria 12/2014 1303 2*10^255442-21 255443 Robert Price 08/2023 1304 2^848502-3173 255425 Yves Minet 07/2016 1305 2^848178-140291 255328 Enzo Doria 01/2014 1306 7*10^255167+87 255168 Robert Price 11/2022 1307 2^847622-2441 255160 Yves Minet 02/2016 1308 2^847291+182843 255061 Enzo Doria 11/2016 1309 2^847174+1879429 255025 Enzo Doria 09/2016 1310 2^846881+215837 254937 Enzo Doria 12/2023 1311 24*29^174239+13361 254809 Curtis Bright 04/2015 1312 22*10^254639+7 254641 Robert Price 10/2022 1313 2^845633-933075 254561 Paul Bourdelais 11/2021 1314 2^845610-1868591 254554 Enzo Doria 04/2016 1315 2^845484+81931 254517 Enzo Doria 08/2016 1316 2^845402-114761 254492 Enzo Doria 05/2015 1317 98*10^254173-9 254175 Robert Price 05/2023 1318 2^844334-2792441 254170 Enzo Doria 02/2016 1319 2*10^254162+69 254163 Robert Price 08/2023 1320 (4*10^254107+11)/3 254108 Tyler Busby 02/2023 1321 11^243796-90 253888 Enzo Doria 12/2012 1322 (10^253891+7)/44777/79843/16940711 253875 Alfred Reich 10/2021 1323 30^171733-29^171733 253671 Jean-Louis Charton 10/2018 1324 2^842325+25907 253566 Enzo Doria 11/2023 1325 2^842209+1876037 253531 Enzo Doria 07/2016 1326 2^842123-59197 253505 Enzo Doria 10/2015 1327 (8*10^253313-53)/9 253313 Serge Batalov 11/2022 1328 (28*10^253210+191)/3 253211 Robert Price 07/2023 1329 2^840797-3 253106 Paul Bourdelais 06/2019 1330 2^840716-2969 253081 Yves Minet 05/2016 1331 2^840358-462491 252973 Enzo Doria 08/2015 1332 2^840310+1878379 252959 Enzo Doria 08/2016 1333 2^840203-21 252927 Stefano Morozzi 07/2022 1334 11^242579-60 252620 Enzo Doria 10/2012 1335 45^152659+2 252378 Robert Price 09/2015 1336 (95^127583+1)/96 252322 Paul Bourdelais 07/2019 1337 7*10^252209-17 252210 Robert Price 12/2022 1338 2^837725+1869377 252181 Enzo Doria 05/2016 1339 2^837536-311039 252124 Enzo Doria 06/2015 1340 21^190632-2 252058 Robert Price 07/2015 1341 2^837242+1873297 252035 Enzo Doria 06/2016 1342 2^836656-2787929 251859 Enzo Doria 11/2015 1343 2^836548+219061 251827 Enzo Doria 02/2024 1344 2^836380+1875541 251776 Enzo Doria 07/2016 1345 (359^98327-1)/358 251233 Alexander Zhirkov 11/2017 1346 tau(41^28288) 250924 Nik Lygeros / Olivier Rozier 10/2013 1347 (28*10^250655+113)/3 250656 Robert Price 06/2023 1348 2^832511-461197 250611 Enzo Doria 07/2015 1349 2^832505+1881137 250609 Enzo Doria 11/2016 1350 2^832363+583295 250567 Enzo Doria 12/2016 1351 2^832244-403635 250531 Enzo Doria 01/2014 1352 (14*10^250336-41)/9 250337 Serge Batalov 01/2023 1353 2^831528+24811 250315 Enzo Doria 11/2023 1354 2^831157+1880657 250204 Enzo Doria 11/2016 1355 2^831088-7200899 250183 Enzo Doria 01/2015 1356 2^830956-1349 250143 Yves Minet 07/2015 1357 2^830699+220583 250066 Enzo Doria 03/2024 1358 2^830037+282317 249867 Enzo Doria 09/2016 1359 2^829589-113653 249732 Enzo Doria 09/2014 1360 (4*10^249550-7)/3 249551 Serge Batalov 01/2023 1361 (103*10^249399+17)/3 249401 Robert Price 04/2023 1362 2^828281-3193 249338 Yves Minet 08/2016 1363 (2^828140-19)/3 249295 Stefano Morozzi 08/2022 1364 2^828064-2785619 249273 Enzo Doria 10/2015 1365 2^827602+60409 249134 Enzo Doria 03/2016 1366 2^827306+212419 249044 Enzo Doria 09/2023 1367 10^249010+348861 249011 Patrick De Geest 04/2016 1368 10^249010-21 249010 Serge Batalov 12/2014 1369 2^826733+1882907 248872 Enzo Doria 12/2016 1370 2^825800+22441 248591 Enzo Doria 10/2023 1371 2^825682+1876549 248556 Enzo Doria 07/2016 1372 2^824991-114121 248348 Enzo Doria 12/2014 1373 2^824642-362727 248242 Enzo Doria 12/2013 1374 2^824565-114265 248219 Enzo Doria 01/2015 1375 (73*10^248145-1)/9 248146 Robert Price 01/2015 1376 2^823321+219407 247845 Enzo Doria 02/2024 1377 (2^823337+1)/(3*362268281) 247841 Gord Palameta 08/2018 1378 (13*10^247793-43)/3 247794 Robert Price 08/2023 1379 (2^822971-1)/6583769/28211445881/21255852651726486149207 247700 Robert Kinser 09/2016 1380 2^822296+76501 247536 Enzo Doria 05/2016 1381 2^821590-114167 247324 Enzo Doria 12/2014 1382 2^821512-2790659 247300 Enzo Doria 12/2015 1383 (21996^57121-1)/(21996^239-1) 247002 Ryan Propper 11/2023 1384 2^820356+7 246952 Jon Grantham 08/2023 1385 2^820077+382847 246868 Enzo Doria 11/2016 1386 2^820001+81269 246845 Enzo Doria 07/2016 1387 2^819463-59197 246683 Enzo Doria 10/2015 1388 2^819296+80581 246633 Enzo Doria 07/2016 1389 2^818764+21573 246473 Enzo Doria 11/2023 1390 2^817852+215491 246198 Enzo Doria 11/2023 1391 2^817160-350369 245990 Enzo Doria 06/2015 1392 2^816039-19 245653 Stefano Morozzi 07/2022 1393 2^816029+219407 245650 Enzo Doria 02/2024 1394 (71*10^245558-17)/9 245559 Serge Batalov 01/2023 1395 5*3^514648+2^514648 245551 Jon Grantham 08/2023 1396 88093#+(653879#)/(88093#) 245374 Makoto Morimoto 11/2017 1397 2^815111-113857 245373 Enzo Doria 10/2014 1398 (34555^54289-1)/(34555^233-1) 245334 Ryan Propper 11/2023 1399 2^814914-4001 245314 Yves Minet 05/2017 1400 846^83761-845^83761 245200 Jean-Louis Charton 12/2012 1401 2^814356-2790449 245146 Enzo Doria 12/2015 1402 2^814276-459029 245122 Enzo Doria 04/2015 1403 2^814023+180923 245046 Enzo Doria 07/2016 1404 2^813496+216751 244887 Enzo Doria 12/2023 1405 (3^513059-2^513059)/(1026119*5430216457) 244776 Mike Oakes 03/2017 1406 3^513007+16 244767 Robert Price 04/2020 1407 2^811882+27289 244401 Enzo Doria 12/2023 1408 2^811842-113675 244389 Enzo Doria 09/2014 1409 2^811132-2787929 244176 Enzo Doria 11/2015 1410 2^809746-2790971 243758 Enzo Doria 01/2016 1411 (14*10^243724-197)/3 243725 Robert Price 03/2023 1412 2^808767-3295 243464 Yves Minet 12/2016 1413 2^808621-113809 243420 Enzo Doria 09/2014 1414 2^808199+29693 243293 Enzo Doria 03/2024 1415 2^807724+1879621 243150 Enzo Doria 09/2016 1416 2^807417+217787 243057 Enzo Doria 01/2024 1417 (23*10^242909+91)/3 242910 Robert Price 03/2023 1418 2^806708+20371 242844 Enzo Doria 08/2023 1419 2*10^242822-91 242823 Robert Price 02/2023 1420 20^186554-3 242713 Paul Bourdelais 12/2020 1421 2^805843-113611 242583 Enzo Doria 08/2014 1422 2^805745-459763 242554 Enzo Doria 05/2015 1423 2^805353+782687 242436 Enzo Doria 11/2016 1424 (19*10^242362-7)/3 242363 Robert Price 12/2023 1425 2^804895+29963 242298 Enzo Doria 03/2024 1426 2^804725+28229 242247 Enzo Doria 01/2024 1427 6^311257+5 242206 Paul Bourdelais 02/2021 1428 2^804277-417933 242112 Enzo Doria 01/2014 1429 2^803468-269039 241868 Enzo Doria 10/2013 1430 2^803172+80851 241779 Enzo Doria 07/2016 1431 2^803011+220073 241731 Enzo Doria 03/2024 1432 3^506233-2 241535 Robert Price 11/2013 1433 2^802025-25999 241434 Enzo Doria 10/2013 1434 (3^505823+3^252912+1)/7 241339 Serge Batalov 03/2014 1435 2^801575+25073 241299 Enzo Doria 11/2023 1436 2^801303+1872923 241217 Enzo Doria 05/2016 1437 2^801105+216977 241157 Enzo Doria 12/2023 1438 (23*10^241048-143)/3 241049 Robert Price 12/2023 1439 2^800579-1862947 240999 Enzo Doria 12/2015 1440 2^799999+16205 240824 Norman Luhn 09/2023 1441 3^504206+2 240568 Luke W. Richards 03/2018 1442 2^798973-26283 240515 Enzo Doria 10/2013 1443 2^798671-69487 240424 Enzo Doria 12/2015 1444 2^797220+79831 239988 Enzo Doria 06/2016 1445 2^796910-26001 239894 Enzo Doria 10/2013 1446 2^796598+653119 239800 Enzo Doria 12/2016 1447 2^796432-1859729 239750 Enzo Doria 11/2015 1448 2^796002-1852211 239621 Enzo Doria 08/2015 1449 2^795884+214081 239585 Enzo Doria 10/2023 1450 2^795709+75767 239533 Enzo Doria 04/2016 1451 2^795708+81721 239532 Enzo Doria 08/2016 1452 2^795468-2786249 239460 Enzo Doria 10/2015 1453 2^795442+80779 239452 Enzo Doria 07/2016 1454 2^795075-1852057 239342 Enzo Doria 08/2015 1455 (86^123677+1)/87 239252 Paul Bourdelais 01/2019 1456 2^794043+1875023 239031 Enzo Doria 06/2016 1457 2^793347-69577 238822 Enzo Doria 01/2016 1458 5*2^793288+3 238805 Jon Grantham 07/2023 1459 2^792988-344429 238714 Enzo Doria 08/2015 1460 2^792700-2786369 238627 Enzo Doria 11/2015 1461 2^792663-1844797 238616 Enzo Doria 06/2015 1462 2^792605-291943 238598 Enzo Doria 07/2015 1463 2^792366+218599 238526 Enzo Doria 01/2024 1464 (2^792061-2^396031+1)/5 238434 Thomas Ritschel 03/2014 1465 2^791321+30077 238212 Enzo Doria 03/2024 1466 4*10^238163+21 238164 Robert Price 12/2022 1467 (26*10^238157-77)/3 238158 Robert Price 03/2023 1468 10^237670+9 237671 Robert Price 08/2023 1469 2^789373+1869377 237625 Enzo Doria 05/2016 1470 ((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961 237544 Serge Batalov 04/2015 1471 2^789033+218537 237523 Enzo Doria 01/2024 1472 2^788942+1866409 237496 Enzo Doria 02/2016 1473 2^788844-114329 237466 Enzo Doria 01/2015 1474 2^788705-1859713 237424 Enzo Doria 11/2015 1475 15^201475+14 236953 Alfred Reich 10/2023 1476 2^786663+219173 236810 Enzo Doria 02/2024 1477 2^786180+1871971 236664 Enzo Doria 05/2016 1478 11^227092-90 236492 Enzo Doria 11/2012 1479 2^785260+1866361 236387 Enzo Doria 02/2016 1480 2^785220+1880611 236375 Enzo Doria 10/2016 1481 (2^784689-15)/7 236215 Stefano Morozzi 08/2022 1482 19^184650-2 236122 Robert Price 10/2014 1483 10^236059+216513 236060 Patrick De Geest 04/2016 1484 10^236059-20909 236059 Robert Price 09/2015 1485 2^783893-21 235976 Stefano Morozzi 07/2022 1486 (87^121487-1)/86 235625 Paul Bourdelais 12/2018 1487 2^782634-113981 235597 Enzo Doria 11/2014 1488 2^782423+1879733 235533 Enzo Doria 09/2016 1489 (10^(2*117707+1)+12*10^117707-1)/3 235415 Robert Price 10/2023 1490 2^781682-2789543 235310 Enzo Doria 12/2015 1491 2^780481+21489 234949 Enzo Doria 05/2024 1492 2^780408-113453 234927 Enzo Doria 08/2014 1493 7*10^234915+9 234916 Robert Price 04/2023 1494 2^780368-1864829 234915 Enzo Doria 01/2016 1495 2^780284+7 234889 Jon Grantham 08/2023 1496 2^779593-1836559 234681 Enzo Doria 05/2015 1497 (8713#+(549391#)/(8713#))/360295171 234487 Makoto Morimoto 11/2017 1498 (5^335429+1)/6 234455 Paul Bourdelais 08/2010 1499 2^778788+22201 234439 Enzo Doria 09/2023 1500 2^778395-113617 234321 Enzo Doria 08/2014

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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