## PRP Records

### Probable Primes Top 10000

#### (295756 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 48358*10^270343-48357 270348 Danilo Nitsche 09/2013 1252 (10^270343-1)/9 270343 Maksym Voznyy 07/2007 1253 2^897867-3217 270285 Yves Minet 12/2016 1254 2^897849-115273 270280 Enzo Doria 07/2015 1255 2^897367+26289 270135 Enzo Doria 03/2024 1256 2^896616-114179 269909 Enzo Doria 12/2014 1257 (12648^66049-1)/(12648^257-1) 269881 Ryan Propper 11/2023 1258 (10^(2*134811+1)+6*10^134811-1)/3 269623 Robert Price 08/2024 1259 (22*10^269517-19)/3 269518 Robert Price 07/2023 1260 10^(2*134739+1)-7*10^134739-1 269479 Robert Price 07/2023 1261 2^894928+583561 269401 Enzo Doria 04/2017 1262 2^894673-39343 269324 Enzo Doria 08/2015 1263 2^893836+23221 269072 Enzo Doria 10/2023 1264 2^892718+29539 268735 Enzo Doria 03/2024 1265 2^892660+213901 268718 Enzo Doria 10/2023 1266 F(1285607) 268676 Henri Lifchitz 11/2008 1267 2^892234+22189 268590 Enzo Doria 09/2023 1268 2^892151+24863 268565 Enzo Doria 11/2023 1269 2^892112+187663 268553 Enzo Doria 08/2016 1270 (266*10^268407-17)/3 268409 Robert Price 02/2023 1271 (10^268207+1)/11 268206 Paul Bourdelais 02/2010 1272 2^890957-69583 268205 Enzo Doria 12/2015 1273 32841!^2+32840!^2+...+2!^2+1!^2 268128 Serge Batalov 07/2017 1274 2^890122-351401 267954 Enzo Doria 07/2015 1275 (19^209359-1)/18 267718 Paul Bourdelais 08/2010 1276 (85^138647+1)/86 267507 Paul Bourdelais 07/2019 1277 (1005^89087-1)/1004 267451 Jinyuan Wang 01/2024 1278 (485^99523-1)/484 267291 Michael Stocker 05/2020 1279 2^886324+77791 266811 Enzo Doria 06/2016 1280 7*10^266731+87 266732 Robert Price 11/2022 1281 2^886040+213901 266725 Enzo Doria 10/2023 1282 2^885242+217909 266485 Enzo Doria 01/2024 1283 2^884738+26809 266333 Enzo Doria 12/2023 1284 2^884714+1880527 266326 Enzo Doria 10/2016 1285 7*10^266024-47 266025 Robert Price 08/2023 1286 11^255426+255426^11 265999 Serge Batalov 05/2014 1287 2^883462-343421 265949 Enzo Doria 07/2015 1288 2^883442+1875019 265943 Enzo Doria 06/2016 1289 2^883333-291583 265910 Enzo Doria 07/2015 1290 2^883132+30421 265850 Enzo Doria 03/2024 1291 10^265566+3593037 265567 Paul Bourdelais 08/2023 1292 (2*10^265321-17)/3 265321 Serge Batalov 11/2022 1293 (16*10^265052-91)/3 265053 Robert Price 11/2022 1294 2^880411+1882673 265031 Enzo Doria 12/2016 1295 (14*10^264791-11)/3 264792 Robert Price 08/2022 1296 2^879530-2788031 264765 Enzo Doria 12/2015 1297 2^879292+25171 264694 Enzo Doria 11/2023 1298 (2*10^264539+61)/9 264539 Serge Batalov 11/2022 1299 2^878118+2793079 264340 Enzo Doria 02/2016 1300 (2^878073-7)/5 264326 Stefano Morozzi 08/2022 1301 (37^168527-1)/36 264283 Paul Bourdelais 08/2019 1302 5^377865+3^377865-1 264117 Jon Grantham 08/2023 1303 (19*10^263971+131)/3 263972 Robert Price 08/2023 1304 2^876202-17 263764 Stefano Morozzi 07/2022 1305 (14*10^263720-11)/3 263721 Robert Price 08/2022 1306 2^875748-461129 263627 Enzo Doria 07/2015 1307 2^875518-15 263558 Stefano Morozzi 07/2022 1308 (29*10^263523-17)/3 263524 Robert Price 01/2023 1309 2^875181-2789923 263456 Enzo Doria 12/2015 1310 2^875101-350083 263432 Enzo Doria 08/2015 1311 2^874684+1883587 263307 Enzo Doria 01/2017 1312 2^874616+1872211 263286 Enzo Doria 05/2016 1313 2^874566+30049 263271 Enzo Doria 03/2024 1314 3^551491+16 263129 Robert Price 04/2020 1315 2^874073+2792957 263123 Enzo Doria 02/2016 1316 (7*10^263006-19)/3 263007 Robert Price 10/2023 1317 2^873628+1878751 262989 Enzo Doria 08/2016 1318 2^873497+20837 262949 Enzo Doria 08/2023 1319 2^873288-269 262886 Yves Minet 01/2015 1320 (2*10^262874+7)/9 262874 Rytis Slatkevicius 01/2023 1321 (28*10^262655-43)/3 262656 Robert Price 04/2023 1322 (2*10^262603-11)/9 262603 Serge Batalov 11/2022 1323 2^871991-4207 262496 Yves Minet 03/2021 1324 (23*10^262324+7)/3 262325 Robert Price 05/2023 1325 2^871146-3173 262242 Yves Minet 07/2016 1326 (10^(2*131020+1)+63*10^131020-1)/9 262041 Robert Price 08/2024 1327 2^869601-163 261776 Yves Minet 01/2015 1328 (2*10^261704+61)/9 261704 Serge Batalov 11/2022 1329 2^869326+282859 261694 Enzo Doria 11/2016 1330 2^869035-114181 261606 Enzo Doria 12/2014 1331 2^868817+26777 261540 Enzo Doria 12/2023 1332 3^547850+9000004 261391 Enzo Doria 10/2023 1333 4*10^261248+91 261249 Robert Price 11/2022 1334 2^866908+34891 260966 Enzo Doria 07/2024 1335 2^865715+80303 260607 Enzo Doria 07/2016 1336 2^865474+23209 260534 Enzo Doria 10/2023 1337 2^865238+214759 260463 Enzo Doria 11/2023 1338 2^865048+1882411 260406 Enzo Doria 12/2016 1339 2^864899-113871 260361 Enzo Doria 10/2014 1340 (16*10^260256-91)/3 260257 Robert Price 11/2022 1341 (7*10^260198-61)/9 260198 Erik Branger 11/2011 1342 2^864298-2788421 260180 Enzo Doria 12/2015 1343 2^864039-2791357 260102 Enzo Doria 01/2016 1344 2^863621-113833 259976 Enzo Doria 10/2014 1345 10^259945-11 259945 Mischa Rodermond 04/2023 1346 2^863433+34877 259920 Enzo Doria 07/2024 1347 (28*10^259897+113)/3 259898 Robert Price 06/2023 1348 2^862837+75767 259740 Enzo Doria 05/2016 1349 2^862637-31 259680 Jorge Menendez 05/2019 1350 2^862088+1874941 259515 Enzo Doria 06/2016 1351 2^861987-134557 259484 Hans Havermann 10/2018 1352 (14*10^259431-143)/3 259432 Robert Price 05/2023 1353 2^861516-1854029 259343 Enzo Doria 09/2015 1354 2^860975-1853977 259180 Enzo Doria 09/2015 1355 3^543128+16 259138 Robert Price 04/2020 1356 2^860625-1858843 259074 Enzo Doria 10/2015 1357 2^860110+77689 258919 Enzo Doria 05/2016 1358 2^859600+1880371 258766 Enzo Doria 10/2016 1359 2^859433+494711 258716 Makoto Morimoto 10/2013 1360 (2^859433-44)/(2^2*3) 258715 Makoto Morimoto 08/2019 1361 (2^859431-11)/3 258715 Stefano Morozzi 08/2022 1362 (13*10^258710-43)/3 258711 Robert Price 08/2023 1363 (2^859433+39899)/(73*3907*46301) 258705 Makoto Morimoto 10/2016 1364 2^859240+1875271 258658 Enzo Doria 06/2016 1365 Tau(971^15738) 258571 Nik Lygeros / Olivier Rozier 05/2015 1366 2^858812+30421 258529 Enzo Doria 03/2024 1367 (23*10^258494-47)/3 258495 Robert Price 09/2023 1368 (144^119671+1)/145 258292 Paul Bourdelais 08/2019 1369 2^857608+105 258166 Stefano Morozzi 05/2021 1370 (11*2^857159-13)/15 258031 Renaud Lifchitz 08/2011 1371 2^857016-633113 257988 Enzo Doria 12/2013 1372 2^855732-113969 257602 Enzo Doria 10/2014 1373 (5*10^257431+91)/3 257432 Robert Price 08/2023 1374 2^853682-3911 256984 Enzo Doria 05/2014 1375 11^246668-90 256879 Enzo Doria 12/2012 1376 2^853181+30287 256834 Enzo Doria 03/2024 1377 5*2^852698+3 256689 Jon Grantham 07/2023 1378 (23*10^256654+7)/3 256655 Robert Price 05/2023 1379 2^851904-113939 256449 Enzo Doria 10/2014 1380 2^851725-851725^2 256395 Henri Lifchitz 03/2019 1381 11^246167-90 256357 Enzo Doria 12/2012 1382 (85*10^256301-1)/3 256303 Robert Price 12/2022 1383 (10^256187+7)/63443/148782853 256175 Alfred Reich 10/2021 1384 2^850700-569049 256087 Enzo Doria 11/2013 1385 2^850675+153 256079 Stefano Morozzi 05/2021 1386 21^193601-20^193601 255983 Jean-Louis Charton 02/2015 1387 (37^163193+1)/38 255918 Paul Bourdelais 07/2019 1388 (14*10^255805-83)/3 255806 Robert Price 11/2022 1389 2^849316+25861 255670 Enzo Doria 12/2023 1390 2^849177-114025 255628 Enzo Doria 12/2014 1391 2*10^255442-21 255443 Robert Price 08/2023 1392 2^848502-3173 255425 Yves Minet 07/2016 1393 2^848178-140291 255328 Enzo Doria 01/2014 1394 7*10^255167+87 255168 Robert Price 11/2022 1395 2^847622-2441 255160 Yves Minet 02/2016 1396 2^847291+182843 255061 Enzo Doria 11/2016 1397 2^847174+1879429 255025 Enzo Doria 09/2016 1398 2^846881+215837 254937 Enzo Doria 12/2023 1399 24*29^174239+13361 254809 Curtis Bright 04/2015 1400 22*10^254639+7 254641 Robert Price 10/2022 1401 2^845633-933075 254561 Paul Bourdelais 11/2021 1402 2^845610-1868591 254554 Enzo Doria 04/2016 1403 2^845484+81931 254517 Enzo Doria 08/2016 1404 2^845402-114761 254492 Enzo Doria 05/2015 1405 98*10^254173-9 254175 Robert Price 05/2023 1406 2^844334-2792441 254170 Enzo Doria 02/2016 1407 2*10^254162+69 254163 Robert Price 08/2023 1408 (4*10^254107+11)/3 254108 Tyler Busby 02/2023 1409 11^243796-90 253888 Enzo Doria 12/2012 1410 (10^253891+7)/44777/79843/16940711 253875 Alfred Reich 10/2021 1411 30^171733-29^171733 253671 Jean-Louis Charton 10/2018 1412 2^842325+25907 253566 Enzo Doria 11/2023 1413 2^842209+1876037 253531 Enzo Doria 07/2016 1414 2^842123-59197 253505 Enzo Doria 10/2015 1415 (8*10^253313-53)/9 253313 Serge Batalov 11/2022 1416 (28*10^253210+191)/3 253211 Robert Price 07/2023 1417 2^840797-3 253106 Paul Bourdelais 06/2019 1418 2^840716-2969 253081 Yves Minet 05/2016 1419 2^840358-462491 252973 Enzo Doria 08/2015 1420 2^840310+1878379 252959 Enzo Doria 08/2016 1421 2^840203-21 252927 Stefano Morozzi 07/2022 1422 11^242579-60 252620 Enzo Doria 10/2012 1423 45^152659+2 252378 Robert Price 09/2015 1424 (95^127583+1)/96 252322 Paul Bourdelais 07/2019 1425 7*10^252209-17 252210 Robert Price 12/2022 1426 2^837725+1869377 252181 Enzo Doria 05/2016 1427 2^837536-311039 252124 Enzo Doria 06/2015 1428 21^190632-2 252058 Robert Price 07/2015 1429 2^837242+1873297 252035 Enzo Doria 06/2016 1430 2^836656-2787929 251859 Enzo Doria 11/2015 1431 2^836548+219061 251827 Enzo Doria 02/2024 1432 2^836380+1875541 251776 Enzo Doria 07/2016 1433 (359^98327-1)/358 251233 Alexander Zhirkov 11/2017 1434 tau(41^28288) 250924 Nik Lygeros / Olivier Rozier 10/2013 1435 (28*10^250655+113)/3 250656 Robert Price 06/2023 1436 2^832511-461197 250611 Enzo Doria 07/2015 1437 2^832505+1881137 250609 Enzo Doria 11/2016 1438 2^832363+583295 250567 Enzo Doria 12/2016 1439 2^832244-403635 250531 Enzo Doria 01/2014 1440 (14*10^250336-41)/9 250337 Serge Batalov 01/2023 1441 2^831528+24811 250315 Enzo Doria 11/2023 1442 2^831157+1880657 250204 Enzo Doria 11/2016 1443 2^831088-7200899 250183 Enzo Doria 01/2015 1444 2^830956-1349 250143 Yves Minet 07/2015 1445 2^830699+220583 250066 Enzo Doria 03/2024 1446 2^830037+282317 249867 Enzo Doria 09/2016 1447 2^829589-113653 249732 Enzo Doria 09/2014 1448 (4*10^249550-7)/3 249551 Serge Batalov 01/2023 1449 (103*10^249399+17)/3 249401 Robert Price 04/2023 1450 2^828281-3193 249338 Yves Minet 08/2016 1451 (2^828140-19)/3 249295 Stefano Morozzi 08/2022 1452 2^828064-2785619 249273 Enzo Doria 10/2015 1453 2^827602+60409 249134 Enzo Doria 03/2016 1454 2^827306+212419 249044 Enzo Doria 09/2023 1455 10^249010+348861 249011 Patrick De Geest 04/2016 1456 10^249010-21 249010 Serge Batalov 12/2014 1457 2^826733+1882907 248872 Enzo Doria 12/2016 1458 2^825800+22441 248591 Enzo Doria 10/2023 1459 2^825682+1876549 248556 Enzo Doria 07/2016 1460 2^824991-114121 248348 Enzo Doria 12/2014 1461 2^824642-362727 248242 Enzo Doria 12/2013 1462 2^824565-114265 248219 Enzo Doria 01/2015 1463 (73*10^248145-1)/9 248146 Robert Price 01/2015 1464 2^823321+219407 247845 Enzo Doria 02/2024 1465 (2^823337+1)/(3*362268281) 247841 Gord Palameta 08/2018 1466 (13*10^247793-43)/3 247794 Robert Price 08/2023 1467 (2^822971-1)/6583769/28211445881/21255852651726486149207 247700 Robert Kinser 09/2016 1468 2^822296+76501 247536 Enzo Doria 05/2016 1469 2^821590-114167 247324 Enzo Doria 12/2014 1470 2^821512-2790659 247300 Enzo Doria 12/2015 1471 (21996^57121-1)/(21996^239-1) 247002 Ryan Propper 11/2023 1472 2^820356+7 246952 Jon Grantham 08/2023 1473 2^820077+382847 246868 Enzo Doria 11/2016 1474 2^820001+81269 246845 Enzo Doria 07/2016 1475 2^819463-59197 246683 Enzo Doria 10/2015 1476 2^819296+80581 246633 Enzo Doria 07/2016 1477 2^818764+21573 246473 Enzo Doria 11/2023 1478 2^817852+215491 246198 Enzo Doria 11/2023 1479 2^817160-350369 245990 Enzo Doria 06/2015 1480 2^816039-19 245653 Stefano Morozzi 07/2022 1481 2^816029+219407 245650 Enzo Doria 02/2024 1482 (71*10^245558-17)/9 245559 Serge Batalov 01/2023 1483 5*3^514648+2^514648 245551 Jon Grantham 08/2023 1484 88093#+(653879#)/(88093#) 245374 Makoto Morimoto 11/2017 1485 2^815111-113857 245373 Enzo Doria 10/2014 1486 (34555^54289-1)/(34555^233-1) 245334 Ryan Propper 11/2023 1487 2^814914-4001 245314 Yves Minet 05/2017 1488 846^83761-845^83761 245200 Jean-Louis Charton 12/2012 1489 2^814356-2790449 245146 Enzo Doria 12/2015 1490 2^814276-459029 245122 Enzo Doria 04/2015 1491 2^814023+180923 245046 Enzo Doria 07/2016 1492 2^813496+216751 244887 Enzo Doria 12/2023 1493 (3^513059-2^513059)/(1026119*5430216457) 244776 Mike Oakes 03/2017 1494 3^513007+16 244767 Robert Price 04/2020 1495 (46^147197-31^147197)/15 244752 Aurel Gibier 06/2024 1496 2^811882+27289 244401 Enzo Doria 12/2023 1497 2^811842-113675 244389 Enzo Doria 09/2014 1498 2^811132-2787929 244176 Enzo Doria 11/2015 1499 2^809746-2790971 243758 Enzo Doria 01/2016 1500 (14*10^243724-197)/3 243725 Robert Price 03/2023

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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