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 | 2^845633-933075 | 254561 | Paul Bourdelais | 11/2021 |
1252 | 2^845610-1868591 | 254554 | Enzo Doria | 04/2016 |
1253 | 2^845484+81931 | 254517 | Enzo Doria | 08/2016 |
1254 | 2^845402-114761 | 254492 | Enzo Doria | 05/2015 |
1255 | 98*10^254173-9 | 254175 | Robert Price | 05/2023 |
1256 | 2^844334-2792441 | 254170 | Enzo Doria | 02/2016 |
1257 | 2*10^254162+69 | 254163 | Robert Price | 08/2023 |
1258 | (4*10^254107+11)/3 | 254108 | Tyler Busby | 02/2023 |
1259 | 11^243796-90 | 253888 | Enzo Doria | 12/2012 |
1260 | (10^253891+7)/44777/79843/16940711 | 253875 | Alfred Reich | 10/2021 |
1261 | 30^171733-29^171733 | 253671 | Jean-Louis Charton | 10/2018 |
1262 | 2^842325+25907 | 253566 | Enzo Doria | 11/2023 |
1263 | 2^842209+1876037 | 253531 | Enzo Doria | 07/2016 |
1264 | 2^842123-59197 | 253505 | Enzo Doria | 10/2015 |
1265 | (8*10^253313-53)/9 | 253313 | Serge Batalov | 11/2022 |
1266 | (28*10^253210+191)/3 | 253211 | Robert Price | 07/2023 |
1267 | 2^840797-3 | 253106 | Paul Bourdelais | 06/2019 |
1268 | 2^840716-2969 | 253081 | Yves Minet | 05/2016 |
1269 | 2^840358-462491 | 252973 | Enzo Doria | 08/2015 |
1270 | 2^840310+1878379 | 252959 | Enzo Doria | 08/2016 |
1271 | 2^840203-21 | 252927 | Stefano Morozzi | 07/2022 |
1272 | 11^242579-60 | 252620 | Enzo Doria | 10/2012 |
1273 | 45^152659+2 | 252378 | Robert Price | 09/2015 |
1274 | (95^127583+1)/96 | 252322 | Paul Bourdelais | 07/2019 |
1275 | 7*10^252209-17 | 252210 | Robert Price | 12/2022 |
1276 | 2^837725+1869377 | 252181 | Enzo Doria | 05/2016 |
1277 | 2^837536-311039 | 252124 | Enzo Doria | 06/2015 |
1278 | 21^190632-2 | 252058 | Robert Price | 07/2015 |
1279 | 2^837242+1873297 | 252035 | Enzo Doria | 06/2016 |
1280 | 2^836656-2787929 | 251859 | Enzo Doria | 11/2015 |
1281 | 2^836548+219061 | 251827 | Enzo Doria | 02/2024 |
1282 | 2^836380+1875541 | 251776 | Enzo Doria | 07/2016 |
1283 | (359^98327-1)/358 | 251233 | Alexander Zhirkov | 11/2017 |
1284 | tau(41^28288) | 250924 | Nik Lygeros / Olivier Rozier | 10/2013 |
1285 | (28*10^250655+113)/3 | 250656 | Robert Price | 06/2023 |
1286 | 2^832511-461197 | 250611 | Enzo Doria | 07/2015 |
1287 | 2^832505+1881137 | 250609 | Enzo Doria | 11/2016 |
1288 | 2^832363+583295 | 250567 | Enzo Doria | 12/2016 |
1289 | 2^832244-403635 | 250531 | Enzo Doria | 01/2014 |
1290 | (14*10^250336-41)/9 | 250337 | Serge Batalov | 01/2023 |
1291 | 2^831528+24811 | 250315 | Enzo Doria | 11/2023 |
1292 | 2^831157+1880657 | 250204 | Enzo Doria | 11/2016 |
1293 | 2^831088-7200899 | 250183 | Enzo Doria | 01/2015 |
1294 | 2^830956-1349 | 250143 | Yves Minet | 07/2015 |
1295 | 2^830037+282317 | 249867 | Enzo Doria | 09/2016 |
1296 | 2^829589-113653 | 249732 | Enzo Doria | 09/2014 |
1297 | (4*10^249550-7)/3 | 249551 | Serge Batalov | 01/2023 |
1298 | (103*10^249399+17)/3 | 249401 | Robert Price | 04/2023 |
1299 | 2^828281-3193 | 249338 | Yves Minet | 08/2016 |
1300 | (2^828140-19)/3 | 249295 | Stefano Morozzi | 08/2022 |
1301 | 2^828064-2785619 | 249273 | Enzo Doria | 10/2015 |
1302 | 2^827602+60409 | 249134 | Enzo Doria | 03/2016 |
1303 | 2^827306+212419 | 249044 | Enzo Doria | 09/2023 |
1304 | 10^249010+348861 | 249011 | Patrick De Geest | 04/2016 |
1305 | 10^249010-21 | 249010 | Serge Batalov | 12/2014 |
1306 | 2^826733+1882907 | 248872 | Enzo Doria | 12/2016 |
1307 | 2^825800+22441 | 248591 | Enzo Doria | 10/2023 |
1308 | 2^825682+1876549 | 248556 | Enzo Doria | 07/2016 |
1309 | 2^824991-114121 | 248348 | Enzo Doria | 12/2014 |
1310 | 2^824642-362727 | 248242 | Enzo Doria | 12/2013 |
1311 | 2^824565-114265 | 248219 | Enzo Doria | 01/2015 |
1312 | (73*10^248145-1)/9 | 248146 | Robert Price | 01/2015 |
1313 | 2^823321+219407 | 247845 | Enzo Doria | 02/2024 |
1314 | (2^823337+1)/(3*362268281) | 247841 | Gord Palameta | 08/2018 |
1315 | (13*10^247793-43)/3 | 247794 | Robert Price | 08/2023 |
1316 | (2^822971-1)/6583769/28211445881/21255852651726486149207 | 247700 | Robert Kinser | 09/2016 |
1317 | 2^822296+76501 | 247536 | Enzo Doria | 05/2016 |
1318 | 2^821590-114167 | 247324 | Enzo Doria | 12/2014 |
1319 | 2^821512-2790659 | 247300 | Enzo Doria | 12/2015 |
1320 | (21996^57121-1)/(21996^239-1) | 247002 | Ryan Propper | 11/2023 |
1321 | 2^820356+7 | 246952 | Jon Grantham | 08/2023 |
1322 | 2^820077+382847 | 246868 | Enzo Doria | 11/2016 |
1323 | 2^820001+81269 | 246845 | Enzo Doria | 07/2016 |
1324 | 2^819463-59197 | 246683 | Enzo Doria | 10/2015 |
1325 | 2^819296+80581 | 246633 | Enzo Doria | 07/2016 |
1326 | 2^818764+21573 | 246473 | Enzo Doria | 11/2023 |
1327 | 2^817852+215491 | 246198 | Enzo Doria | 11/2023 |
1328 | 2^817160-350369 | 245990 | Enzo Doria | 06/2015 |
1329 | 2^816039-19 | 245653 | Stefano Morozzi | 07/2022 |
1330 | 2^816029+219407 | 245650 | Enzo Doria | 02/2024 |
1331 | (71*10^245558-17)/9 | 245559 | Serge Batalov | 01/2023 |
1332 | 5*3^514648+2^514648 | 245551 | Jon Grantham | 08/2023 |
1333 | 88093#+(653879#)/(88093#) | 245374 | Makoto Morimoto | 11/2017 |
1334 | 2^815111-113857 | 245373 | Enzo Doria | 10/2014 |
1335 | (34555^54289-1)/(34555^233-1) | 245334 | Ryan Propper | 11/2023 |
1336 | 2^814914-4001 | 245314 | Yves Minet | 05/2017 |
1337 | 846^83761-845^83761 | 245200 | Jean-Louis Charton | 12/2012 |
1338 | 2^814356-2790449 | 245146 | Enzo Doria | 12/2015 |
1339 | 2^814276-459029 | 245122 | Enzo Doria | 04/2015 |
1340 | 2^814023+180923 | 245046 | Enzo Doria | 07/2016 |
1341 | 2^813496+216751 | 244887 | Enzo Doria | 12/2023 |
1342 | (3^513059-2^513059)/(1026119*5430216457) | 244776 | Mike Oakes | 03/2017 |
1343 | 3^513007+16 | 244767 | Robert Price | 04/2020 |
1344 | 2^811882+27289 | 244401 | Enzo Doria | 12/2023 |
1345 | 2^811842-113675 | 244389 | Enzo Doria | 09/2014 |
1346 | 2^811132-2787929 | 244176 | Enzo Doria | 11/2015 |
1347 | 2^809746-2790971 | 243758 | Enzo Doria | 01/2016 |
1348 | (14*10^243724-197)/3 | 243725 | Robert Price | 03/2023 |
1349 | 2^808767-3295 | 243464 | Yves Minet | 12/2016 |
1350 | 2^808621-113809 | 243420 | Enzo Doria | 09/2014 |
1351 | 2^808199+29693 | 243293 | Enzo Doria | 03/2024 |
1352 | 2^807724+1879621 | 243150 | Enzo Doria | 09/2016 |
1353 | 2^807417+217787 | 243057 | Enzo Doria | 01/2024 |
1354 | (23*10^242909+91)/3 | 242910 | Robert Price | 03/2023 |
1355 | 2^806708+20371 | 242844 | Enzo Doria | 08/2023 |
1356 | 2*10^242822-91 | 242823 | Robert Price | 02/2023 |
1357 | 20^186554-3 | 242713 | Paul Bourdelais | 12/2020 |
1358 | 2^805843-113611 | 242583 | Enzo Doria | 08/2014 |
1359 | 2^805745-459763 | 242554 | Enzo Doria | 05/2015 |
1360 | 2^805353+782687 | 242436 | Enzo Doria | 11/2016 |
1361 | (19*10^242362-7)/3 | 242363 | Robert Price | 12/2023 |
1362 | 2^804725+28229 | 242247 | Enzo Doria | 01/2024 |
1363 | 6^311257+5 | 242206 | Paul Bourdelais | 02/2021 |
1364 | 2^804277-417933 | 242112 | Enzo Doria | 01/2014 |
1365 | 2^803468-269039 | 241868 | Enzo Doria | 10/2013 |
1366 | 2^803172+80851 | 241779 | Enzo Doria | 07/2016 |
1367 | 2^803011+220073 | 241731 | Enzo Doria | 03/2024 |
1368 | 3^506233-2 | 241535 | Robert Price | 11/2013 |
1369 | 2^802025-25999 | 241434 | Enzo Doria | 10/2013 |
1370 | (3^505823+3^252912+1)/7 | 241339 | Serge Batalov | 03/2014 |
1371 | 2^801575+25073 | 241299 | Enzo Doria | 11/2023 |
1372 | 2^801303+1872923 | 241217 | Enzo Doria | 05/2016 |
1373 | 2^801105+216977 | 241157 | Enzo Doria | 12/2023 |
1374 | (23*10^241048-143)/3 | 241049 | Robert Price | 12/2023 |
1375 | 2^800579-1862947 | 240999 | Enzo Doria | 12/2015 |
1376 | 2^799999+16205 | 240824 | Norman Luhn | 09/2023 |
1377 | 3^504206+2 | 240568 | Luke W. Richards | 03/2018 |
1378 | 2^798973-26283 | 240515 | Enzo Doria | 10/2013 |
1379 | 2^798671-69487 | 240424 | Enzo Doria | 12/2015 |
1380 | 2^797220+79831 | 239988 | Enzo Doria | 06/2016 |
1381 | 2^796910-26001 | 239894 | Enzo Doria | 10/2013 |
1382 | 2^796598+653119 | 239800 | Enzo Doria | 12/2016 |
1383 | 2^796432-1859729 | 239750 | Enzo Doria | 11/2015 |
1384 | 2^796002-1852211 | 239621 | Enzo Doria | 08/2015 |
1385 | 2^795884+214081 | 239585 | Enzo Doria | 10/2023 |
1386 | 2^795709+75767 | 239533 | Enzo Doria | 04/2016 |
1387 | 2^795708+81721 | 239532 | Enzo Doria | 08/2016 |
1388 | 2^795468-2786249 | 239460 | Enzo Doria | 10/2015 |
1389 | 2^795442+80779 | 239452 | Enzo Doria | 07/2016 |
1390 | 2^795075-1852057 | 239342 | Enzo Doria | 08/2015 |
1391 | (86^123677+1)/87 | 239252 | Paul Bourdelais | 01/2019 |
1392 | 2^794043+1875023 | 239031 | Enzo Doria | 06/2016 |
1393 | 2^793347-69577 | 238822 | Enzo Doria | 01/2016 |
1394 | 5*2^793288+3 | 238805 | Jon Grantham | 07/2023 |
1395 | 2^792988-344429 | 238714 | Enzo Doria | 08/2015 |
1396 | 2^792700-2786369 | 238627 | Enzo Doria | 11/2015 |
1397 | 2^792663-1844797 | 238616 | Enzo Doria | 06/2015 |
1398 | 2^792605-291943 | 238598 | Enzo Doria | 07/2015 |
1399 | 2^792366+218599 | 238526 | Enzo Doria | 01/2024 |
1400 | (2^792061-2^396031+1)/5 | 238434 | Thomas Ritschel | 03/2014 |
1401 | 4*10^238163+21 | 238164 | Robert Price | 12/2022 |
1402 | (26*10^238157-77)/3 | 238158 | Robert Price | 03/2023 |
1403 | 10^237670+9 | 237671 | Robert Price | 08/2023 |
1404 | 2^789373+1869377 | 237625 | Enzo Doria | 05/2016 |
1405 | ((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961 | 237544 | Serge Batalov | 04/2015 |
1406 | 2^789033+218537 | 237523 | Enzo Doria | 01/2024 |
1407 | 2^788942+1866409 | 237496 | Enzo Doria | 02/2016 |
1408 | 2^788844-114329 | 237466 | Enzo Doria | 01/2015 |
1409 | 2^788705-1859713 | 237424 | Enzo Doria | 11/2015 |
1410 | 15^201475+14 | 236953 | Alfred Reich | 10/2023 |
1411 | 2^786663+219173 | 236810 | Enzo Doria | 02/2024 |
1412 | 2^786180+1871971 | 236664 | Enzo Doria | 05/2016 |
1413 | 11^227092-90 | 236492 | Enzo Doria | 11/2012 |
1414 | 2^785260+1866361 | 236387 | Enzo Doria | 02/2016 |
1415 | 2^785220+1880611 | 236375 | Enzo Doria | 10/2016 |
1416 | (2^784689-15)/7 | 236215 | Stefano Morozzi | 08/2022 |
1417 | 19^184650-2 | 236122 | Robert Price | 10/2014 |
1418 | 10^236059+216513 | 236060 | Patrick De Geest | 04/2016 |
1419 | 10^236059-20909 | 236059 | Robert Price | 09/2015 |
1420 | 2^783893-21 | 235976 | Stefano Morozzi | 07/2022 |
1421 | (87^121487-1)/86 | 235625 | Paul Bourdelais | 12/2018 |
1422 | 2^782634-113981 | 235597 | Enzo Doria | 11/2014 |
1423 | 2^782423+1879733 | 235533 | Enzo Doria | 09/2016 |
1424 | (10^(2*117707+1)+12*10^117707-1)/3 | 235415 | Robert Price | 10/2023 |
1425 | 2^781682-2789543 | 235310 | Enzo Doria | 12/2015 |
1426 | 2^780408-113453 | 234927 | Enzo Doria | 08/2014 |
1427 | 7*10^234915+9 | 234916 | Robert Price | 04/2023 |
1428 | 2^780368-1864829 | 234915 | Enzo Doria | 01/2016 |
1429 | 2^780284+7 | 234889 | Jon Grantham | 08/2023 |
1430 | 2^779593-1836559 | 234681 | Enzo Doria | 05/2015 |
1431 | (8713#+(549391#)/(8713#))/360295171 | 234487 | Makoto Morimoto | 11/2017 |
1432 | (5^335429+1)/6 | 234455 | Paul Bourdelais | 08/2010 |
1433 | 2^778788+22201 | 234439 | Enzo Doria | 09/2023 |
1434 | 2^778395-113617 | 234321 | Enzo Doria | 08/2014 |
1435 | 5*2^778090+3 | 234230 | Jon Grantham | 07/2023 |
1436 | (21430^54289-1)/(21430^233-1) | 234118 | Ryan Propper | 11/2023 |
1437 | (5*10^234054-101)/3 | 234055 | Robert Price | 08/2023 |
1438 | 23*10^234025-7 | 234027 | Robert Price | 10/2022 |
1439 | Phi(78125,5517) | 233857 | Anonymous | 09/2022 |
1440 | 5^334359-3^334359-1 | 233707 | Jon Grantham | 08/2023 |
1441 | 2^776245-2792353 | 233674 | Enzo Doria | 02/2016 |
1442 | 2^776060-114029 | 233618 | Enzo Doria | 11/2014 |
1443 | 2^775987-2789557 | 233596 | Enzo Doria | 12/2015 |
1444 | 2*10^233564-91 | 233565 | Robert Price | 02/2023 |
1445 | 2^775672+1866721 | 233501 | Enzo Doria | 03/2016 |
1446 | 2^775238+57 | 233370 | Stefano Morozzi | 05/2021 |
1447 | (11^223999+1)/12 | 233270 | Paul Bourdelais | 02/2010 |
1448 | 2^774118+1885789 | 233033 | Enzo Doria | 04/2017 |
1449 | 21^176191-20^176191 | 232964 | Jean-Louis Charton | 01/2015 |
1450 | 2^773723+217523 | 232914 | Enzo Doria | 01/2024 |
1451 | 2^773679-113425 | 232901 | Enzo Doria | 08/2014 |
1452 | (7*10^232620+23)/3 | 232621 | Robert Price | 05/2023 |
1453 | 10^232599+192489 | 232600 | Patrick De Geest | 12/2013 |
1454 | 10^232599-3 | 232599 | Markus Tervooren | 10/2010 |
1455 | 2^772552-458879 | 232562 | Enzo Doria | 04/2015 |
1456 | 2^772214+1874899 | 232460 | Enzo Doria | 06/2016 |
1457 | 2^771994-1862771 | 232394 | Enzo Doria | 12/2015 |
1458 | 2^771889+1876037 | 232362 | Enzo Doria | 07/2016 |
1459 | 2^771660+1866511 | 232293 | Enzo Doria | 02/2016 |
1460 | 5^332150-18188 | 232163 | Enzo Doria | 06/2014 |
1461 | 2^770623+212543 | 231981 | Enzo Doria | 09/2023 |
1462 | 3^485977-2^485977 | 231870 | Mike Oakes | 09/2009 |
1463 | 2^770082-114161 | 231818 | Enzo Doria | 01/2015 |
1464 | 2^769791+25523 | 231731 | Enzo Doria | 11/2023 |
1465 | 7^274120-2 | 231659 | Paul Bourdelais | 08/2023 |
1466 | (20^177967+1)/21 | 231540 | Paul Bourdelais | 05/2013 |
1467 | (4*10^231254+23)/9 | 231254 | Serge Batalov | 11/2022 |
1468 | 2^768205+22217 | 231253 | Enzo Doria | 09/2023 |
1469 | 2^767622-9221 | 231078 | Lelio R Paula | 01/2016 |
1470 | 2^767344+1880311 | 230994 | Enzo Doria | 09/2016 |
1471 | 8*10^230921-13 | 230922 | Robert Price | 08/2023 |
1472 | (3^483611-1)/2 | 230741 | Paul Bourdelais | 02/2010 |
1473 | (10^230706+179)/9 | 230706 | Serge Batalov | 12/2014 |
1474 | 2^766309+1875257 | 230682 | Enzo Doria | 06/2016 |
1475 | (26131^52441-1)/(26131^229-1) | 230629 | Ryan Propper | 11/2023 |
1476 | 2^765635+1879883 | 230480 | Enzo Doria | 09/2016 |
1477 | 43^141090+141090 | 230467 | Kellen Shenton | 06/2023 |
1478 | (26*10^230394-119)/3 | 230395 | Robert Price | 07/2023 |
1479 | 2^764348-113697 | 230092 | Enzo Doria | 09/2014 |
1480 | 2^764131+78863 | 230027 | Enzo Doria | 05/2016 |
1481 | 2^763701+60197 | 229897 | Enzo Doria | 03/2016 |
1482 | 4*10^229836+21 | 229837 | Robert Price | 12/2022 |
1483 | 2^763362+27799 | 229795 | Enzo Doria | 01/2024 |
1484 | 2^762841-25905 | 229639 | Enzo Doria | 10/2013 |
1485 | 2^762659+212633 | 229584 | Enzo Doria | 09/2023 |
1486 | 77*10^229211+3 | 229213 | Robert Price | 11/2023 |
1487 | 2^761117-113569 | 229120 | Enzo Doria | 08/2014 |
1488 | (29022^51529-1)/(29022^227-1) | 228947 | Ryan Propper | 11/2023 |
1489 | (98^114859+1)/99 | 228709 | Paul Bourdelais | 12/2018 |
1490 | 5*3^479067-2^479067 | 228574 | Jon Grantham | 08/2023 |
1491 | 2^758645+216011 | 228375 | Enzo Doria | 12/2023 |
1492 | (2^758231+1)/(3*27146942976539*73236839266867) | 228223 | Gord Palameta | 12/2018 |
1493 | (298*10^228177-7)/3 | 228179 | Robert Price | 02/2023 |
1494 | 2^757985-2790013 | 228177 | Enzo Doria | 12/2015 |
1495 | 34*10^228129-9 | 228131 | Robert Price | 05/2023 |
1496 | 2^757038-1862081 | 227892 | Enzo Doria | 12/2015 |
1497 | 2^756839+95849 | 227832 | Makoto Morimoto | 10/2013 |
1499 | (2^756839+6989)/756091 | 227826 | Makoto Morimoto | 09/2016 |
1498 | (2^756839-50211)/(137*3203) | 227826 | Makoto Morimoto | 08/2019 |
1500 | 2^756773-112723 | 227812 | Enzo Doria | 07/2014 |