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 | 111443^516+516^111443 | 302306 | Hans Havermann | 12/2021 |
1252 | 67638^29387+29387^67638 | 302218 | Hans Havermann | 11/2021 |
1253 | 2^1003494+1874899 | 302082 | Enzo Doria | 06/2016 |
1254 | 75189^10400+10400^75189 | 302037 | Hans Havermann | 12/2021 |
1255 | 67237^31042+31042^67237 | 302026 | Hans Havermann | 12/2021 |
1256 | 64540^47791+47791^64540 | 302005 | Hans Havermann | 11/2021 |
1257 | 2^1003046+60529 | 301947 | Enzo Doria | 04/2016 |
1258 | 83278^4209+4209^83278 | 301815 | Hans Havermann | 09/2021 |
1259 | 64431^48250+48250^64431 | 301763 | Hans Havermann | 09/2021 |
1260 | 67237^30714+30714^67237 | 301716 | Hans Havermann | 09/2021 |
1261 | 2^1002144+235861 | 301676 | Enzo Doria | 05/2025 |
1262 | 64641^46288+46288^64641 | 301581 | Hans Havermann | 09/2021 |
1263 | 71513^16482+16482^71513 | 301572 | Hans Havermann | 10/2021 |
1264 | 72017^15396+15396^72017 | 301565 | Hans Havermann | 09/2021 |
1265 | 65534^39927+39927^65534 | 301540 | Hans Havermann | 10/2021 |
1266 | (23^221411-1)/22 | 301501 | Paul Bourdelais | 08/2020 |
1267 | 63169^59152+59152^63169 | 301441 | Hans Havermann | 09/2021 |
1268 | 75055^10348+10348^75055 | 301336 | Hans Havermann | 09/2021 |
1269 | 2^1000647+1881353 | 301225 | Enzo Doria | 11/2016 |
1270 | 83686^3961+3961^83686 | 301086 | Hans Havermann | 10/2021 |
1271 | 68529^24742+24742^68529 | 301078 | Hans Havermann | 09/2021 |
1272 | 65207^41416+41416^65207 | 301072 | Hans Havermann | 10/2021 |
1274 | 2^1000000+821751 | 301030 | Tony Prest / Never Odd Or Even | 10/2015 |
1273 | 2^999999+77151 | 301030 | Norman Luhn | 09/2023 |
1275 | 90762^2071+2071^90762 | 300984 | Hans Havermann | 06/2021 |
1276 | 63909^51142+51142^63909 | 300934 | Hans Havermann | 08/2021 |
1277 | 2^999646+1874029 | 300924 | Enzo Doria | 06/2016 |
1278 | 66280^34607+34607^66280 | 300856 | Hans Havermann | 06/2021 |
1279 | 65534^38925+38925^65534 | 300817 | Hans Havermann | 07/2021 |
1280 | 63296^56517+56517^63296 | 300794 | Hans Havermann | 06/2021 |
1281 | 110610^523+523^110610 | 300694 | Hans Havermann | 06/2021 |
1282 | 66428^33609+33609^66428 | 300684 | Hans Havermann | 06/2021 |
1283 | 74247^11210+11210^74247 | 300672 | Hans Havermann | 06/2021 |
1284 | (59^169777-1)/58 | 300649 | Paul Bourdelais | 08/2020 |
1285 | 10^300476+3 | 300477 | Ed Trice | 10/2012 |
1286 | 10^300476-530913 | 300476 | Patrick De Geest | 03/2016 |
1287 | 66703^31960+31960^66703 | 300471 | Hans Havermann | 06/2021 |
1288 | 63722^51915+51915^63722 | 300468 | Hans Havermann | 06/2021 |
1289 | 2^998053+1879667 | 300444 | Enzo Doria | 09/2016 |
1290 | 77018^7959+7959^77018 | 300437 | Hans Havermann | 07/2021 |
1291 | 314738^9+9^314738 | 300337 | Anatoly F. Selevich | 02/2011 |
1292 | 2^997689+217787 | 300335 | Enzo Doria | 01/2024 |
1293 | 69478^20987+20987^69478 | 300281 | Hans Havermann | 07/2021 |
1294 | 64088^48393+48393^64088 | 300239 | Hans Havermann | 07/2021 |
1295 | 2^997369+237917 | 300238 | Enzo Doria | 06/2025 |
1296 | 64605^44146+44146^64605 | 300084 | Hans Havermann | 08/2021 |
1297 | 2^996845+29027 | 300081 | Enzo Doria | 02/2024 |
1298 | 7^355039-6^355039 | 300043 | Jean-Louis Charton | 05/2011 |
1299 | 67594^27465+27465^67594 | 300035 | Hans Havermann | 06/2021 |
1300 | 10^300000+287389 | 300001 | Patrick De Geest | 10/2019 |
1301 | 10^300000-83657 | 300000 | Patrick De Geest | 10/2019 |
1302 | 70599^17756+17756^70599 | 300000 | Hans Havermann | 06/2021 |
1303 | numbpart(72526161452) | 299999 | Serge Batalov | 04/2017 |
1304 | 2^996182-114431 | 299881 | Enzo Doria | 02/2015 |
1305 | 3*2^996126+5 | 299865 | Jon Grantham | 07/2023 |
1306 | 2^996034-17 | 299837 | Stefano Morozzi | 07/2022 |
1307 | 2^995793+36587 | 299764 | Enzo Doria | 09/2024 |
1308 | (19*10^299640+77)/3 | 299641 | Robert Price | 03/2023 |
1309 | 2^995214-2788361 | 299590 | Enzo Doria | 12/2015 |
1310 | 2^994791-114319 | 299462 | Enzo Doria | 01/2015 |
1311 | 2^994490-1863791 | 299372 | Enzo Doria | 01/2016 |
1312 | 2^993322+1885729 | 299020 | Enzo Doria | 03/2017 |
1313 | 2^993227+230033 | 298992 | Enzo Doria | 12/2024 |
1314 | (36395^65536+36393^65536)/2 | 298913 | Kellen Shenton | 04/2022 |
1315 | 2^992711-2788807 | 298836 | Enzo Doria | 12/2015 |
1316 | 2^992525-114199 | 298780 | Enzo Doria | 12/2014 |
1317 | (7^353501-3^353501)/4 | 298743 | Jon Grantham | 08/2023 |
1318 | 2^992329+1884707 | 298721 | Enzo Doria | 02/2017 |
1319 | 2^992292+229801 | 298710 | Enzo Doria | 12/2024 |
1320 | 2^992052+215491 | 298638 | Enzo Doria | 11/2023 |
1321 | 2^991968-23 | 298613 | Stefano Morozzi | 07/2022 |
1322 | 2^991715-19 | 298536 | Stefano Morozzi | 07/2022 |
1323 | 2^991387+237383 | 298438 | Enzo Doria | 06/2025 |
1324 | (10^298414+7)/191/823/56921/1334467 | 298398 | Alfred Reich | 10/2021 |
1325 | 2^989562+25 | 297888 | Stefano Morozzi | 05/2021 |
1326 | 2^988580+214051 | 297593 | Enzo Doria | 10/2023 |
1327 | 2^988537+218837 | 297580 | Enzo Doria | 03/2024 |
1328 | (19*10^297497+77)/3 | 297498 | Robert Price | 03/2023 |
1329 | (2*10^297488-23)/3 | 297488 | Robert Price | 10/2022 |
1330 | 2^987033+46427 | 297127 | Enzo Doria | 05/2025 |
1331 | (2^986191+1)/3 | 296873 | Vincent Diepeveen | 06/2008 |
1332 | 2^985217-114553 | 296580 | Enzo Doria | 03/2015 |
1333 | (76^157649-1)/75 | 296507 | Paul Bourdelais | 07/2019 |
1334 | 2^984650+21529 | 296410 | Enzo Doria | 08/2023 |
1335 | 2^984131-1828009 | 296253 | Enzo Doria | 01/2015 |
1336 | 2^983620+60451 | 296100 | Phil Moore | 03/2008 |
1337 | 2^982721-2683 | 295829 | Yves Minet | 02/2016 |
1338 | (23*10^295581+7)/3 | 295582 | Robert Price | 05/2023 |
1339 | 2^981298-2788421 | 295401 | Enzo Doria | 12/2015 |
1340 | 2^981163-2790967 | 295360 | Enzo Doria | 12/2015 |
1341 | 2^981016-15 | 295316 | Stefano Morozzi | 07/2022 |
1342 | 8*10^295160-13 | 295161 | Robert Price | 08/2023 |
1343 | 2^979594+1865839 | 294888 | Enzo Doria | 02/2016 |
1344 | 2^979502+221029 | 294860 | Enzo Doria | 03/2024 |
1345 | 2*10^294527-91 | 294528 | Robert Price | 02/2023 |
1346 | (49363^63001-1)/(49363^251-1) | 294511 | Ryan Propper | 11/2023 |
1347 | 10^294475+49 | 294476 | Robert Price | 02/2023 |
1348 | 2^977896+234601 | 294377 | Enzo Doria | 04/2025 |
1349 | (11*10^294308+91)/3 | 294309 | Robert Price | 03/2023 |
1350 | 2^976760+1885021 | 294035 | Enzo Doria | 02/2017 |
1351 | 3*2^976518+5 | 293962 | Jon Grantham | 07/2023 |
1352 | 2^975798+218599 | 293745 | Enzo Doria | 01/2024 |
1353 | 2^974441+1878407 | 293336 | Enzo Doria | 08/2016 |
1354 | 2^974180+1876831 | 293258 | Enzo Doria | 07/2016 |
1355 | 2^974170+453319 | 293255 | Enzo Doria | 01/2017 |
1356 | (211^126023-1)/210 | 292911 | Anonymous | 05/2024 |
1357 | 2^972744-114419 | 292826 | Enzo Doria | 03/2015 |
1358 | 11^281143+6 | 292781 | Paul Bourdelais | 03/2021 |
1359 | (4*10^292619-91)/3 | 292620 | Robert Price | 12/2022 |
1360 | E(69468)/13247122135 | 292549 | Sergey Batalov | 10/2023 |
1361 | CopelandErdos(292447) | 292447 | Mark Rodenkirch | 12/2015 |
1362 | 3*10^292344-97 | 292345 | Robert Price | 01/2023 |
1363 | 2^970911+1873373 | 292274 | Enzo Doria | 07/2016 |
1364 | 2^970670+383059 | 292201 | Enzo Doria | 12/2016 |
1365 | 2^970141-100363 | 292042 | Enzo Doria | 02/2014 |
1366 | 2^969945+1874717 | 291983 | Enzo Doria | 06/2016 |
1367 | 2^969384+1880701 | 291814 | Enzo Doria | 10/2016 |
1368 | (13*10^291721-43)/3 | 291722 | Robert Price | 08/2023 |
1369 | (3^611333-2^611333)/(99035947*87109884549431) | 291659 | Mike Oakes | 02/2017 |
1370 | 10^(2*145126+1)-2*10^145126-1 | 290253 | Robert Price | 03/2025 |
1371 | 3*2^963892+5 | 290161 | Jon Grantham | 07/2023 |
1372 | (151*10^289877-1)/3 | 289879 | Robert Price | 07/2023 |
1373 | 2^962194+60139 | 289650 | Enzo Doria | 02/2016 |
1374 | 2^961409+44267 | 289413 | Enzo Doria | 04/2025 |
1375 | 2^959307-1861507 | 288781 | Enzo Doria | 11/2015 |
1376 | (17*10^288692+31)/3 | 288693 | Robert Price | 04/2023 |
1377 | 14^251797-3 | 288592 | Paul Bourdelais | 12/2020 |
1378 | (8745^73441-1)/(8745^271-1) | 288419 | Ryan Propper | 11/2023 |
1379 | (2*10^288371-23)/3 | 288371 | Robert Price | 10/2022 |
1380 | (31*10^288238-1)/3 | 288240 | Robert Price | 02/2023 |
1381 | (7^341063-2^341063)/5 | 288231 | Jon Grantham | 08/2023 |
1382 | 2^957372+283531 | 288198 | Enzo Doria | 02/2017 |
1383 | 2^957192-1864049 | 288144 | Enzo Doria | 01/2016 |
1384 | (95774^58081-1)/(95774^241-1) | 288116 | Ryan Propper | 11/2023 |
1385 | 2^956446+1875199 | 287919 | Enzo Doria | 06/2016 |
1386 | 2^956283+219143 | 287870 | Enzo Doria | 02/2024 |
1387 | 7*10^287854+39 | 287855 | Robert Price | 01/2023 |
1388 | 2^956082+28309 | 287810 | Enzo Doria | 02/2024 |
1389 | (17^233689+1)/18 | 287542 | Paul Bourdelais | 09/2013 |
1390 | 2^955178+1883587 | 287538 | Enzo Doria | 12/2016 |
1391 | 2^954127-954127^2 | 287221 | Henri Lifchitz | 01/2021 |
1392 | 2^954001+1875257 | 287183 | Enzo Doria | 07/2016 |
1393 | 2*10^287175-49 | 287176 | Robert Price | 05/2023 |
1394 | (22*10^287085-19)/3 | 287086 | Robert Price | 07/2023 |
1395 | 2^953667+38573 | 287083 | Enzo Doria | 11/2024 |
1396 | 2^953488+22411 | 287029 | Enzo Doria | 09/2023 |
1397 | (23891^65536+1)/2 | 286932 | Serge Batalov | 03/2018 |
1398 | 5*3^601336-2^601336 | 286911 | Jon Grantham | 08/2023 |
1399 | 2^952268+1878601 | 286662 | Enzo Doria | 09/2016 |
1400 | 2^950801+81557 | 286220 | Enzo Doria | 08/2016 |
1401 | 2^949403+217523 | 285799 | Enzo Doria | 01/2024 |
1402 | 22845^65536+22844^65536 | 285658 | Kellen Shenton | 03/2021 |
1403 | (19*10^285615+53)/9 | 285616 | Rytis Slatkevicius | 12/2024 |
1404 | (11*2^948635-13)/15 | 285568 | Renaud Lifchitz | 11/2011 |
1405 | (54^164839+1)/55 | 285565 | Paul Bourdelais | 07/2019 |
1406 | 2^948510+782569 | 285530 | Enzo Doria | 10/2016 |
1407 | 2^948374-114137 | 285490 | Enzo Doria | 01/2015 |
1408 | 2^947739+1872923 | 285298 | Enzo Doria | 06/2016 |
1409 | 2^946274+218407 | 284857 | Enzo Doria | 03/2024 |
1410 | 7*10^284751+9 | 284752 | Robert Price | 04/2023 |
1411 | 2^944561-21 | 284342 | Stefano Morozzi | 07/2022 |
1412 | (4*10^284330-31)/9 | 284330 | Serge Batalov | 11/2022 |
1413 | (32*10^283826-23)/9 | 283827 | Serge Batalov | 01/2023 |
1414 | 2^942533+82067 | 283731 | Enzo Doria | 09/2016 |
1415 | 2^941469+39 | 283411 | Jon Grantham | 08/2023 |
1416 | (10^283342-31)/3 | 283342 | Robert Price | 03/2023 |
1417 | 2^940950+1874989 | 283255 | Enzo Doria | 06/2016 |
1418 | 2^940426-2786141 | 283097 | Enzo Doria | 11/2015 |
1419 | 2^940155+226973 | 283015 | Enzo Doria | 09/2024 |
1420 | (2*10^282948-11)/9 | 282948 | Serge Batalov | 11/2022 |
1421 | 2^939881-114115 | 282933 | Enzo Doria | 12/2014 |
1422 | (14*10^282673-143)/3 | 282674 | Robert Price | 05/2023 |
1423 | 10^282493+632551 | 282494 | Patrick De Geest | 02/2017 |
1425 | 10^282493-9^282493 | 282493 | Jean-Louis Charton | 03/2007 |
1424 | 10^282493-132327 | 282493 | Patrick De Geest | 02/2017 |
1426 | 3^591827-2^591827 | 282374 | Mike Oakes | 08/2009 |
1427 | Tau(509^18946) | 282048 | Nik Lygeros / Olivier Rozier | 05/2015 |
1428 | 2^936716-1835519 | 281980 | Enzo Doria | 04/2015 |
1429 | 2^936588+79411 | 281942 | Enzo Doria | 06/2016 |
1430 | 2^936047+1877423 | 281779 | Enzo Doria | 08/2016 |
1431 | 2^935713+1869377 | 281678 | Enzo Doria | 05/2016 |
1432 | 2^933082+1877059 | 280886 | Enzo Doria | 08/2016 |
1433 | (5*10^280710+1)/3 | 280711 | Serge Batalov | 10/2014 |
1434 | 2^932443+225893 | 280694 | Enzo Doria | 08/2024 |
1435 | 2^932064+26521 | 280580 | Enzo Doria | 12/2023 |
1436 | 2^931976+25 | 280553 | Stefano Morozzi | 05/2021 |
1437 | (42^172663+1)/43 | 280274 | Paul Bourdelais | 07/2019 |
1438 | (10^279978+11)/3 | 279978 | Serge Batalov | 07/2015 |
1439 | 2^929524-1864829 | 279815 | Enzo Doria | 01/2016 |
1440 | 2^929329+22697 | 279756 | Enzo Doria | 09/2023 |
1441 | 2^929152+60181 | 279703 | Enzo Doria | 02/2016 |
1442 | 2^928621-2787883 | 279543 | Enzo Doria | 11/2015 |
1443 | (2^927763+lucasV(-1,2,927763)+1)/2 | 279285 | Mike Oakes | 04/2017 |
1444 | 3*10^279271+77 | 279272 | Robert Price | 06/2024 |
1445 | 2^927429+1882277 | 279184 | Enzo Doria | 12/2016 |
1446 | 2^926766-11 | 278985 | Stefano Morozzi | 07/2022 |
1447 | (71^150697-1)/70 | 278978 | Paul Bourdelais | 07/2019 |
1448 | (33^183661-1)/32 | 278891 | Paul Bourdelais | 12/2018 |
1449 | (166*10^278633-7)/3 | 278635 | Robert Price | 02/2023 |
1450 | (2^925391+lucasV(-1,2,925391)+1)/2 | 278571 | Mike Oakes | 03/2017 |
1451 | 2^925330-1301 | 278553 | Yves Minet | 06/2015 |
1452 | (299*10^278546+1)/3 | 278548 | Robert Price | 01/2023 |
1453 | 2^925299+216053 | 278543 | Enzo Doria | 11/2023 |
1455 | (21^210599+1)/22 | 278457 | Paul Bourdelais | 08/2013 |
1454 | (79^146749-1)/6395645198026062186 | 278457 | Paul Vanderveen | 06/2025 |
1456 | (266*10^278325+1)/3 | 278327 | Robert Price | 01/2023 |
1457 | 2^923261-69175 | 277930 | Enzo Doria | 11/2015 |
1458 | 757^96487-756^96487 | 277796 | Jean-Louis Charton | 12/2012 |
1459 | 2^922301+57 | 277641 | Stefano Morozzi | 05/2021 |
1460 | 7*10^277478-39 | 277479 | Robert Price | 07/2023 |
1461 | ((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2 | 277369 | Serge Batalov | 07/2016 |
1462 | (5^396413-1)/4 | 277081 | Paul Bourdelais | 06/2010 |
1463 | 2^920318+2792299 | 277044 | Enzo Doria | 02/2016 |
1464 | (16*10^276537-31)/3 | 276538 | Robert Price | 03/2023 |
1465 | 2^918596-2786939 | 276525 | Enzo Doria | 11/2015 |
1466 | 2^917910+28369 | 276319 | Enzo Doria | 01/2024 |
1467 | 2^917328+228571 | 276144 | Enzo Doria | 11/2024 |
1468 | (6737^72361-1)/(6737^269-1) | 276002 | Ryan Propper | 11/2023 |
1469 | 2^916639+60563 | 275936 | Enzo Doria | 04/2016 |
1470 | (2*10^275922+1)/3 | 275922 | Serge Batalov | 11/2022 |
1471 | 2^916385-2786383 | 275860 | Enzo Doria | 11/2015 |
1472 | 2^915928+82081 | 275722 | Enzo Doria | 09/2016 |
1473 | (4*10^275671+11)/3 | 275672 | Tyler Busby | 02/2023 |
1474 | 2^915576-114137 | 275616 | Enzo Doria | 01/2015 |
1475 | 2^914828+1876741 | 275391 | Enzo Doria | 07/2016 |
1476 | 2^914757-2203 | 275370 | Yves Minet | 12/2015 |
1477 | 7*10^275157-27 | 275158 | Robert Price | 11/2022 |
1478 | 2^912744+20011 | 274764 | Enzo Doria | 06/2023 |
1479 | 2^911900+1871245 | 274510 | Enzo Doria | 05/2016 |
1480 | (16*10^274251-91)/3 | 274252 | Robert Price | 11/2022 |
1481 | 2^910999+9 | 274239 | Stefano Morozzi | 05/2021 |
1482 | (2^910869-7)/5 | 274199 | Stefano Morozzi | 08/2022 |
1483 | 2^910490+283429 | 274085 | Enzo Doria | 01/2017 |
1484 | 7*10^273983+39 | 273984 | Robert Price | 01/2023 |
1485 | 2^909988-1862249 | 273934 | Enzo Doria | 12/2015 |
1486 | 2^909901+378567 | 273908 | Boyan Hu | 08/2024 |
1487 | 2^909297+1879157 | 273726 | Enzo Doria | 08/2016 |
1488 | 2^909257-1864423 | 273714 | Enzo Doria | 01/2016 |
1489 | 2^909254+31309 | 273713 | Enzo Doria | 03/2024 |
1490 | 2^908739-7 | 273558 | Stefano Morozzi | 07/2022 |
1491 | 2^908579-1861747 | 273510 | Enzo Doria | 12/2015 |
1492 | 3*2^908005-5 | 273338 | Jon Grantham | 07/2023 |
1493 | 2^907635-2791597 | 273226 | Enzo Doria | 01/2016 |
1494 | 2^907059+211193 | 273052 | Enzo Doria | 08/2023 |
1495 | (53^158341+1)/54 | 273022 | Paul Bourdelais | 07/2019 |
1496 | 2^906594-113201 | 272912 | Enzo Doria | 08/2014 |
1497 | 9*10^272800+91 | 272801 | Robert Price | 05/2023 |
1498 | 2*10^272710-49 | 272711 | Robert Price | 05/2023 |
1499 | 2*10^272403-91 | 272404 | Robert Price | 02/2023 |
1500 | 2^904773+1872167 | 272364 | Enzo Doria | 06/2016 |