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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See the Latest PRPs
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
1251 | 4*5^247217-9 | 172798 | Lelio R Paula | 10/2015 |
1252 | 69061#+(467617#)/(69061#) | 172766 | Makoto Morimoto | 10/2017 |
1253 | 5*10^172692+57 | 172693 | Robert Price | 12/2018 |
1254 | 2^573668-2782319 | 172692 | Enzo Doria | 09/2015 |
1255 | 2^573444-1855109 | 172624 | Enzo Doria | 09/2015 |
1256 | 3^361608+2 | 172531 | Robert Price | 08/2014 |
1257 | (54^99563+1)/55 | 172481 | Paul Bourdelais | 11/2017 |
1258 | 2^572592-114893 | 172368 | Enzo Doria | 05/2015 |
1259 | 5^246497-4^246497 | 172295 | Jean-Louis Charton | 11/2008 |
1260 | (38^109037-1)/37 | 172254 | Paul Bourdelais | 10/2017 |
1261 | 3*10^172219+73 | 172220 | Robert Price | 08/2018 |
1262 | (36^110503+1)/37 | 171975 | Lelio R Paula | 04/2017 |
1263 | (22*10^171929-73)/3 | 171930 | Robert Price | 04/2019 |
1264 | 4*10^171891-63 | 171892 | Robert Price | 10/2018 |
1265 | 2^570980-2782289 | 171883 | Enzo Doria | 09/2015 |
1266 | (25*10^171849-37)/3 | 171850 | Robert Price | 10/2019 |
1267 | (2^(12*47563+13)-9)/7 | 171818 | Kevin Acres | 11/2013 |
1268 | 7*10^171535-99 | 171536 | Robert Price | 06/2019 |
1269 | 2^569563-1854607 | 171456 | Enzo Doria | 09/2015 |
1270 | 3*10^171391+59 | 171392 | Robert Price | 08/2018 |
1271 | (13*10^171306-37)/3 | 171307 | Robert Price | 01/2019 |
1272 | 8*10^171296+87 | 171297 | Robert Price | 10/2019 |
1273 | (55^98419-1)/54 | 171284 | Paul Bourdelais | 12/2017 |
1274 | 2^568642+1876129 | 171179 | Enzo Doria | 07/2016 |
1275 | (46*10^170932+143)/9 | 170933 | Robert Price | 01/2019 |
1276 | (58*10^170842+221)/9 | 170843 | Robert Price | 02/2017 |
1277 | 3*10^170800+73 | 170801 | Robert Price | 08/2018 |
1278 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
1279 | 2*10^170767+41 | 170768 | Robert Price | 05/2018 |
1280 | 3^357706-112358 | 170670 | Enzo Doria | 07/2014 |
1281 | TheodorusPrime(170657) | 170657 | Eric W. Weisstein | 08/2013 |
1282 | 2^566871+1876163 | 170646 | Enzo Doria | 07/2016 |
1283 | (10657#+(404267#)/(10657#))/(1675379) | 170624 | Makoto Morimoto | 10/2017 |
1284 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
1285 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
1286 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
1287 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
1288 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
1289 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
1290 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
1291 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
1292 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
1293 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
1294 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
1295 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
1296 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
1297 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
1298 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
1299 | 2^560405-39943 | 168699 | Enzo Doria | 09/2015 |
1300 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
1301 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
1302 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
1303 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
1304 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
1305 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
1306 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
1307 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
1308 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
1309 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
1310 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
1311 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
1312 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
1313 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
1314 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
1315 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |
1316 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
1317 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
1318 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
1319 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
1320 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
1321 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
1322 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
1323 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
1324 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
1325 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
1326 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
1327 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
1328 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
1329 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
1330 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
1331 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
1332 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
1333 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
1334 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
1335 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
1336 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
1337 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
1338 | 8*10^166227+87 | 166228 | Robert Price | 10/2019 |
1339 | 2^552137+1879397 | 166210 | Enzo Doria | 09/2016 |
1340 | (23^121949-1)/22 | 166061 | Paul Bourdelais | 10/2017 |
1341 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
1342 | 2^551535-23821 | 166029 | Enzo Doria | 08/2013 |
1343 | 2^551507-23557 | 166021 | Enzo Doria | 08/2013 |
1344 | 7*10^165916-3 | 165917 | Robert Price | 08/2015 |
1345 | 81^86837-80^86837 | 165728 | Robert Price | 01/2015 |
1346 | (71*10^165663-539)/9 | 165664 | Robert Price | 07/2019 |
1347 | 2^550270-69551 | 165648 | Enzo Doria | 12/2015 |
1348 | 2^550000-23625 | 165567 | Enzo Doria | 08/2013 |
1349 | 2^549675-1852057 | 165469 | Enzo Doria | 08/2015 |
1350 | -tau(103^14938) | 165374 | Nik Lygeros / Olivier Rozier | 10/2013 |
1351 | (28*10^165358-1)/9 | 165359 | Serge Batalov | 10/2014 |
1353 | 2^549278+1879669 | 165350 | Enzo Doria | 09/2016 |
1352 | (7*10^165350-439)/9 | 165350 | Robert Price | 02/2018 |
1354 | 2^549252-351269 | 165342 | Enzo Doria | 06/2015 |
1355 | (14*10^165282+73)/3 | 165283 | Robert Price | 12/2018 |
1356 | 2^549049+2797607 | 165281 | Enzo Doria | 04/2016 |
1357 | (7*10^165239+107)/3 | 165240 | Robert Price | 02/2018 |
1358 | (44^100511-1)/43 | 165184 | Paul Bourdelais | 11/2017 |
1359 | (7*10^165134+107)/3 | 165135 | Robert Price | 02/2018 |
1360 | (23*10^165060-83)/3 | 165061 | Robert Price | 08/2019 |
1361 | (76*10^164984+77)/9 | 164985 | Robert Price | 10/2019 |
1362 | 2^547178-1856501 | 164717 | Enzo Doria | 10/2015 |
1363 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
1364 | (26*10^164643-167)/3 | 164644 | Robert Price | 10/2019 |
1365 | 2^546398-59201 | 164483 | Enzo Doria | 10/2015 |
1366 | 2^546332-114893 | 164463 | Enzo Doria | 05/2015 |
1367 | 2^545958+1876189 | 164350 | Enzo Doria | 07/2016 |
1368 | 2^545878-49841 | 164326 | Enzo Doria | 10/2015 |
1369 | (10^164284+77)/3 | 164284 | Robert Price | 01/2018 |
1370 | 2^545668-4019 | 164263 | Yves Minet | 04/2017 |
1371 | (13*53^238539*617^9)/10^247183 | 164151 | Hans Havermann | 07/2017 |
1372 | (16*10^164122+197)/3 | 164123 | Robert Price | 04/2019 |
1373 | 2^545185+76757 | 164118 | Enzo Doria | 05/2016 |
1374 | 2^545076-114329 | 164085 | Enzo Doria | 01/2015 |
1375 | (2*10^164043-143)/3 | 164043 | Robert Price | 03/2018 |
1376 | (29^112153+1)/30 | 164011 | Lelio R Paula | 03/2017 |
1377 | 2^544757+1874777 | 163989 | Enzo Doria | 06/2016 |
1378 | 2^544444-457199 | 163894 | Enzo Doria | 01/2015 |
1379 | 2^544264-343529 | 163840 | Enzo Doria | 07/2015 |
1380 | 7*10^163780+9 | 163781 | Robert Price | 09/2015 |
1381 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
1382 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
1383 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
1384 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
1385 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
1386 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
1387 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
1388 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
1389 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
1390 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
1391 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
1392 | 2^539807-114081 | 162499 | Enzo Doria | 12/2014 |
1393 | 2^539654-114893 | 162453 | Enzo Doria | 05/2015 |
1394 | 2^539617-1851583 | 162441 | Enzo Doria | 08/2015 |
1395 | 2^539346+81049 | 162360 | Enzo Doria | 07/2016 |
1396 | 2^539220-115499 | 162322 | Enzo Doria | 07/2015 |
1397 | 2^539217-113713 | 162321 | Enzo Doria | 09/2014 |
1398 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
1399 | (115*10^162153-1)/3 | 162155 | Serge Batalov | 12/2014 |
1400 | (10^162138+11)/3 | 162138 | Serge Batalov | 07/2015 |
1401 | 2^538473-112723 | 162097 | Enzo Doria | 06/2014 |
1402 | 2^538157+79337 | 162002 | Enzo Doria | 06/2016 |
1403 | 2^538136-114749 | 161996 | Enzo Doria | 05/2015 |
1404 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
1405 | (9*29^110727-1199)/14 | 161927 | Curtis Bright | 05/2015 |
1406 | 2^537815-22737 | 161899 | Enzo Doria | 07/2013 |
1407 | 2^537804-39839 | 161896 | Enzo Doria | 09/2015 |
1408 | 2^537458-59201 | 161791 | Enzo Doria | 10/2015 |
1409 | 2*10^161766+51 | 161767 | Robert Price | 05/2018 |
1410 | 2^537209-49849 | 161717 | Enzo Doria | 10/2015 |
1411 | (58*10^161691+329)/9 | 161692 | Robert Price | 05/2019 |
1412 | 2^536937+1879397 | 161635 | Enzo Doria | 09/2016 |
1413 | 2^536569-22881 | 161524 | Enzo Doria | 07/2013 |
1414 | 10^161253+573493 | 161254 | Patrick De Geest | 07/2018 |
1415 | 10^161253-8001 | 161253 | Robert Price | 03/2018 |
1416 | 7*10^161192-9 | 161193 | Robert Price | 10/2015 |
1417 | 2^535269-113803 | 161133 | Enzo Doria | 09/2014 |
1418 | 2^535205-23295 | 161113 | Enzo Doria | 08/2013 |
1419 | (89^82609+1)/90 | 161036 | Paul Bourdelais | 10/2017 |
1420 | 2^534359-23229 | 160859 | Enzo Doria | 08/2013 |
1421 | 67^88037-66^88037 | 160763 | Robert Price | 10/2013 |
1422 | 2^533948-1852559 | 160735 | Enzo Doria | 08/2015 |
1423 | 2^533665-23335 | 160650 | Enzo Doria | 08/2013 |
1424 | (19*10^160619+77)/3 | 160620 | Robert Price | 05/2019 |
1425 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
1426 | 2^532253+1868417 | 160225 | Enzo Doria | 04/2016 |
1427 | 2^532108-291989 | 160181 | Enzo Doria | 07/2015 |
1428 | (26*10^160166-131)/3 | 160167 | Robert Price | 10/2019 |
1429 | (17*10^160143+67)/3 | 160144 | Robert Price | 01/2019 |
1430 | (19*10^159921-49)/3 | 159922 | Robert Price | 05/2019 |
1431 | 2^531110-1853771 | 159881 | Enzo Doria | 09/2015 |
1432 | 2^530992-1845299 | 159845 | Enzo Doria | 07/2015 |
1433 | (136*10^159736-1)/9 | 159738 | Serge Batalov | 12/2014 |
1434 | 2^530417-113833 | 159672 | Enzo Doria | 09/2014 |
1435 | 2^530406-69701 | 159669 | Enzo Doria | 02/2016 |
1436 | 5*10^159656+41 | 159657 | Robert Price | 03/2019 |
1437 | 7^188858-188858^7 | 159604 | Norbert Schneider | 05/2018 |
1438 | (24^115597-1)/23 | 159547 | Paul Bourdelais | 09/2017 |
1439 | (17*10^159438-377)/9 | 159439 | Robert Price | 03/2018 |
1440 | 2^528944-461315 | 159229 | Enzo Doria | 07/2015 |
1441 | (13*10^159147+161)/3 | 159148 | Robert Price | 11/2018 |
1442 | 2^528620-113879 | 159131 | Enzo Doria | 10/2014 |
1443 | 2^528000-23307 | 158944 | Enzo Doria | 08/2013 |
1444 | (29*10^158909+61)/9 | 158910 | Robert Price | 08/2018 |
1445 | 2^527817+1876817 | 158889 | Enzo Doria | 07/2016 |
1446 | 2^527774-49451 | 158876 | Enzo Doria | 10/2015 |
1447 | 2^527745-291553 | 158868 | Enzo Doria | 07/2015 |
1448 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
1449 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
1450 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
1451 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
1452 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
1453 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
1454 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
1455 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
1456 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
1457 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
1458 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
1459 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
1460 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
1461 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
1462 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
1463 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
1464 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
1465 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
1466 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
1467 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
1468 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
1469 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
1470 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
1471 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
1472 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
1473 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
1474 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
1475 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
1476 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
1477 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
1478 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
1479 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
1480 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
1481 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
1482 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
1483 | 2^521401-29593 | 156958 | Enzo Doria | 08/2015 |
1484 | 7*10^156956+87 | 156957 | Robert Price | 07/2019 |
1485 | 2^521348-23397 | 156942 | Enzo Doria | 08/2013 |
1486 | (98^78797+1)/99 | 156901 | Paul Bourdelais | 12/2017 |
1487 | 65^86522+64 | 156857 | Lelio R Paula | 04/2016 |
1488 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
1489 | 2^520977-1858183 | 156830 | Enzo Doria | 10/2015 |
1490 | (8*10^156718-101)/3 | 156719 | Robert Price | 08/2018 |
1491 | 2^520314-1849481 | 156631 | Enzo Doria | 08/2015 |
1492 | (13*10^156522+89)/3 | 156523 | Robert Price | 09/2018 |
1493 | (2^(6*86654+1)-5)/3 | 156513 | Kevin Acres | 12/2013 |
1494 | 3*10^156435-97 | 156436 | Robert Price | 07/2018 |
1495 | (8*10^156371-77)/3 | 156372 | Robert Price | 07/2018 |
1496 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
1497 | 2^519106-59141 | 156267 | Enzo Doria | 10/2015 |
1498 | 2^519053+6077 | 156251 | Enzo Doria | 02/2016 |
1499 | 2^518968-1860989 | 156225 | Enzo Doria | 11/2015 |
1500 | (25*10^156221-7)/9 | 156222 | Robert Price | 05/2018 |