Henri & Renaud Lifchitz's PRP Top records

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

See the Top discoverers
See the Latest PRPs
Search by form


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	2^551507-23557	166021	Enzo Doria	08/2013
1252	7*10^165916-3	165917	Robert Price	08/2015
1253	81^86837-80^86837	165728	Robert Price	01/2015
1254	2^550270-69551	165648	Enzo Doria	12/2015
1255	2^550000-23625	165567	Enzo Doria	08/2013
1256	2^549675-1852057	165469	Enzo Doria	08/2015
1257	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1258	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1259	2^549278+1879669	165350	Enzo Doria	09/2016
1260	(7*10^165350-439)/9	165350	Robert Price	02/2018
1261	2^549252-351269	165342	Enzo Doria	06/2015
1262	(14*10^165282+73)/3	165283	Robert Price	12/2018
1263	2^549049+2797607	165281	Enzo Doria	04/2016
1264	(7*10^165239+107)/3	165240	Robert Price	02/2018
1265	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1266	(7*10^165134+107)/3	165135	Robert Price	02/2018
1267	2^547178-1856501	164717	Enzo Doria	10/2015
1268	11^158160-60	164707	Enzo Doria	07/2012
1269	2^546398-59201	164483	Enzo Doria	10/2015
1270	2^546332-114893	164463	Enzo Doria	05/2015
1271	2^545958+1876189	164350	Enzo Doria	07/2016
1272	2^545878-49841	164326	Enzo Doria	10/2015
1273	(10^164284+77)/3	164284	Robert Price	01/2018
1274	2^545668-4019	164263	Yves Minet	04/2017
1275	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1276	(16*10^164122+197)/3	164123	Robert Price	04/2019
1277	2^545185+76757	164118	Enzo Doria	05/2016
1278	2^545076-114329	164085	Enzo Doria	01/2015
1279	(2*10^164043-143)/3	164043	Robert Price	03/2018
1280	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1281	2^544757+1874777	163989	Enzo Doria	06/2016
1282	2^544444-457199	163894	Enzo Doria	01/2015
1283	2^544264-343529	163840	Enzo Doria	07/2015
1284	7*10^163780+9	163781	Robert Price	09/2015
1285	2^543989+2793047	163758	Enzo Doria	02/2016
1286	2^542870-69551	163421	Enzo Doria	12/2015
1287	2^542395+72533	163278	Enzo Doria	04/2016
1288	2^542072-3683	163180	Yves Minet	03/2017
1289	2^541779-1867357	163092	Enzo Doria	04/2016
1290	8*10^162924+9	162925	Robert Price	12/2015
1291	2^540905+81557	162829	Enzo Doria	08/2016
1292	2^540628-2939	162746	Yves Minet	09/2014
1293	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1294	3*10^162620-59	162621	Robert Price	09/2018
1295	3^340694-112960	162553	Enzo Doria	07/2014
1296	2^539807-114081	162499	Enzo Doria	12/2014
1297	2^539654-114893	162453	Enzo Doria	05/2015
1298	2^539617-1851583	162441	Enzo Doria	08/2015
1299	2^539346+81049	162360	Enzo Doria	07/2016
1300	2^539220-115499	162322	Enzo Doria	07/2015
1301	2^539217-113713	162321	Enzo Doria	09/2014
1302	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1303	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1304	(10^162138+11)/3	162138	Serge Batalov	07/2015
1305	2^538473-112723	162097	Enzo Doria	06/2014
1306	2^538157+79337	162002	Enzo Doria	06/2016
1307	2^538136-114749	161996	Enzo Doria	05/2015
1308	2^538104+1531	161986	Lelio R Paula	01/2013
1309	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1310	2^537815-22737	161899	Enzo Doria	07/2013
1311	2^537804-39839	161896	Enzo Doria	09/2015
1312	2^537458-59201	161791	Enzo Doria	10/2015
1313	2*10^161766+51	161767	Robert Price	05/2018
1314	2^537209-49849	161717	Enzo Doria	10/2015
1315	2^536937+1879397	161635	Enzo Doria	09/2016
1316	2^536569-22881	161524	Enzo Doria	07/2013
1317	10^161253+573493	161254	Patrick De Geest	07/2018
1318	10^161253-8001	161253	Robert Price	03/2018
1319	7*10^161192-9	161193	Robert Price	10/2015
1320	2^535269-113803	161133	Enzo Doria	09/2014
1321	2^535205-23295	161113	Enzo Doria	08/2013
1322	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1323	2^534359-23229	160859	Enzo Doria	08/2013
1324	67^88037-66^88037	160763	Robert Price	10/2013
1325	2^533948-1852559	160735	Enzo Doria	08/2015
1326	2^533665-23335	160650	Enzo Doria	08/2013
1327	3^336353-2^336353	160482	Mike Oakes	10/2007
1328	2^532253+1868417	160225	Enzo Doria	04/2016
1329	2^532108-291989	160181	Enzo Doria	07/2015
1330	(17*10^160143+67)/3	160144	Robert Price	01/2019
1331	2^531110-1853771	159881	Enzo Doria	09/2015
1332	2^530992-1845299	159845	Enzo Doria	07/2015
1333	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1334	2^530417-113833	159672	Enzo Doria	09/2014
1335	2^530406-69701	159669	Enzo Doria	02/2016
1336	5*10^159656+41	159657	Robert Price	03/2019
1337	7^188858-188858^7	159604	Norbert Schneider	05/2018
1338	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1339	(17*10^159438-377)/9	159439	Robert Price	03/2018
1340	2^528944-461315	159229	Enzo Doria	07/2015
1341	(13*10^159147+161)/3	159148	Robert Price	11/2018
1342	2^528620-113879	159131	Enzo Doria	10/2014
1343	2^528000-23307	158944	Enzo Doria	08/2013
1344	(29*10^158909+61)/9	158910	Robert Price	08/2018
1345	2^527817+1876817	158889	Enzo Doria	07/2016
1346	2^527774-49451	158876	Enzo Doria	10/2015
1347	2^527745-291553	158868	Enzo Doria	07/2015
1348	2^527644-1856999	158837	Enzo Doria	10/2015
1349	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1350	2^527573-1863253	158816	Enzo Doria	12/2015
1351	2^527553-23401	158810	Enzo Doria	08/2013
1352	11^152420-210	158730	Enzo Doria	09/2012
1353	(13*10^158694+401)/9	158695	Robert Price	01/2018
1354	2^527052-69059	158659	Enzo Doria	11/2015
1355	2^526849-113233	158598	Enzo Doria	07/2014
1356	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
1357	2^526658-3551	158540	Yves Minet	03/2017
1358	2^526375-23115	158455	Enzo Doria	08/2013
1359	2^526028-112793	158351	Enzo Doria	07/2014
1360	2^525690-9221	158249	Lelio R Paula	01/2013
1361	2*10^158242-7	158243	Robert Price	10/2015
1362	2^525667-525667^2	158242	Henri Lifchitz	12/2017
1363	2^525186-1857431	158097	Enzo Doria	10/2015
1364	2^524515-23245	157895	Enzo Doria	08/2013
1365	2^524499-109087	157890	Enzo Doria	04/2014
1366	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
1367	2^524288+189093	157827	Makoto Morimoto	01/2016
1368	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
1369	(10^157792+359)/9	157792	Serge Batalov	12/2014
1370	2^523924+1876591	157717	Enzo Doria	07/2016
1371	(17*10^157705+67)/3	157706	Robert Price	01/2019
1372	(46^94841+1)/47	157696	Robert Price	01/2014
1373	2^523774+77839	157672	Enzo Doria	05/2016
1374	2^523587+2799143	157616	Enzo Doria	04/2016
1375	2^523371+1872113	157551	Enzo Doria	05/2016
1376	2^522535-351457	157299	Enzo Doria	07/2015
1377	2^522226+2799079	157206	Enzo Doria	04/2016
1378	2^522134-1849451	157178	Enzo Doria	08/2015
1379	4*10^157150+93	157151	Robert Price	08/2018
1380	2^521401-29593	156958	Enzo Doria	08/2015
1381	2^521348-23397	156942	Enzo Doria	08/2013
1382	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
1383	65^86522+64	156857	Lelio R Paula	04/2016
1384	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
1385	2^520977-1858183	156830	Enzo Doria	10/2015
1386	(8*10^156718-101)/3	156719	Robert Price	08/2018
1387	2^520314-1849481	156631	Enzo Doria	08/2015
1388	(13*10^156522+89)/3	156523	Robert Price	09/2018
1389	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
1390	3*10^156435-97	156436	Robert Price	07/2018
1391	(8*10^156371-77)/3	156372	Robert Price	07/2018
1392	53^90679-52^90679	156356	Robert Price	01/2013
1393	2^519106-59141	156267	Enzo Doria	10/2015
1394	2^519053+6077	156251	Enzo Doria	02/2016
1395	2^518968-1860989	156225	Enzo Doria	11/2015
1396	(25*10^156221-7)/9	156222	Robert Price	05/2018
1397	2^518931-2782297	156214	Enzo Doria	09/2015
1398	2^518608-2939	156117	Yves Minet	09/2014
1399	10*27^109005+697	156027	Curtis Bright	05/2015
1400	2^517967-113485	155924	Enzo Doria	08/2014
1401	2^517698+4429	155843	Lelio R Paula	01/2013
1402	2^517543-113257	155796	Enzo Doria	07/2014
1403	(14*10^155740-143)/3	155741	Robert Price	11/2018
1404	31^104309-30^104309	155563	Henri Lifchitz	08/2013
1405	2^516742-39851	155555	Enzo Doria	09/2015
1406	2^516440+1878421	155464	Enzo Doria	08/2016
1407	2^515863-1867237	155291	Enzo Doria	03/2016
1408	2^515786-461861	155268	Enzo Doria	07/2015
1409	2^515644-113247	155225	Enzo Doria	07/2014
1410	(7*10^155203+107)/3	155204	Robert Price	02/2018
1411	(17*10^155133-89)/9	155134	Robert Price	07/2018
1412	2^515227-114997	155099	Enzo Doria	06/2015
1414	EPrime(155025)	155025	Eric W. Weisstein	10/2010
1413	(14*10^155024-221)/9	155025	Robert Price	04/2018
1415	(4*10^155022+173)/3	155023	Robert Price	02/2018
1416	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
1417	2^514361+78167	154839	Enzo Doria	05/2016
1418	2^514281-115033	154815	Enzo Doria	06/2015
1419	2^514194-3311	154788	Yves Minet	12/2014
1420	(14*10^154773+37)/3	154774	Robert Price	12/2018
1421	2^513437+1879337	154560	Enzo Doria	09/2016
1422	2^513306-113201	154521	Enzo Doria	07/2014
1423	(10^154494-13)/3	154494	Robert Price	12/2017
1424	2^513042-113787	154442	Enzo Doria	09/2014
1425	2^512628-114053	154317	Enzo Doria	11/2014
1426	2^512529-49783	154287	Enzo Doria	10/2015
1427	2^512315-115297	154223	Enzo Doria	06/2015
1428	2^512168+79561	154178	Enzo Doria	06/2016
1429	4*10^154078-57	154079	Robert Price	10/2018
1430	2^511658-114371	154025	Enzo Doria	02/2015
1431	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
1432	2^511580-1846679	154001	Enzo Doria	07/2015
1433	2^511541-113713	153990	Enzo Doria	09/2014
1434	2^511077-112723	153850	Enzo Doria	06/2014
1435	69^83653-68^83653	153826	Robert Price	12/2013
1436	2^510963-113707	153816	Enzo Doria	09/2014
1437	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
1438	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
1439	2*10^153746-3	153747	Robert Price	07/2015
1440	2^510626+1179379	153714	Enzo Doria	05/2016
1441	(7*10^153664+113)/3	153665	Robert Price	02/2018
1442	2^510420+81121	153652	Enzo Doria	07/2016
1443	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
1444	2^509894-459161	153494	Enzo Doria	05/2015
1445	2^509841+71657	153478	Enzo Doria	04/2016
1446	2^509533-1846723	153385	Enzo Doria	07/2015
1447	2^509468-39989	153366	Enzo Doria	09/2015
1448	70^83117-69^83117	153360	Robert Price	01/2014
1449	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
1450	2^508174-1855151	152976	Enzo Doria	09/2015
1451	181^67757-2	152974	Lelio R Paula	12/2017
1452	2^508160-1864829	152972	Enzo Doria	01/2016
1453	2^507857-1848199	152881	Enzo Doria	07/2015
1454	2^507638-115361	152815	Enzo Doria	07/2015
1455	2^507551-114025	152789	Enzo Doria	11/2014
1456	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
1457	(22*10^152670-13)/9	152671	Robert Price	06/2018
1458	2^506451-22339	152457	Enzo Doria	07/2013
1459	2^505995-113185	152320	Enzo Doria	07/2014
1460	(4*10^152253+149)/9	152253	Robert Price	04/2018
1461	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
1462	2^505431-505431	152150	Henri Lifchitz	04/2005
1463	2^505053+73097	152037	Enzo Doria	04/2016
1464	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
1465	350377#+797581	151937	Nicolas PALAU	08/2017
1466	2^504618-343991	151906	Enzo Doria	07/2015
1467	2^504212-461939	151783	Enzo Doria	07/2015
1468	2^504054-2231	151736	Yves Minet	10/2011
1469	2^503361-39883	151527	Enzo Doria	09/2015
1470	2^503225+382667	151486	Enzo Doria	10/2016
1471	(26*10^151391-503)/9	151392	Robert Price	07/2018
1472	2^502769+1877567	151349	Enzo Doria	08/2016
1473	2^502576-4019	151291	Yves Minet	10/2011
1474	5*10^151257+41	151258	Robert Price	03/2019
1475	2^502290-2792501	151205	Enzo Doria	02/2016
1476	2^502181+1868417	151172	Enzo Doria	04/2016
1477	2^501781-1850503	151052	Enzo Doria	08/2015
1478	(5*10^151007+37)/3	151008	Robert Price	03/2018
1479	2^501627-991	151005	Yves Minet	02/2014
1480	2^501577-115333	150990	Enzo Doria	07/2015
1481	8*10^150975+3	150976	Robert Price	08/2015
1482	2^501512-113669	150971	Enzo Doria	09/2014
1483	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
1484	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
1485	2^500899-500899	150786	Henri Lifchitz	04/2005
1486	2^500832+1876801	150766	Enzo Doria	07/2016
1487	(23*10^150763-59)/9	150764	Robert Price	05/2018
1488	2^500699+1884953	150726	Enzo Doria	02/2017
1489	(13*10^150675-37)/3	150676	Robert Price	01/2019
1490	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
1491	2^500337-71101	150617	Enzo Doria	04/2016
1492	4*10^150577+91	150578	Robert Price	08/2018
1493	2^500160+80071	150564	Enzo Doria	06/2016
1494	(2^500120+5)/9	150551	Lelio R Paula	12/2017
1495	(43*10^150515-421)/9	150516	Robert Price	01/2019
1496	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
1497	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
1498	2^499861-29503	150474	Enzo Doria	08/2015
1499	2^499653-113533	150411	Enzo Doria	08/2014
1500	2^499534-221	150375	Yves Minet	06/2012

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)