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 (> 30000)	Who ?	When ?
1251	2^530406-69701	159669	Enzo Doria	02/2016
1252	7^188858-188858^7	159604	Norbert Schneider	05/2018
1253	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1254	(17*10^159438-377)/9	159439	Robert Price	03/2018
1255	2^528944-461315	159229	Enzo Doria	07/2015
1256	2^528620-113879	159131	Enzo Doria	10/2014
1257	2^528000-23307	158944	Enzo Doria	08/2013
1258	(29*10^158909+61)/9	158910	Robert Price	08/2018
1259	2^527817+1876817	158889	Enzo Doria	07/2016
1260	2^527774-49451	158876	Enzo Doria	10/2015
1261	2^527745-291553	158868	Enzo Doria	07/2015
1262	2^527644-1856999	158837	Enzo Doria	10/2015
1263	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1264	2^527573-1863253	158816	Enzo Doria	12/2015
1265	2^527553-23401	158810	Enzo Doria	08/2013
1266	11^152420-210	158730	Enzo Doria	09/2012
1267	(13*10^158694+401)/9	158695	Robert Price	01/2018
1268	2^527052-69059	158659	Enzo Doria	11/2015
1269	2^526849-113233	158598	Enzo Doria	07/2014
1270	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
1271	2^526658-3551	158540	Yves Minet	03/2017
1272	2^526375-23115	158455	Enzo Doria	08/2013
1273	2^526028-112793	158351	Enzo Doria	07/2014
1274	2^525690-9221	158249	Lelio R Paula	01/2013
1275	2*10^158242-7	158243	Robert Price	10/2015
1276	2^525667-525667^2	158242	Henri Lifchitz	12/2017
1277	2^525186-1857431	158097	Enzo Doria	10/2015
1278	2^524515-23245	157895	Enzo Doria	08/2013
1279	2^524499-109087	157890	Enzo Doria	04/2014
1280	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
1281	2^524288+189093	157827	Makoto Morimoto	01/2016
1282	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
1283	(10^157792+359)/9	157792	Serge Batalov	12/2014
1284	2^523924+1876591	157717	Enzo Doria	07/2016
1285	(46^94841+1)/47	157696	Robert Price	01/2014
1286	2^523774+77839	157672	Enzo Doria	05/2016
1287	2^523587+2799143	157616	Enzo Doria	04/2016
1288	2^523371+1872113	157551	Enzo Doria	05/2016
1289	2^522535-351457	157299	Enzo Doria	07/2015
1290	2^522226+2799079	157206	Enzo Doria	04/2016
1291	2^522134-1849451	157178	Enzo Doria	08/2015
1292	4*10^157150+93	157151	Robert Price	08/2018
1293	2^521401-29593	156958	Enzo Doria	08/2015
1294	2^521348-23397	156942	Enzo Doria	08/2013
1295	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
1296	65^86522+64	156857	Lelio R Paula	04/2016
1297	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
1298	2^520977-1858183	156830	Enzo Doria	10/2015
1299	(8*10^156718-101)/3	156719	Robert Price	08/2018
1300	2^520314-1849481	156631	Enzo Doria	08/2015
1301	(13*10^156522+89)/3	156523	Robert Price	09/2018
1302	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
1303	3*10^156435-97	156436	Robert Price	07/2018
1304	(8*10^156371-77)/3	156372	Robert Price	07/2018
1305	53^90679-52^90679	156356	Robert Price	01/2013
1306	2^519106-59141	156267	Enzo Doria	10/2015
1307	2^519053+6077	156251	Enzo Doria	02/2016
1308	2^518968-1860989	156225	Enzo Doria	11/2015
1309	(25*10^156221-7)/9	156222	Robert Price	05/2018
1310	2^518931-2782297	156214	Enzo Doria	09/2015
1311	2^518608-2939	156117	Yves Minet	09/2014
1312	10*27^109005+697	156027	Curtis Bright	05/2015
1313	2^517967-113485	155924	Enzo Doria	08/2014
1314	2^517698+4429	155843	Lelio R Paula	01/2013
1315	2^517543-113257	155796	Enzo Doria	07/2014
1316	31^104309-30^104309	155563	Henri Lifchitz	08/2013
1317	2^516742-39851	155555	Enzo Doria	09/2015
1318	2^516440+1878421	155464	Enzo Doria	08/2016
1319	2^515863-1867237	155291	Enzo Doria	03/2016
1320	2^515786-461861	155268	Enzo Doria	07/2015
1321	2^515644-113247	155225	Enzo Doria	07/2014
1322	(7*10^155203+107)/3	155204	Robert Price	02/2018
1323	(17*10^155133-89)/9	155134	Robert Price	07/2018
1324	2^515227-114997	155099	Enzo Doria	06/2015
1326	EPrime(155025)	155025	Eric W. Weisstein	10/2010
1325	(14*10^155024-221)/9	155025	Robert Price	04/2018
1327	(4*10^155022+173)/3	155023	Robert Price	02/2018
1328	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
1329	2^514361+78167	154839	Enzo Doria	05/2016
1330	2^514281-115033	154815	Enzo Doria	06/2015
1331	2^514194-3311	154788	Yves Minet	12/2014
1332	2^513437+1879337	154560	Enzo Doria	09/2016
1333	2^513306-113201	154521	Enzo Doria	07/2014
1334	(10^154494-13)/3	154494	Robert Price	12/2017
1335	2^513042-113787	154442	Enzo Doria	09/2014
1336	2^512628-114053	154317	Enzo Doria	11/2014
1337	2^512529-49783	154287	Enzo Doria	10/2015
1338	2^512315-115297	154223	Enzo Doria	06/2015
1339	2^512168+79561	154178	Enzo Doria	06/2016
1340	4*10^154078-57	154079	Robert Price	10/2018
1341	2^511658-114371	154025	Enzo Doria	02/2015
1342	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
1343	2^511580-1846679	154001	Enzo Doria	07/2015
1344	2^511541-113713	153990	Enzo Doria	09/2014
1345	2^511077-112723	153850	Enzo Doria	06/2014
1346	69^83653-68^83653	153826	Robert Price	12/2013
1347	2^510963-113707	153816	Enzo Doria	09/2014
1348	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
1349	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
1350	2*10^153746-3	153747	Robert Price	07/2015
1351	2^510626+1179379	153714	Enzo Doria	05/2016
1352	(7*10^153664+113)/3	153665	Robert Price	02/2018
1353	2^510420+81121	153652	Enzo Doria	07/2016
1354	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
1355	2^509894-459161	153494	Enzo Doria	05/2015
1356	2^509841+71657	153478	Enzo Doria	04/2016
1357	2^509533-1846723	153385	Enzo Doria	07/2015
1358	2^509468-39989	153366	Enzo Doria	09/2015
1359	70^83117-69^83117	153360	Robert Price	01/2014
1360	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
1361	2^508174-1855151	152976	Enzo Doria	09/2015
1362	181^67757-2	152974	Lelio R Paula	12/2017
1363	2^508160-1864829	152972	Enzo Doria	01/2016
1364	2^507857-1848199	152881	Enzo Doria	07/2015
1365	2^507638-115361	152815	Enzo Doria	07/2015
1366	2^507551-114025	152789	Enzo Doria	11/2014
1367	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
1368	(22*10^152670-13)/9	152671	Robert Price	06/2018
1369	2^506451-22339	152457	Enzo Doria	07/2013
1370	2^505995-113185	152320	Enzo Doria	07/2014
1371	(4*10^152253+149)/9	152253	Robert Price	04/2018
1372	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
1373	2^505431-505431	152150	Henri Lifchitz	04/2005
1374	2^505053+73097	152037	Enzo Doria	04/2016
1375	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
1376	350377#+797581	151937	Nicolas PALAU	08/2017
1377	2^504618-343991	151906	Enzo Doria	07/2015
1378	2^504212-461939	151783	Enzo Doria	07/2015
1379	2^504054-2231	151736	Yves Minet	10/2011
1380	2^503361-39883	151527	Enzo Doria	09/2015
1381	2^503225+382667	151486	Enzo Doria	10/2016
1382	(26*10^151391-503)/9	151392	Robert Price	07/2018
1383	2^502769+1877567	151349	Enzo Doria	08/2016
1384	2^502576-4019	151291	Yves Minet	10/2011
1385	2^502290-2792501	151205	Enzo Doria	02/2016
1386	2^502181+1868417	151172	Enzo Doria	04/2016
1387	2^501781-1850503	151052	Enzo Doria	08/2015
1388	(5*10^151007+37)/3	151008	Robert Price	03/2018
1389	2^501627-991	151005	Yves Minet	02/2014
1390	2^501577-115333	150990	Enzo Doria	07/2015
1391	8*10^150975+3	150976	Robert Price	08/2015
1392	2^501512-113669	150971	Enzo Doria	09/2014
1393	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
1394	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
1395	2^500899-500899	150786	Henri Lifchitz	04/2005
1396	2^500832+1876801	150766	Enzo Doria	07/2016
1397	(23*10^150763-59)/9	150764	Robert Price	05/2018
1398	2^500699+1884953	150726	Enzo Doria	02/2017
1399	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
1400	2^500337-71101	150617	Enzo Doria	04/2016
1401	4*10^150577+91	150578	Robert Price	08/2018
1402	2^500160+80071	150564	Enzo Doria	06/2016
1403	(2^500120+5)/9	150551	Lelio R Paula	12/2017
1405	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
1404	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
1406	2^499861-29503	150474	Enzo Doria	08/2015
1407	2^499653-113533	150411	Enzo Doria	08/2014
1408	2^499534-221	150375	Yves Minet	06/2012
1409	2^499225+49727	150282	Enzo Doria	09/2016
1410	2^499054-29261	150231	Enzo Doria	07/2015
1411	(2^498898-7)/9	150183	Lelio R Paula	10/2015
1412	3*10^150182+17	150183	Robert Price	07/2018
1413	2^498623+1866983	150101	Enzo Doria	03/2016
1414	numbpart(18140942830)	150033	Serge Batalov	04/2017
1415	10^150029+4381	150030	Patrick De Geest	05/2016
1416	10^150029-41	150029	Serge Batalov	12/2014
1417	10^150000+1158603	150001	Patrick De Geest	09/2018
1418	10^150000-245703	150000	Patrick De Geest	09/2018
1419	2^498238-53	149985	Lelio R Paula	12/2017
1420	2^497850+81049	149868	Enzo Doria	07/2016
1421	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
1422	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
1423	(2*10^149803-143)/3	149803	Robert Price	03/2018
1424	2^497434-2784191	149743	Enzo Doria	10/2015
1425	2^497068-113579	149633	Enzo Doria	08/2014
1426	2^497037+73727	149624	Enzo Doria	04/2016
1427	2^496773+77747	149544	Enzo Doria	05/2016
1428	2^496477-113485	149455	Enzo Doria	08/2014
1429	2^496270-49451	149393	Enzo Doria	10/2015
1430	2^496238-1865081	149383	Enzo Doria	01/2016
1431	2^495968-1853699	149302	Enzo Doria	09/2015
1432	2^495935-4117	149292	Yves Minet	02/2018
1433	2^495712-396765	149225	Enzo Doria	07/2013
1434	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
1435	2^495420+1880701	149137	Enzo Doria	10/2016
1436	2^495337-1847293	149112	Enzo Doria	07/2015
1437	(2^495193-7)/5	149068	Lelio R Paula	10/2015
1438	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
1439	47^89113-46^89113	149006	Robert Price	10/2012
1440	2^494916+87855	148985	Lelio R Paula	01/2016
1441	2^494586-2791991	148886	Enzo Doria	02/2016
1442	8*10^148860-3	148861	Ray Chandler	04/2011
1443	2^494333-286183	148810	Enzo Doria	06/2015
1444	2^494144-264119	148753	Enzo Doria	05/2014
1445	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
1446	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
1447	2^493636+82081	148600	Enzo Doria	09/2016
1448	((((((((((((((34251^2-2)^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	148593	Serge Batalov	07/2016
1449	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
1450	(2*10^148460-23)/3	148460	Robert Price	04/2018
1451	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
1452	5^211959-12874	148153	Enzo Doria	05/2014
1453	187^65175-2	148068	Lelio R Paula	11/2017
1454	2^491851+1871453	148062	Enzo Doria	05/2016
1455	2^491521-1865323	147963	Enzo Doria	02/2016
1456	(2^491476+7)/71	147948	Lelio R Paula	10/2015
1457	2^491391-7807	147924	Lelio R Paula	01/2013
1458	2^491370-113297	147918	Enzo Doria	07/2014
1459	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
1460	2^490660-17	147704	Lelio R Paula	12/2017
1461	2^490550+1179439	147671	Enzo Doria	06/2016
1462	(23*10^147649-59)/9	147650	Robert Price	05/2018
1463	2^490303+2793653	147596	Enzo Doria	03/2016
1464	199^64181-2	147543	Lelio R Paula	11/2017
1465	2^489871-286987	147466	Enzo Doria	07/2015
1466	2^489864-351899	147464	Enzo Doria	07/2015
1467	175^65724-2	147422	Lelio R Paula	11/2017
1468	2^489712+1874851	147419	Enzo Doria	06/2016
1469	63^81896-2	147359	Lelio R Paula	10/2017
1470	(11*10^147313-107)/3	147314	Robert Price	09/2018
1471	2^489305-59815	147296	Enzo Doria	10/2015
1472	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
1473	2^489125+80357	147242	Enzo Doria	06/2016
1474	2^488648-112799	147098	Enzo Doria	07/2014
1475	2^488627-350317	147092	Enzo Doria	06/2015
1476	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
1477	2^488280-2165	146987	Yves Minet	07/2014
1478	2^488278+45	146987	Lelio R Paula	12/2017
1479	2^487927-39	146881	Lelio R Paula	12/2017
1480	(7*10^146860-13)/3	146861	Robert Price	07/2018
1481	2^487726-1863341	146821	Enzo Doria	12/2015
1482	2^487121-39523	146639	Enzo Doria	09/2015
1483	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
1484	2^486893-79	146570	Yves Minet	09/2017
1485	2^486840+1879141	146554	Enzo Doria	08/2016
1486	2^486774-87	146534	Lelio R Paula	12/2017
1487	96^73877-95^73877	146445	Robert Price	10/2015
1488	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
1489	179^64935+2	146290	Lelio R Paula	10/2017
1490	2^485531-114621	146160	Enzo Doria	05/2015
1491	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1492	2^485389+81887	146117	Enzo Doria	08/2016
1493	(10^146063+71)/9	146063	Serge Batalov	07/2015
1494	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1495	(22*10^146029+257)/9	146030	Robert Price	06/2018
1496	2^484743+1872923	145923	Enzo Doria	05/2016
1497	2^484341+1879157	145802	Enzo Doria	08/2016
1498	2^484271-51	145781	Lelio R Paula	11/2017
1499	70^78989-69^78989	145743	Robert Price	01/2014
1500	51^85334+2	145714	Robert Price	07/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(224926 PRPs in the top)