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) !!!

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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	(10^162138+11)/3	162138	Serge Batalov	07/2015
1252	2^538473-112723	162097	Enzo Doria	06/2014
1253	2^538157+79337	162002	Enzo Doria	06/2016
1254	2^538136-114749	161996	Enzo Doria	05/2015
1255	2^538104+1531	161986	Lelio R Paula	01/2013
1256	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1257	2^537815-22737	161899	Enzo Doria	07/2013
1258	2^537804-39839	161896	Enzo Doria	09/2015
1259	2^537458-59201	161791	Enzo Doria	10/2015
1260	2*10^161766+51	161767	Robert Price	05/2018
1261	2^537209-49849	161717	Enzo Doria	10/2015
1262	2^536937+1879397	161635	Enzo Doria	09/2016
1263	2^536569-22881	161524	Enzo Doria	07/2013
1264	10^161253+573493	161254	Patrick De Geest	07/2018
1265	10^161253-8001	161253	Robert Price	03/2018
1266	7*10^161192-9	161193	Robert Price	10/2015
1267	2^535269-113803	161133	Enzo Doria	09/2014
1268	2^535205-23295	161113	Enzo Doria	08/2013
1269	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1270	2^534359-23229	160859	Enzo Doria	08/2013
1271	67^88037-66^88037	160763	Robert Price	10/2013
1272	2^533948-1852559	160735	Enzo Doria	08/2015
1273	2^533665-23335	160650	Enzo Doria	08/2013
1274	3^336353-2^336353	160482	Mike Oakes	10/2007
1275	2^532253+1868417	160225	Enzo Doria	04/2016
1276	2^532108-291989	160181	Enzo Doria	07/2015
1277	2^531110-1853771	159881	Enzo Doria	09/2015
1278	2^530992-1845299	159845	Enzo Doria	07/2015
1279	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1280	2^530417-113833	159672	Enzo Doria	09/2014
1281	2^530406-69701	159669	Enzo Doria	02/2016
1282	7^188858-188858^7	159604	Norbert Schneider	05/2018
1283	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1284	(17*10^159438-377)/9	159439	Robert Price	03/2018
1285	2^528944-461315	159229	Enzo Doria	07/2015
1286	(13*10^159147+161)/3	159148	Robert Price	11/2018
1287	2^528620-113879	159131	Enzo Doria	10/2014
1288	2^528000-23307	158944	Enzo Doria	08/2013
1289	(29*10^158909+61)/9	158910	Robert Price	08/2018
1290	2^527817+1876817	158889	Enzo Doria	07/2016
1291	2^527774-49451	158876	Enzo Doria	10/2015
1292	2^527745-291553	158868	Enzo Doria	07/2015
1293	2^527644-1856999	158837	Enzo Doria	10/2015
1294	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1295	2^527573-1863253	158816	Enzo Doria	12/2015
1296	2^527553-23401	158810	Enzo Doria	08/2013
1297	11^152420-210	158730	Enzo Doria	09/2012
1298	(13*10^158694+401)/9	158695	Robert Price	01/2018
1299	2^527052-69059	158659	Enzo Doria	11/2015
1300	2^526849-113233	158598	Enzo Doria	07/2014
1301	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
1302	2^526658-3551	158540	Yves Minet	03/2017
1303	2^526375-23115	158455	Enzo Doria	08/2013
1304	2^526028-112793	158351	Enzo Doria	07/2014
1305	2^525690-9221	158249	Lelio R Paula	01/2013
1306	2*10^158242-7	158243	Robert Price	10/2015
1307	2^525667-525667^2	158242	Henri Lifchitz	12/2017
1308	2^525186-1857431	158097	Enzo Doria	10/2015
1309	2^524515-23245	157895	Enzo Doria	08/2013
1310	2^524499-109087	157890	Enzo Doria	04/2014
1311	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
1312	2^524288+189093	157827	Makoto Morimoto	01/2016
1313	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
1314	(10^157792+359)/9	157792	Serge Batalov	12/2014
1315	2^523924+1876591	157717	Enzo Doria	07/2016
1316	(46^94841+1)/47	157696	Robert Price	01/2014
1317	2^523774+77839	157672	Enzo Doria	05/2016
1318	2^523587+2799143	157616	Enzo Doria	04/2016
1319	2^523371+1872113	157551	Enzo Doria	05/2016
1320	2^522535-351457	157299	Enzo Doria	07/2015
1321	2^522226+2799079	157206	Enzo Doria	04/2016
1322	2^522134-1849451	157178	Enzo Doria	08/2015
1323	4*10^157150+93	157151	Robert Price	08/2018
1324	2^521401-29593	156958	Enzo Doria	08/2015
1325	2^521348-23397	156942	Enzo Doria	08/2013
1326	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
1327	65^86522+64	156857	Lelio R Paula	04/2016
1328	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
1329	2^520977-1858183	156830	Enzo Doria	10/2015
1330	(8*10^156718-101)/3	156719	Robert Price	08/2018
1331	2^520314-1849481	156631	Enzo Doria	08/2015
1332	(13*10^156522+89)/3	156523	Robert Price	09/2018
1333	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
1334	3*10^156435-97	156436	Robert Price	07/2018
1335	(8*10^156371-77)/3	156372	Robert Price	07/2018
1336	53^90679-52^90679	156356	Robert Price	01/2013
1337	2^519106-59141	156267	Enzo Doria	10/2015
1338	2^519053+6077	156251	Enzo Doria	02/2016
1339	2^518968-1860989	156225	Enzo Doria	11/2015
1340	(25*10^156221-7)/9	156222	Robert Price	05/2018
1341	2^518931-2782297	156214	Enzo Doria	09/2015
1342	2^518608-2939	156117	Yves Minet	09/2014
1343	10*27^109005+697	156027	Curtis Bright	05/2015
1344	2^517967-113485	155924	Enzo Doria	08/2014
1345	2^517698+4429	155843	Lelio R Paula	01/2013
1346	2^517543-113257	155796	Enzo Doria	07/2014
1347	(14*10^155740-143)/3	155741	Robert Price	11/2018
1348	31^104309-30^104309	155563	Henri Lifchitz	08/2013
1349	2^516742-39851	155555	Enzo Doria	09/2015
1350	2^516440+1878421	155464	Enzo Doria	08/2016
1351	2^515863-1867237	155291	Enzo Doria	03/2016
1352	2^515786-461861	155268	Enzo Doria	07/2015
1353	2^515644-113247	155225	Enzo Doria	07/2014
1354	(7*10^155203+107)/3	155204	Robert Price	02/2018
1355	(17*10^155133-89)/9	155134	Robert Price	07/2018
1356	2^515227-114997	155099	Enzo Doria	06/2015
1358	EPrime(155025)	155025	Eric W. Weisstein	10/2010
1357	(14*10^155024-221)/9	155025	Robert Price	04/2018
1359	(4*10^155022+173)/3	155023	Robert Price	02/2018
1360	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
1361	2^514361+78167	154839	Enzo Doria	05/2016
1362	2^514281-115033	154815	Enzo Doria	06/2015
1363	2^514194-3311	154788	Yves Minet	12/2014
1364	(14*10^154773+37)/3	154774	Robert Price	12/2018
1365	2^513437+1879337	154560	Enzo Doria	09/2016
1366	2^513306-113201	154521	Enzo Doria	07/2014
1367	(10^154494-13)/3	154494	Robert Price	12/2017
1368	2^513042-113787	154442	Enzo Doria	09/2014
1369	2^512628-114053	154317	Enzo Doria	11/2014
1370	2^512529-49783	154287	Enzo Doria	10/2015
1371	2^512315-115297	154223	Enzo Doria	06/2015
1372	2^512168+79561	154178	Enzo Doria	06/2016
1373	4*10^154078-57	154079	Robert Price	10/2018
1374	2^511658-114371	154025	Enzo Doria	02/2015
1375	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
1376	2^511580-1846679	154001	Enzo Doria	07/2015
1377	2^511541-113713	153990	Enzo Doria	09/2014
1378	2^511077-112723	153850	Enzo Doria	06/2014
1379	69^83653-68^83653	153826	Robert Price	12/2013
1380	2^510963-113707	153816	Enzo Doria	09/2014
1381	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
1382	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
1383	2*10^153746-3	153747	Robert Price	07/2015
1384	2^510626+1179379	153714	Enzo Doria	05/2016
1385	(7*10^153664+113)/3	153665	Robert Price	02/2018
1386	2^510420+81121	153652	Enzo Doria	07/2016
1387	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
1388	2^509894-459161	153494	Enzo Doria	05/2015
1389	2^509841+71657	153478	Enzo Doria	04/2016
1390	2^509533-1846723	153385	Enzo Doria	07/2015
1391	2^509468-39989	153366	Enzo Doria	09/2015
1392	70^83117-69^83117	153360	Robert Price	01/2014
1393	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
1394	2^508174-1855151	152976	Enzo Doria	09/2015
1395	181^67757-2	152974	Lelio R Paula	12/2017
1396	2^508160-1864829	152972	Enzo Doria	01/2016
1397	2^507857-1848199	152881	Enzo Doria	07/2015
1398	2^507638-115361	152815	Enzo Doria	07/2015
1399	2^507551-114025	152789	Enzo Doria	11/2014
1400	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
1401	(22*10^152670-13)/9	152671	Robert Price	06/2018
1402	2^506451-22339	152457	Enzo Doria	07/2013
1403	2^505995-113185	152320	Enzo Doria	07/2014
1404	(4*10^152253+149)/9	152253	Robert Price	04/2018
1405	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
1406	2^505431-505431	152150	Henri Lifchitz	04/2005
1407	2^505053+73097	152037	Enzo Doria	04/2016
1408	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
1409	350377#+797581	151937	Nicolas PALAU	08/2017
1410	2^504618-343991	151906	Enzo Doria	07/2015
1411	2^504212-461939	151783	Enzo Doria	07/2015
1412	2^504054-2231	151736	Yves Minet	10/2011
1413	2^503361-39883	151527	Enzo Doria	09/2015
1414	2^503225+382667	151486	Enzo Doria	10/2016
1415	(26*10^151391-503)/9	151392	Robert Price	07/2018
1416	2^502769+1877567	151349	Enzo Doria	08/2016
1417	2^502576-4019	151291	Yves Minet	10/2011
1418	2^502290-2792501	151205	Enzo Doria	02/2016
1419	2^502181+1868417	151172	Enzo Doria	04/2016
1420	2^501781-1850503	151052	Enzo Doria	08/2015
1421	(5*10^151007+37)/3	151008	Robert Price	03/2018
1422	2^501627-991	151005	Yves Minet	02/2014
1423	2^501577-115333	150990	Enzo Doria	07/2015
1424	8*10^150975+3	150976	Robert Price	08/2015
1425	2^501512-113669	150971	Enzo Doria	09/2014
1426	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
1427	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
1428	2^500899-500899	150786	Henri Lifchitz	04/2005
1429	2^500832+1876801	150766	Enzo Doria	07/2016
1430	(23*10^150763-59)/9	150764	Robert Price	05/2018
1431	2^500699+1884953	150726	Enzo Doria	02/2017
1432	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
1433	2^500337-71101	150617	Enzo Doria	04/2016
1434	4*10^150577+91	150578	Robert Price	08/2018
1435	2^500160+80071	150564	Enzo Doria	06/2016
1436	(2^500120+5)/9	150551	Lelio R Paula	12/2017
1438	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
1437	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
1439	2^499861-29503	150474	Enzo Doria	08/2015
1440	2^499653-113533	150411	Enzo Doria	08/2014
1441	2^499534-221	150375	Yves Minet	06/2012
1442	2^499225+49727	150282	Enzo Doria	09/2016
1443	2^499054-29261	150231	Enzo Doria	07/2015
1444	(2^498898-7)/9	150183	Lelio R Paula	10/2015
1445	3*10^150182+17	150183	Robert Price	07/2018
1446	2^498623+1866983	150101	Enzo Doria	03/2016
1447	numbpart(18140942830)	150033	Serge Batalov	04/2017
1448	10^150029+4381	150030	Patrick De Geest	05/2016
1449	10^150029-41	150029	Serge Batalov	12/2014
1450	10^150000+1158603	150001	Patrick De Geest	09/2018
1451	10^150000-245703	150000	Patrick De Geest	09/2018
1452	(38*10^149999+691)/9	150000	Robert Price	10/2018
1453	2^498238-53	149985	Lelio R Paula	12/2017
1454	2^497850+81049	149868	Enzo Doria	07/2016
1455	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
1456	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
1457	(2*10^149803-143)/3	149803	Robert Price	03/2018
1458	2^497434-2784191	149743	Enzo Doria	10/2015
1459	2^497068-113579	149633	Enzo Doria	08/2014
1460	2^497037+73727	149624	Enzo Doria	04/2016
1461	2^496773+77747	149544	Enzo Doria	05/2016
1462	2^496477-113485	149455	Enzo Doria	08/2014
1463	2^496270-49451	149393	Enzo Doria	10/2015
1464	2^496238-1865081	149383	Enzo Doria	01/2016
1465	2^495968-1853699	149302	Enzo Doria	09/2015
1466	2^495935-4117	149292	Yves Minet	02/2018
1467	2^495712-396765	149225	Enzo Doria	07/2013
1468	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
1469	2^495420+1880701	149137	Enzo Doria	10/2016
1470	2^495337-1847293	149112	Enzo Doria	07/2015
1471	(2^495193-7)/5	149068	Lelio R Paula	10/2015
1472	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
1473	47^89113-46^89113	149006	Robert Price	10/2012
1474	2^494916+87855	148985	Lelio R Paula	01/2016
1475	2^494586-2791991	148886	Enzo Doria	02/2016
1476	8*10^148860-3	148861	Ray Chandler	04/2011
1477	2^494333-286183	148810	Enzo Doria	06/2015
1478	2^494144-264119	148753	Enzo Doria	05/2014
1479	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
1480	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
1481	2^493636+82081	148600	Enzo Doria	09/2016
1482	((((((((((((((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
1483	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
1484	(2*10^148460-23)/3	148460	Robert Price	04/2018
1485	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
1486	5^211959-12874	148153	Enzo Doria	05/2014
1487	187^65175-2	148068	Lelio R Paula	11/2017
1488	2^491851+1871453	148062	Enzo Doria	05/2016
1489	2^491521-1865323	147963	Enzo Doria	02/2016
1490	(2^491476+7)/71	147948	Lelio R Paula	10/2015
1491	2^491391-7807	147924	Lelio R Paula	01/2013
1492	2^491370-113297	147918	Enzo Doria	07/2014
1493	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
1494	2^490660-17	147704	Lelio R Paula	12/2017
1495	2^490550+1179439	147671	Enzo Doria	06/2016
1496	(23*10^147649-59)/9	147650	Robert Price	05/2018
1497	2^490303+2793653	147596	Enzo Doria	03/2016
1498	199^64181-2	147543	Lelio R Paula	11/2017
1499	2^489871-286987	147466	Enzo Doria	07/2015
1500	2^489864-351899	147464	Enzo Doria	07/2015

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Probable Primes Top 10000

(252402 PRPs in the top)