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 (> 30000)	Who ?	When ?
1251	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
1252	2^514361+78167	154839	Enzo Doria	05/2016
1253	2^514281-115033	154815	Enzo Doria	06/2015
1254	2^514194-3311	154788	Yves Minet	12/2014
1255	2^513437+1879337	154560	Enzo Doria	09/2016
1256	2^513306-113201	154521	Enzo Doria	07/2014
1257	(10^154494-13)/3	154494	Robert Price	12/2017
1258	2^513042-113787	154442	Enzo Doria	09/2014
1259	2^512628-114053	154317	Enzo Doria	11/2014
1260	2^512529-49783	154287	Enzo Doria	10/2015
1261	2^512315-115297	154223	Enzo Doria	06/2015
1262	2^512168+79561	154178	Enzo Doria	06/2016
1263	2^511658-114371	154025	Enzo Doria	02/2015
1264	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
1265	2^511580-1846679	154001	Enzo Doria	07/2015
1266	2^511541-113713	153990	Enzo Doria	09/2014
1267	2^511077-112723	153850	Enzo Doria	06/2014
1268	69^83653-68^83653	153826	Robert Price	12/2013
1269	2^510963-113707	153816	Enzo Doria	09/2014
1270	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
1271	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
1272	2*10^153746-3	153747	Robert Price	07/2015
1273	2^510626+1179379	153714	Enzo Doria	05/2016
1274	(7*10^153664+113)/3	153665	Robert Price	02/2018
1275	2^510420+81121	153652	Enzo Doria	07/2016
1276	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
1277	2^509894-459161	153494	Enzo Doria	05/2015
1278	2^509841+71657	153478	Enzo Doria	04/2016
1279	2^509533-1846723	153385	Enzo Doria	07/2015
1280	2^509468-39989	153366	Enzo Doria	09/2015
1281	70^83117-69^83117	153360	Robert Price	01/2014
1282	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
1283	2^508174-1855151	152976	Enzo Doria	09/2015
1284	181^67757-2	152974	Lelio R Paula	12/2017
1285	2^508160-1864829	152972	Enzo Doria	01/2016
1286	2^507857-1848199	152881	Enzo Doria	07/2015
1287	2^507638-115361	152815	Enzo Doria	07/2015
1288	2^507551-114025	152789	Enzo Doria	11/2014
1289	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
1290	2^506451-22339	152457	Enzo Doria	07/2013
1291	2^505995-113185	152320	Enzo Doria	07/2014
1292	(4*10^152253+149)/9	152253	Robert Price	04/2018
1293	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
1294	2^505431-505431	152150	Henri Lifchitz	04/2005
1295	2^505053+73097	152037	Enzo Doria	04/2016
1296	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
1297	350377#+797581	151937	Nicolas PALAU	08/2017
1298	2^504618-343991	151906	Enzo Doria	07/2015
1299	2^504212-461939	151783	Enzo Doria	07/2015
1300	2^504054-2231	151736	Yves Minet	10/2011
1301	2^503361-39883	151527	Enzo Doria	09/2015
1302	2^503225+382667	151486	Enzo Doria	10/2016
1303	2^502769+1877567	151349	Enzo Doria	08/2016
1304	2^502576-4019	151291	Yves Minet	10/2011
1305	2^502290-2792501	151205	Enzo Doria	02/2016
1306	2^502181+1868417	151172	Enzo Doria	04/2016
1307	2^501781-1850503	151052	Enzo Doria	08/2015
1308	(5*10^151007+37)/3	151008	Robert Price	03/2018
1309	2^501627-991	151005	Yves Minet	02/2014
1310	2^501577-115333	150990	Enzo Doria	07/2015
1311	8*10^150975+3	150976	Robert Price	08/2015
1312	2^501512-113669	150971	Enzo Doria	09/2014
1313	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
1314	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
1315	2^500899-500899	150786	Henri Lifchitz	04/2005
1316	2^500832+1876801	150766	Enzo Doria	07/2016
1317	2^500699+1884953	150726	Enzo Doria	02/2017
1318	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
1319	2^500337-71101	150617	Enzo Doria	04/2016
1320	2^500160+80071	150564	Enzo Doria	06/2016
1321	(2^500120+5)/9	150551	Lelio R Paula	12/2017
1323	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
1322	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
1324	2^499861-29503	150474	Enzo Doria	08/2015
1325	2^499653-113533	150411	Enzo Doria	08/2014
1326	2^499534-221	150375	Yves Minet	06/2012
1327	2^499225+49727	150282	Enzo Doria	09/2016
1328	2^499054-29261	150231	Enzo Doria	07/2015
1329	(2^498898-7)/9	150183	Lelio R Paula	10/2015
1330	2^498623+1866983	150101	Enzo Doria	03/2016
1331	numbpart(18140942830)	150033	Serge Batalov	04/2017
1332	10^150029+4381	150030	Patrick De Geest	05/2016
1333	10^150029-41	150029	Serge Batalov	12/2014
1334	2^498238-53	149985	Lelio R Paula	12/2017
1335	2^497850+81049	149868	Enzo Doria	07/2016
1336	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
1337	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
1338	(2*10^149803-143)/3	149803	Robert Price	03/2018
1339	2^497434-2784191	149743	Enzo Doria	10/2015
1340	2^497068-113579	149633	Enzo Doria	08/2014
1341	2^497037+73727	149624	Enzo Doria	04/2016
1342	2^496773+77747	149544	Enzo Doria	05/2016
1343	2^496477-113485	149455	Enzo Doria	08/2014
1344	2^496270-49451	149393	Enzo Doria	10/2015
1345	2^496238-1865081	149383	Enzo Doria	01/2016
1346	2^495968-1853699	149302	Enzo Doria	09/2015
1347	2^495935-4117	149292	Yves Minet	02/2018
1348	2^495712-396765	149225	Enzo Doria	07/2013
1349	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
1350	2^495420+1880701	149137	Enzo Doria	10/2016
1351	2^495337-1847293	149112	Enzo Doria	07/2015
1352	(2^495193-7)/5	149068	Lelio R Paula	10/2015
1353	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
1354	47^89113-46^89113	149006	Robert Price	10/2012
1355	2^494916+87855	148985	Lelio R Paula	01/2016
1356	2^494586-2791991	148886	Enzo Doria	02/2016
1357	8*10^148860-3	148861	Ray Chandler	04/2011
1358	2^494333-286183	148810	Enzo Doria	06/2015
1359	2^494144-264119	148753	Enzo Doria	05/2014
1360	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
1361	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
1362	2^493636+82081	148600	Enzo Doria	09/2016
1363	((((((((((((((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
1364	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
1365	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
1366	5^211959-12874	148153	Enzo Doria	05/2014
1367	187^65175-2	148068	Lelio R Paula	11/2017
1368	2^491851+1871453	148062	Enzo Doria	05/2016
1369	2^491521-1865323	147963	Enzo Doria	02/2016
1370	(2^491476+7)/71	147948	Lelio R Paula	10/2015
1371	2^491391-7807	147924	Lelio R Paula	01/2013
1372	2^491370-113297	147918	Enzo Doria	07/2014
1373	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
1374	2^490660-17	147704	Lelio R Paula	12/2017
1375	2^490550+1179439	147671	Enzo Doria	06/2016
1376	2^490303+2793653	147596	Enzo Doria	03/2016
1377	199^64181-2	147543	Lelio R Paula	11/2017
1378	2^489871-286987	147466	Enzo Doria	07/2015
1379	2^489864-351899	147464	Enzo Doria	07/2015
1380	175^65724-2	147422	Lelio R Paula	11/2017
1381	2^489712+1874851	147419	Enzo Doria	06/2016
1382	63^81896-2	147359	Lelio R Paula	10/2017
1383	2^489305-59815	147296	Enzo Doria	10/2015
1384	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
1385	2^489125+80357	147242	Enzo Doria	06/2016
1386	2^488648-112799	147098	Enzo Doria	07/2014
1387	2^488627-350317	147092	Enzo Doria	06/2015
1388	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
1389	2^488280-2165	146987	Yves Minet	07/2014
1390	2^488278+45	146987	Lelio R Paula	12/2017
1391	2^487927-39	146881	Lelio R Paula	12/2017
1392	2^487726-1863341	146821	Enzo Doria	12/2015
1393	2^487121-39523	146639	Enzo Doria	09/2015
1394	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
1395	2^486893-79	146570	Yves Minet	09/2017
1396	2^486840+1879141	146554	Enzo Doria	08/2016
1397	2^486774-87	146534	Lelio R Paula	12/2017
1398	96^73877-95^73877	146445	Robert Price	10/2015
1399	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
1400	179^64935+2	146290	Lelio R Paula	10/2017
1401	2^485531-114621	146160	Enzo Doria	05/2015
1402	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1403	2^485389+81887	146117	Enzo Doria	08/2016
1404	(10^146063+71)/9	146063	Serge Batalov	07/2015
1405	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1406	2^484743+1872923	145923	Enzo Doria	05/2016
1407	2^484341+1879157	145802	Enzo Doria	08/2016
1408	2^484271-51	145781	Lelio R Paula	11/2017
1409	70^78989-69^78989	145743	Robert Price	01/2014
1410	51^85334+2	145714	Robert Price	07/2015
1411	2^483886-1857101	145665	Enzo Doria	10/2015
1412	2^483563-1863457	145567	Enzo Doria	12/2015
1413	2^483516-1861409	145553	Enzo Doria	11/2015
1414	2^483384-115019	145514	Enzo Doria	06/2015
1415	2^483302-3221	145489	Lelio R Paula	12/2012
1416	2^483046+1874029	145412	Enzo Doria	06/2016
1417	2^482991-2789317	145395	Enzo Doria	12/2015
1418	2^482978-2789711	145391	Enzo Doria	12/2015
1419	2^482966-2789711	145388	Enzo Doria	12/2015
1420	2^482817-1858843	145343	Enzo Doria	10/2015
1421	2^482751-113635	145323	Enzo Doria	08/2014
1422	2^482705-459763	145309	Enzo Doria	05/2015
1423	(4^241306+11)/3	145281	Robert Price	03/2017
1424	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1425	53^84239-52^84239	145252	Robert Price	01/2013
1426	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1427	2^482087+72623	145123	Enzo Doria	04/2016
1428	2^482016-286565	145102	Enzo Doria	07/2015
1429	2^481840+15	145049	Robert Price	09/2015
1430	2^481801-481801	145037	Henri Lifchitz	03/2005
1431	2^481775+1869083	145029	Enzo Doria	05/2016
1432	29^99167+2	145022	Ray Chandler	08/2011
1433	2^481663+1875653	144996	Enzo Doria	07/2016
1434	2^481149-459073	144841	Enzo Doria	05/2015
1435	2^481045-113215	144809	Enzo Doria	07/2014
1436	2^480859-113695	144753	Enzo Doria	09/2014
1437	2^480766-2787191	144725	Enzo Doria	11/2015
1438	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1439	2^480678+1874239	144699	Enzo Doria	06/2016
1440	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1441	L(692147)	144651	Henri Lifchitz	10/2008
1442	2^480417+35	144620	Robert Price	11/2015
1443	2^480296-59879	144584	Enzo Doria	10/2015
1444	2^479844+3	144448	Donovan Johnson	06/2006
1445	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1446	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1447	2^479348-2792219	144299	Enzo Doria	02/2016
1448	3^302389-6242	144277	Enzo Doria	05/2014
1449	2*10^144220-3	144221	Robert Price	07/2015
1450	2^478904-109109	144165	Enzo Doria	04/2014
1451	2^478337-115333	143994	Enzo Doria	07/2015
1452	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1453	88^74047-87^74047	143984	Robert Price	05/2015
1454	(19*10^143963+467)/9	143964	Robert Price	02/2018
1455	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
1456	2^478088+27	143919	Robert Price	11/2015
1457	2^477475-22071	143735	Enzo Doria	07/2013
1458	2^477417-22123	143717	Enzo Doria	07/2013
1459	2^477359-3577	143700	Yves Minet	03/2017
1460	2^476936-396765	143573	Enzo Doria	07/2013
1461	2^476888-2791229	143558	Enzo Doria	01/2016
1462	2^476868-1859939	143552	Enzo Doria	11/2015
1463	2^476558-113627	143459	Enzo Doria	08/2014
1464	2^476478-45	143435	Lelio R Paula	11/2017
1465	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1466	2^475813-113239	143234	Enzo Doria	07/2014
1467	2^475624-114059	143178	Enzo Doria	11/2014
1468	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1469	2^475480-2786129	143134	Enzo Doria	10/2015
1470	2^475299-111937	143080	Enzo Doria	05/2014
1471	2^475160-2797859	143038	Enzo Doria	04/2016
1472	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1473	2^475027-461437	142998	Enzo Doria	07/2015
1474	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1475	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
1476	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1477	2^474417-59923	142814	Enzo Doria	10/2015
1478	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1479	2^474053+2897	142705	Lelio R Paula	08/2012
1480	(10^142699+359)/9	142699	Serge Batalov	12/2014
1481	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1482	2^473740-1856639	142610	Enzo Doria	09/2015
1483	2^473617-114223	142573	Enzo Doria	12/2014
1484	2^473257+1873217	142465	Enzo Doria	06/2016
1485	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1486	(10^142425+359)/9	142425	Serge Batalov	12/2014
1487	2^473101+773027	142418	Enzo Doria	05/2016
1488	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1489	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1490	2^472634-109511	142278	Enzo Doria	04/2014
1491	(48^84589+1)/49	142213	Robert Price	01/2014
1492	2^472258+7	142164	Lelio R Paula	08/2015
1493	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1494	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1495	2^471792+1880881	142024	Enzo Doria	11/2016
1496	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1497	(4*10^141926-79)/3	141927	Robert Price	02/2018
1498	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1499	4*5^202913-9	141831	Lelio R Paula	04/2015
1500	2*7^167812-3	141818	Lelio R Paula	12/2014

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Probable Primes Top 10000

(205869 PRPs in the top)