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	2^520977-1858183	156830	Enzo Doria	10/2015
1252	2^520314-1849481	156631	Enzo Doria	08/2015
1253	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
1254	53^90679-52^90679	156356	Robert Price	01/2013
1255	2^519106-59141	156267	Enzo Doria	10/2015
1256	2^519053+6077	156251	Enzo Doria	02/2016
1257	2^518968-1860989	156225	Enzo Doria	11/2015
1258	(25*10^156221-7)/9	156222	Robert Price	05/2018
1259	2^518931-2782297	156214	Enzo Doria	09/2015
1260	2^518608-2939	156117	Yves Minet	09/2014
1261	10*27^109005+697	156027	Curtis Bright	05/2015
1262	2^517967-113485	155924	Enzo Doria	08/2014
1263	2^517698+4429	155843	Lelio R Paula	01/2013
1264	2^517543-113257	155796	Enzo Doria	07/2014
1265	31^104309-30^104309	155563	Henri Lifchitz	08/2013
1266	2^516742-39851	155555	Enzo Doria	09/2015
1267	2^516440+1878421	155464	Enzo Doria	08/2016
1268	2^515863-1867237	155291	Enzo Doria	03/2016
1269	2^515786-461861	155268	Enzo Doria	07/2015
1270	2^515644-113247	155225	Enzo Doria	07/2014
1271	(7*10^155203+107)/3	155204	Robert Price	02/2018
1272	2^515227-114997	155099	Enzo Doria	06/2015
1273	EPrime(155025)	155025	Eric W. Weisstein	10/2010
1274	(14*10^155024-221)/9	155025	Robert Price	04/2018
1275	(4*10^155022+173)/3	155023	Robert Price	02/2018
1276	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
1277	2^514361+78167	154839	Enzo Doria	05/2016
1278	2^514281-115033	154815	Enzo Doria	06/2015
1279	2^514194-3311	154788	Yves Minet	12/2014
1280	2^513437+1879337	154560	Enzo Doria	09/2016
1281	2^513306-113201	154521	Enzo Doria	07/2014
1282	(10^154494-13)/3	154494	Robert Price	12/2017
1283	2^513042-113787	154442	Enzo Doria	09/2014
1284	2^512628-114053	154317	Enzo Doria	11/2014
1285	2^512529-49783	154287	Enzo Doria	10/2015
1286	2^512315-115297	154223	Enzo Doria	06/2015
1287	2^512168+79561	154178	Enzo Doria	06/2016
1288	2^511658-114371	154025	Enzo Doria	02/2015
1289	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
1290	2^511580-1846679	154001	Enzo Doria	07/2015
1291	2^511541-113713	153990	Enzo Doria	09/2014
1292	2^511077-112723	153850	Enzo Doria	06/2014
1293	69^83653-68^83653	153826	Robert Price	12/2013
1294	2^510963-113707	153816	Enzo Doria	09/2014
1295	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
1296	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
1297	2*10^153746-3	153747	Robert Price	07/2015
1298	2^510626+1179379	153714	Enzo Doria	05/2016
1299	(7*10^153664+113)/3	153665	Robert Price	02/2018
1300	2^510420+81121	153652	Enzo Doria	07/2016
1301	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
1302	2^509894-459161	153494	Enzo Doria	05/2015
1303	2^509841+71657	153478	Enzo Doria	04/2016
1304	2^509533-1846723	153385	Enzo Doria	07/2015
1305	2^509468-39989	153366	Enzo Doria	09/2015
1306	70^83117-69^83117	153360	Robert Price	01/2014
1307	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
1308	2^508174-1855151	152976	Enzo Doria	09/2015
1309	181^67757-2	152974	Lelio R Paula	12/2017
1310	2^508160-1864829	152972	Enzo Doria	01/2016
1311	2^507857-1848199	152881	Enzo Doria	07/2015
1312	2^507638-115361	152815	Enzo Doria	07/2015
1313	2^507551-114025	152789	Enzo Doria	11/2014
1314	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
1315	(22*10^152670-13)/9	152671	Robert Price	06/2018
1316	2^506451-22339	152457	Enzo Doria	07/2013
1317	2^505995-113185	152320	Enzo Doria	07/2014
1318	(4*10^152253+149)/9	152253	Robert Price	04/2018
1319	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
1320	2^505431-505431	152150	Henri Lifchitz	04/2005
1321	2^505053+73097	152037	Enzo Doria	04/2016
1322	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
1323	350377#+797581	151937	Nicolas PALAU	08/2017
1324	2^504618-343991	151906	Enzo Doria	07/2015
1325	2^504212-461939	151783	Enzo Doria	07/2015
1326	2^504054-2231	151736	Yves Minet	10/2011
1327	2^503361-39883	151527	Enzo Doria	09/2015
1328	2^503225+382667	151486	Enzo Doria	10/2016
1329	2^502769+1877567	151349	Enzo Doria	08/2016
1330	2^502576-4019	151291	Yves Minet	10/2011
1331	2^502290-2792501	151205	Enzo Doria	02/2016
1332	2^502181+1868417	151172	Enzo Doria	04/2016
1333	2^501781-1850503	151052	Enzo Doria	08/2015
1334	(5*10^151007+37)/3	151008	Robert Price	03/2018
1335	2^501627-991	151005	Yves Minet	02/2014
1336	2^501577-115333	150990	Enzo Doria	07/2015
1337	8*10^150975+3	150976	Robert Price	08/2015
1338	2^501512-113669	150971	Enzo Doria	09/2014
1339	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
1340	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
1341	2^500899-500899	150786	Henri Lifchitz	04/2005
1342	2^500832+1876801	150766	Enzo Doria	07/2016
1343	(23*10^150763-59)/9	150764	Robert Price	05/2018
1344	2^500699+1884953	150726	Enzo Doria	02/2017
1345	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
1346	2^500337-71101	150617	Enzo Doria	04/2016
1347	2^500160+80071	150564	Enzo Doria	06/2016
1348	(2^500120+5)/9	150551	Lelio R Paula	12/2017
1349	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
1350	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
1351	2^499861-29503	150474	Enzo Doria	08/2015
1352	2^499653-113533	150411	Enzo Doria	08/2014
1353	2^499534-221	150375	Yves Minet	06/2012
1354	2^499225+49727	150282	Enzo Doria	09/2016
1355	2^499054-29261	150231	Enzo Doria	07/2015
1356	(2^498898-7)/9	150183	Lelio R Paula	10/2015
1357	2^498623+1866983	150101	Enzo Doria	03/2016
1358	numbpart(18140942830)	150033	Serge Batalov	04/2017
1359	10^150029+4381	150030	Patrick De Geest	05/2016
1360	10^150029-41	150029	Serge Batalov	12/2014
1361	2^498238-53	149985	Lelio R Paula	12/2017
1362	2^497850+81049	149868	Enzo Doria	07/2016
1363	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
1364	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
1365	(2*10^149803-143)/3	149803	Robert Price	03/2018
1366	2^497434-2784191	149743	Enzo Doria	10/2015
1367	2^497068-113579	149633	Enzo Doria	08/2014
1368	2^497037+73727	149624	Enzo Doria	04/2016
1369	2^496773+77747	149544	Enzo Doria	05/2016
1370	2^496477-113485	149455	Enzo Doria	08/2014
1371	2^496270-49451	149393	Enzo Doria	10/2015
1372	2^496238-1865081	149383	Enzo Doria	01/2016
1373	2^495968-1853699	149302	Enzo Doria	09/2015
1374	2^495935-4117	149292	Yves Minet	02/2018
1375	2^495712-396765	149225	Enzo Doria	07/2013
1376	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
1377	2^495420+1880701	149137	Enzo Doria	10/2016
1378	2^495337-1847293	149112	Enzo Doria	07/2015
1379	(2^495193-7)/5	149068	Lelio R Paula	10/2015
1380	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
1381	47^89113-46^89113	149006	Robert Price	10/2012
1382	2^494916+87855	148985	Lelio R Paula	01/2016
1383	2^494586-2791991	148886	Enzo Doria	02/2016
1384	8*10^148860-3	148861	Ray Chandler	04/2011
1385	2^494333-286183	148810	Enzo Doria	06/2015
1386	2^494144-264119	148753	Enzo Doria	05/2014
1387	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
1388	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
1389	2^493636+82081	148600	Enzo Doria	09/2016
1390	((((((((((((((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
1391	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
1392	(2*10^148460-23)/3	148460	Robert Price	04/2018
1393	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
1394	5^211959-12874	148153	Enzo Doria	05/2014
1395	187^65175-2	148068	Lelio R Paula	11/2017
1396	2^491851+1871453	148062	Enzo Doria	05/2016
1397	2^491521-1865323	147963	Enzo Doria	02/2016
1398	(2^491476+7)/71	147948	Lelio R Paula	10/2015
1399	2^491391-7807	147924	Lelio R Paula	01/2013
1400	2^491370-113297	147918	Enzo Doria	07/2014
1401	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
1402	2^490660-17	147704	Lelio R Paula	12/2017
1403	2^490550+1179439	147671	Enzo Doria	06/2016
1404	(23*10^147649-59)/9	147650	Robert Price	05/2018
1405	2^490303+2793653	147596	Enzo Doria	03/2016
1406	199^64181-2	147543	Lelio R Paula	11/2017
1407	2^489871-286987	147466	Enzo Doria	07/2015
1408	2^489864-351899	147464	Enzo Doria	07/2015
1409	175^65724-2	147422	Lelio R Paula	11/2017
1410	2^489712+1874851	147419	Enzo Doria	06/2016
1411	63^81896-2	147359	Lelio R Paula	10/2017
1412	2^489305-59815	147296	Enzo Doria	10/2015
1413	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
1414	2^489125+80357	147242	Enzo Doria	06/2016
1415	2^488648-112799	147098	Enzo Doria	07/2014
1416	2^488627-350317	147092	Enzo Doria	06/2015
1417	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
1418	2^488280-2165	146987	Yves Minet	07/2014
1419	2^488278+45	146987	Lelio R Paula	12/2017
1420	2^487927-39	146881	Lelio R Paula	12/2017
1421	2^487726-1863341	146821	Enzo Doria	12/2015
1422	2^487121-39523	146639	Enzo Doria	09/2015
1423	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
1424	2^486893-79	146570	Yves Minet	09/2017
1425	2^486840+1879141	146554	Enzo Doria	08/2016
1426	2^486774-87	146534	Lelio R Paula	12/2017
1427	96^73877-95^73877	146445	Robert Price	10/2015
1428	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
1429	179^64935+2	146290	Lelio R Paula	10/2017
1430	2^485531-114621	146160	Enzo Doria	05/2015
1431	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1432	2^485389+81887	146117	Enzo Doria	08/2016
1433	(10^146063+71)/9	146063	Serge Batalov	07/2015
1434	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1435	(22*10^146029+257)/9	146030	Robert Price	06/2018
1436	2^484743+1872923	145923	Enzo Doria	05/2016
1437	2^484341+1879157	145802	Enzo Doria	08/2016
1438	2^484271-51	145781	Lelio R Paula	11/2017
1439	70^78989-69^78989	145743	Robert Price	01/2014
1440	51^85334+2	145714	Robert Price	07/2015
1441	2^483886-1857101	145665	Enzo Doria	10/2015
1442	2^483563-1863457	145567	Enzo Doria	12/2015
1443	2^483516-1861409	145553	Enzo Doria	11/2015
1444	2^483384-115019	145514	Enzo Doria	06/2015
1445	2^483302-3221	145489	Lelio R Paula	12/2012
1446	2^483046+1874029	145412	Enzo Doria	06/2016
1447	2^482991-2789317	145395	Enzo Doria	12/2015
1448	2^482978-2789711	145391	Enzo Doria	12/2015
1449	2^482966-2789711	145388	Enzo Doria	12/2015
1450	2^482817-1858843	145343	Enzo Doria	10/2015
1451	2^482751-113635	145323	Enzo Doria	08/2014
1452	2^482705-459763	145309	Enzo Doria	05/2015
1453	(4^241306+11)/3	145281	Robert Price	03/2017
1454	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1455	53^84239-52^84239	145252	Robert Price	01/2013
1456	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1457	2^482087+72623	145123	Enzo Doria	04/2016
1458	2^482016-286565	145102	Enzo Doria	07/2015
1459	2^481840+15	145049	Robert Price	09/2015
1460	2^481801-481801	145037	Henri Lifchitz	03/2005
1461	2^481775+1869083	145029	Enzo Doria	05/2016
1462	29^99167+2	145022	Ray Chandler	08/2011
1463	2^481663+1875653	144996	Enzo Doria	07/2016
1464	2^481149-459073	144841	Enzo Doria	05/2015
1465	2^481045-113215	144809	Enzo Doria	07/2014
1466	2^480859-113695	144753	Enzo Doria	09/2014
1467	2^480766-2787191	144725	Enzo Doria	11/2015
1468	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1469	2^480678+1874239	144699	Enzo Doria	06/2016
1470	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1471	L(692147)	144651	Henri Lifchitz	10/2008
1472	2^480417+35	144620	Robert Price	11/2015
1473	2^480296-59879	144584	Enzo Doria	10/2015
1474	2^479844+3	144448	Donovan Johnson	06/2006
1475	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1476	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1477	2^479348-2792219	144299	Enzo Doria	02/2016
1478	3^302389-6242	144277	Enzo Doria	05/2014
1479	2*10^144220-3	144221	Robert Price	07/2015
1480	2^478904-109109	144165	Enzo Doria	04/2014
1481	2^478337-115333	143994	Enzo Doria	07/2015
1482	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1483	88^74047-87^74047	143984	Robert Price	05/2015
1484	(19*10^143963+467)/9	143964	Robert Price	02/2018
1485	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
1486	2^478088+27	143919	Robert Price	11/2015
1487	2^477475-22071	143735	Enzo Doria	07/2013
1488	2^477417-22123	143717	Enzo Doria	07/2013
1489	2^477359-3577	143700	Yves Minet	03/2017
1490	2^476936-396765	143573	Enzo Doria	07/2013
1491	2^476888-2791229	143558	Enzo Doria	01/2016
1492	2^476868-1859939	143552	Enzo Doria	11/2015
1493	2^476558-113627	143459	Enzo Doria	08/2014
1494	2^476478-45	143435	Lelio R Paula	11/2017
1495	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1496	2^475813-113239	143234	Enzo Doria	07/2014
1497	2^475624-114059	143178	Enzo Doria	11/2014
1498	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1499	2^475480-2786129	143134	Enzo Doria	10/2015
1500	2^475299-111937	143080	Enzo Doria	05/2014

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Probable Primes Top 10000

(212140 PRPs in the top)