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	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
1252	11^202357-1140	210734	Enzo Doria	12/2012
1253	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
1254	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
1255	2^699740+25	210643	Stefano Morozzi	05/2021
1256	2^698929-2788423	210399	Enzo Doria	11/2015
1257	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
1258	2^698316+1878601	210215	Enzo Doria	08/2016
1259	34*10^210097-9	210099	Robert Price	05/2023
1260	6*10^209846-91	209847	Robert Price	05/2023
1261	2^697036+1878751	209829	Enzo Doria	08/2016
1262	6^269407+5	209640	Paul Bourdelais	02/2021
1263	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
1264	2^696254-115151	209594	Enzo Doria	06/2015
1265	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
1266	7*10^209161+39	209162	Robert Price	01/2023
1267	2^694633+1887257	209106	Enzo Doria	05/2017
1268	2^693959+180923	208903	Enzo Doria	07/2016
1269	(2^693747-11)/3	208839	Stefano Morozzi	08/2022
1270	2^693462-1847561	208753	Enzo Doria	07/2015
1271	2^690890-59981	207979	Enzo Doria	11/2015
1272	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
1273	2^690163+1877063	207760	Enzo Doria	07/2016
1274	7^245608-2	207563	Paul Bourdelais	01/2021
1275	(67*10^207556+23)/9	207557	Serge Batalov	01/2023
1276	2^689286-29381	207496	Enzo Doria	08/2015
1277	2^689122-114521	207447	Enzo Doria	04/2015
1278	9*10^207254-89	207255	Robert Price	02/2023
1279	2^688373+6077	207221	Enzo Doria	02/2016
1280	2^688201+1875527	207170	Enzo Doria	07/2016
1281	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
1282	2^687619+81563	206994	Enzo Doria	08/2016
1283	2^686572-1845299	206679	Enzo Doria	07/2015
1284	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
1285	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
1286	2^685578+3	206380	Paul Bourdelais	04/2012
1287	2^684836-49349	206157	Enzo Doria	10/2015
1288	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
1289	2^684163-2790967	205954	Enzo Doria	12/2015
1290	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
1291	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
1292	(68*10^205510+13)/9	205511	Serge Batalov	01/2023
1293	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
1294	2^681545+467	205166	Lelio R Paula	11/2013
1295	2^681306+81049	205094	Enzo Doria	07/2016
1296	2^680697+1877057	204911	Enzo Doria	07/2016
1297	2^680415+71783	204826	Enzo Doria	04/2016
1298	10^204764-8001	204764	Robert Price	03/2023
1299	(26*10^204730-77)/3	204731	Robert Price	03/2023
1300	2^679860-459995	204659	Enzo Doria	06/2015
1301	2^679593+1879547	204578	Enzo Doria	09/2016
1302	2^678651+1875023	204295	Enzo Doria	07/2016
1303	2^678561+678561	204268	Henri Lifchitz	05/2006
1304	2^678101-114043	204129	Enzo Doria	11/2014
1305	2^678028+1875631	204107	Enzo Doria	06/2016
1306	2^676992-59783	203795	Enzo Doria	10/2015
1307	2^676972+1866871	203789	Enzo Doria	03/2016
1308	2^676761-9	203726	Robert Price	01/2017
1309	2^676592-23	203675	Stefano Morozzi	07/2022
1310	2^676563-2792407	203666	Enzo Doria	02/2016
1311	2^676306-114713	203589	Enzo Doria	04/2015
1312	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
1313	10247^50678-50678^10247	203250	Norbert Schneider	03/2022
1314	2^674627-25161	203083	Enzo Doria	09/2013
1315	2^674603-69337	203076	Enzo Doria	12/2015
1316	2^674459+74213	203033	Enzo Doria	04/2016
1317	2^674116-458879	202930	Enzo Doria	04/2015
1318	2^674076-114755	202918	Enzo Doria	04/2015
1319	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
1320	(2^673184-7)/3	202649	Stefano Morozzi	08/2022
1321	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
1322	2^672556-1835519	202460	Enzo Doria	04/2015
1323	(7*10^202267+179)/3	202268	Robert Price	02/2023
1324	2^671446-351401	202126	Enzo Doria	07/2015
1325	2^671373+77747	202104	Enzo Doria	05/2016
1326	(2*10^202059+7)/9	202059	Rytis Slatkevicius	01/2023
1327	98*10^202021-9	202023	Robert Price	05/2023
1328	2^670726-114845	201909	Enzo Doria	05/2015
1329	2^670539-25045	201853	Enzo Doria	09/2013
1330	10^201801-93	201801	Robert Price	02/2023
1331	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
1332	2^670213+282317	201755	Enzo Doria	09/2016
1333	2^670133+89	201731	Stefano Morozzi	05/2021
1334	2^669854-113501	201647	Enzo Doria	08/2014
1335	2^669718+81619	201606	Enzo Doria	08/2016
1336	(299*10^201547-17)/3	201549	Robert Price	02/2023
1337	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
1338	2^668938-1839821	201371	Enzo Doria	06/2015
1339	2^668492+1879303	201237	Enzo Doria	08/2016
1340	7*10^201140-87	201141	Robert Price	03/2023
1341	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
1342	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
1343	2^667894+1875589	201057	Enzo Doria	06/2016
1344	2^667569-1836559	200959	Enzo Doria	05/2015
1345	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
1346	2^666430+782569	200616	Enzo Doria	10/2016
1347	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
1348	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
1349	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
1350	numbpart(32235776596)	200002	Serge Batalov	04/2017
1351	(10^200001+149)/3	200001	Serge Batalov	12/2014
1352	10^200000+571791	200001	Patrick De Geest	08/2019
1353	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
1354	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
1355	10^200000-45557	200000	Patrick De Geest	08/2019
1357	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
1356	2593604092947240127723272^8192+2593604092947240127722755^8192	200000	Youcef Lemsafer	01/2023
1358	(2593604092947240127723019^8192+2593604092947240127723011^8192)/2	199999	Youcef Lemsafer	01/2023
1359	(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457	199994	Youcef Lemsafer	01/2023
1360	(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986	199989	Youcef Lemsafer	01/2023
1361	(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169	199986	Youcef Lemsafer	01/2023
1362	92*10^199980-9	199982	Robert Price	12/2021
1363	(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649	199977	Youcef Lemsafer	01/2023
1364	(85*10^199951-139)/9	199952	Robert Price	08/2021
1365	(10^199926+7)/29/373/2339	199919	Alfred Reich	08/2021
1366	23*10^199833-9	199835	Robert Price	10/2021
1367	(299*10^199801-17)/3	199803	Robert Price	04/2020
1368	6*10^199788+77	199789	Robert Price	06/2020
1369	(23*10^199615+37)/3	199616	Robert Price	02/2022
1370	(17*10^199607-167)/3	199608	Robert Price	05/2022
1371	2^663020-933075	199589	Paul Bourdelais	06/2021
1372	(14*10^199447+73)/3	199448	Robert Price	12/2018
1373	(2^662424-15)/7	199409	Stefano Morozzi	08/2022
1374	2^662103-29287	199313	Enzo Doria	08/2015
1375	(2*10^199283+457)/9	199283	Robert Price	01/2018
1376	(10^199248-19)/9	199248	Robert Price	01/2018
1377	(83*10^199213+529)/9	199214	Robert Price	12/2021
1378	(194*10^199146-17)/3	199148	Robert Price	09/2020
1379	(151*10^199003-1)/3	199005	Robert Price	03/2020
1380	9*10^198946-73	198947	Robert Price	01/2021
1381	45*10^198931-7	198933	Robert Price	07/2020
1382	2^660482-2891	198825	Yves Minet	05/2016
1383	2^659589-21	198557	Stefano Morozzi	07/2022
1384	2^659583+1879223	198555	Enzo Doria	08/2016
1385	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
1386	(49*10^198403+311)/9	198404	Robert Price	06/2019
1387	96*10^198376-7	198378	Robert Price	03/2021
1388	(10^198375+7)/59/1201/87589	198366	Alfred Reich	08/2021
1389	2^658828-29819	198327	Enzo Doria	08/2015
1390	2^658776-2791229	198312	Enzo Doria	01/2016
1391	(35*10^198294-377)/9	198295	Robert Price	07/2018
1392	(4*10^198268+137)/3	198269	Robert Price	03/2018
1393	2^658544-1854029	198242	Enzo Doria	09/2015
1394	(62*10^198229-233)/9	198230	Robert Price	02/2022
1395	(26*10^198200-41)/3	198201	Robert Price	02/2022
1396	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
1397	2*10^197959-37	197960	Robert Price	11/2021
1398	(232*10^197897+17)/3	197899	Robert Price	04/2021
1399	(4*10^197778+173)/3	197779	Robert Price	02/2018
1400	78*10^197702-7	197704	Robert Price	10/2020
1401	(17*10^197640-23)/3	197641	Robert Price	03/2021
1402	(29*10^197629-77)/3	197630	Robert Price	02/2020
1403	2^656462+1874419	197615	Enzo Doria	06/2016
1404	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
1405	2^655893-344563	197444	Enzo Doria	07/2015
1406	2^655875+71333	197439	Enzo Doria	04/2016
1407	2^655845-9	197430	Robert Price	01/2017
1408	(299*10^197426+1)/3	197428	Robert Price	04/2020
1409	2^655682-1849121	197380	Enzo Doria	08/2015
1410	4*10^197268-89	197269	Robert Price	11/2018
1411	(11*10^197198-89)/3	197199	Robert Price	05/2021
1412	2^655045-49603	197189	Enzo Doria	10/2015
1413	2^655000-2784089	197175	Enzo Doria	10/2015
1414	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
1415	(4*10^197061+41)/9	197061	Serge Batalov	11/2022
1416	(154*10^197005+17)/9	197007	Robert Price	06/2022
1417	2^654400-39719	196995	Enzo Doria	09/2015
1418	(14*10^196965-221)/9	196966	Robert Price	04/2018
1419	2^654216-459995	196939	Enzo Doria	06/2015
1420	(17*10^196921+31)/3	196922	Robert Price	01/2019
1421	(14*10^196885-89)/3	196886	Robert Price	05/2020
1422	3*10^196881-59	196882	Robert Price	09/2018
1423	2^653851+82295	196829	Enzo Doria	09/2016
1424	(38*10^196792+691)/9	196793	Robert Price	10/2018
1425	(65*10^196768+493)/9	196769	Robert Price	08/2021
1427	2^653636-29429	196765	Enzo Doria	08/2015
1426	2^653638-11	196765	Stefano Morozzi	07/2022
1428	2^653601-69673	196754	Enzo Doria	02/2016
1429	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
1430	2^652786-1852571	196509	Enzo Doria	08/2015
1431	2^652752-1325	196498	Yves Minet	07/2015
1432	2^652470-1859141	196414	Enzo Doria	10/2015
1433	2^652307+1877483	196364	Enzo Doria	08/2016
1434	2^652293-115273	196360	Enzo Doria	06/2015
1435	(47*10^196281+403)/9	196282	Robert Price	03/2019
1436	(7*10^196125-31)/3	196126	Robert Price	12/2021
1437	33^129128+129128^33	196083	Norbert Schneider	06/2022
1438	6*10^196070+73	196071	Robert Price	04/2019
1439	2^651218-1868201	196037	Enzo Doria	04/2016
1440	2^651047-49687	195985	Enzo Doria	10/2015
1441	10^195968-700001	195968	Robert Price	08/2021
1442	(29*10^195875-197)/3	195876	Robert Price	08/2021
1443	(25*10^195808-97)/9	195809	Robert Price	01/2022
1444	2^650285-2785333	195756	Enzo Doria	10/2015
1445	(10^195732+7)/18089/49605893	195721	Alfred Reich	08/2021
1446	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
1447	2^649811+1877573	195613	Enzo Doria	08/2016
1448	2^649662-170531	195568	Hans Havermann	10/2018
1449	2^649586+182839	195545	Enzo Doria	11/2016
1450	2^649537-1867363	195531	Enzo Doria	04/2016
1451	2^649536-1861499	195530	Enzo Doria	12/2015
1452	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
1453	2^649102-59351	195400	Enzo Doria	10/2015
1454	(2*10^195399+529)/9	195399	Robert Price	01/2018
1455	(202*10^195383-13)/9	195385	Robert Price	01/2020
1456	2^648988+1178971	195365	Enzo Doria	06/2016
1457	2^648975-114319	195361	Enzo Doria	02/2015
1458	(11*10^195350-137)/9	195351	Robert Price	01/2018
1459	2^648619-24835	195254	Enzo Doria	09/2013
1460	5*10^195250-21	195251	Robert Price	12/2021
1461	(14*10^195234-83)/3	195235	Robert Price	12/2018
1462	5*10^195221+81	195222	Robert Price	03/2019
1463	10^195143-5001	195143	Robert Price	12/2021
1464	2^648190-24737	195125	Enzo Doria	09/2013
1465	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
1466	(29*10^195098-197)/3	195099	Robert Price	08/2021
1467	10^195060+89701	195061	Patrick De Geest	02/2021
1469	10^195060-40000000001	195060	Robert Price	09/2020
1468	10^195060-110337	195060	Patrick De Geest	02/2021
1470	56*10^195032-3	195034	Robert Price	03/2020
1471	11^187185-90	194934	Enzo Doria	09/2012
1472	(86*10^194818-437)/9	194819	Robert Price	03/2021
1473	2^647068+77281	194787	Enzo Doria	05/2016
1474	2*10^194716-93	194717	Robert Price	12/2021
1475	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
1476	F(931517)	194676	Henri Lifchitz	09/2008
1477	4*10^194668+49	194669	Robert Price	01/2019
1478	2^646589+1179407	194643	Enzo Doria	06/2016
1479	2^646289-114621	194553	Enzo Doria	05/2015
1480	2^646236-39659	194537	Enzo Doria	09/2015
1481	(16*10^194536+53)/3	194537	Robert Price	03/2019
1482	2^646161-59833	194514	Enzo Doria	11/2015
1483	(17*10^194502+31)/3	194503	Robert Price	01/2019
1484	(19*10^194428+287)/9	194429	Robert Price	10/2021
1485	2*10^194413+3	194414	Robert Price	07/2015
1486	2^645360-1848599	194273	Enzo Doria	08/2015
1487	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
1488	2*10^193981-43	193982	Robert Price	04/2018
1489	2^644382+75169	193979	Enzo Doria	04/2016
1490	2^644304-1861409	193955	Enzo Doria	11/2015
1491	(29*10^193950-23)/3	193951	Robert Price	03/2022
1492	5*10^193907-9	193908	Robert Price	05/2015
1493	2^644043+1876703	193877	Enzo Doria	07/2016
1494	2*10^193841-63	193842	Robert Price	01/2022
1495	2^643735+1879733	193784	Enzo Doria	09/2016
1496	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
1497	9*10^193712+71	193713	Robert Price	08/2020
1498	2^643216-286565	193628	Enzo Doria	07/2015
1499	10^193566+1126339	193567	Patrick De Geest	09/2022
1500	10^193566-454041	193566	Patrick De Geest	08/2021

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