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	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
1252	2^670213+282317	201755	Enzo Doria	09/2016
1253	2^670133+89	201731	Stefano Morozzi	05/2021
1254	2^669854-113501	201647	Enzo Doria	08/2014
1255	2^669718+81619	201606	Enzo Doria	08/2016
1256	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
1257	2^668938-1839821	201371	Enzo Doria	06/2015
1258	2^668492+1879303	201237	Enzo Doria	08/2016
1259	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
1260	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
1261	2^667894+1875589	201057	Enzo Doria	06/2016
1262	2^667569-1836559	200959	Enzo Doria	05/2015
1263	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
1264	2^666430+782569	200616	Enzo Doria	10/2016
1265	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
1266	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
1267	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
1268	numbpart(32235776596)	200002	Serge Batalov	04/2017
1269	(10^200001+149)/3	200001	Serge Batalov	12/2014
1270	10^200000+571791	200001	Patrick De Geest	08/2019
1271	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
1272	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
1273	10^200000-45557	200000	Patrick De Geest	08/2019
1274	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
1275	2593604092947240127723272^8192+2593604092947240127722755^8192	200000	Youcef Lemsafer	01/2023
1276	(2593604092947240127723019^8192+2593604092947240127723011^8192)/2	199999	Youcef Lemsafer	01/2023
1277	(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457	199994	Youcef Lemsafer	01/2023
1278	(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986	199989	Youcef Lemsafer	01/2023
1279	(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169	199986	Youcef Lemsafer	01/2023
1280	92*10^199980-9	199982	Robert Price	12/2021
1281	(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649	199977	Youcef Lemsafer	01/2023
1282	(85*10^199951-139)/9	199952	Robert Price	08/2021
1283	(10^199926+7)/29/373/2339	199919	Alfred Reich	08/2021
1284	23*10^199833-9	199835	Robert Price	10/2021
1285	(299*10^199801-17)/3	199803	Robert Price	04/2020
1286	6*10^199788+77	199789	Robert Price	06/2020
1287	(23*10^199615+37)/3	199616	Robert Price	02/2022
1288	(17*10^199607-167)/3	199608	Robert Price	05/2022
1289	2^663020-933075	199589	Paul Bourdelais	06/2021
1290	(14*10^199447+73)/3	199448	Robert Price	12/2018
1291	(2^662424-15)/7	199409	Stefano Morozzi	08/2022
1292	2^662103-29287	199313	Enzo Doria	08/2015
1293	(2*10^199283+457)/9	199283	Robert Price	01/2018
1294	(10^199248-19)/9	199248	Robert Price	01/2018
1295	(83*10^199213+529)/9	199214	Robert Price	12/2021
1296	(194*10^199146-17)/3	199148	Robert Price	09/2020
1297	(151*10^199003-1)/3	199005	Robert Price	03/2020
1298	9*10^198946-73	198947	Robert Price	01/2021
1299	45*10^198931-7	198933	Robert Price	07/2020
1300	2^660482-2891	198825	Yves Minet	05/2016
1301	2^659589-21	198557	Stefano Morozzi	07/2022
1302	2^659583+1879223	198555	Enzo Doria	08/2016
1303	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
1304	(49*10^198403+311)/9	198404	Robert Price	06/2019
1305	96*10^198376-7	198378	Robert Price	03/2021
1306	(10^198375+7)/59/1201/87589	198366	Alfred Reich	08/2021
1307	2^658828-29819	198327	Enzo Doria	08/2015
1308	2^658776-2791229	198312	Enzo Doria	01/2016
1309	(35*10^198294-377)/9	198295	Robert Price	07/2018
1310	(4*10^198268+137)/3	198269	Robert Price	03/2018
1311	2^658544-1854029	198242	Enzo Doria	09/2015
1312	(62*10^198229-233)/9	198230	Robert Price	02/2022
1313	(26*10^198200-41)/3	198201	Robert Price	02/2022
1314	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
1315	2*10^197959-37	197960	Robert Price	11/2021
1316	(232*10^197897+17)/3	197899	Robert Price	04/2021
1317	(4*10^197778+173)/3	197779	Robert Price	02/2018
1318	78*10^197702-7	197704	Robert Price	10/2020
1319	(17*10^197640-23)/3	197641	Robert Price	03/2021
1320	(29*10^197629-77)/3	197630	Robert Price	02/2020
1321	2^656462+1874419	197615	Enzo Doria	06/2016
1322	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
1323	2^655893-344563	197444	Enzo Doria	07/2015
1324	2^655875+71333	197439	Enzo Doria	04/2016
1325	2^655845-9	197430	Robert Price	01/2017
1326	(299*10^197426+1)/3	197428	Robert Price	04/2020
1327	2^655682-1849121	197380	Enzo Doria	08/2015
1328	4*10^197268-89	197269	Robert Price	11/2018
1329	(11*10^197198-89)/3	197199	Robert Price	05/2021
1330	2^655045-49603	197189	Enzo Doria	10/2015
1331	2^655000-2784089	197175	Enzo Doria	10/2015
1332	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
1333	(4*10^197061+41)/9	197061	Serge Batalov	11/2022
1334	(154*10^197005+17)/9	197007	Robert Price	06/2022
1335	2^654400-39719	196995	Enzo Doria	09/2015
1336	(14*10^196965-221)/9	196966	Robert Price	04/2018
1337	2^654216-459995	196939	Enzo Doria	06/2015
1338	(17*10^196921+31)/3	196922	Robert Price	01/2019
1339	(14*10^196885-89)/3	196886	Robert Price	05/2020
1340	3*10^196881-59	196882	Robert Price	09/2018
1341	2^653851+82295	196829	Enzo Doria	09/2016
1342	(38*10^196792+691)/9	196793	Robert Price	10/2018
1343	(65*10^196768+493)/9	196769	Robert Price	08/2021
1345	2^653636-29429	196765	Enzo Doria	08/2015
1344	2^653638-11	196765	Stefano Morozzi	07/2022
1346	2^653601-69673	196754	Enzo Doria	02/2016
1347	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
1348	2^652786-1852571	196509	Enzo Doria	08/2015
1349	2^652752-1325	196498	Yves Minet	07/2015
1350	2^652470-1859141	196414	Enzo Doria	10/2015
1351	2^652307+1877483	196364	Enzo Doria	08/2016
1352	2^652293-115273	196360	Enzo Doria	06/2015
1353	(47*10^196281+403)/9	196282	Robert Price	03/2019
1354	(7*10^196125-31)/3	196126	Robert Price	12/2021
1355	33^129128+129128^33	196083	Norbert Schneider	06/2022
1356	6*10^196070+73	196071	Robert Price	04/2019
1357	2^651218-1868201	196037	Enzo Doria	04/2016
1358	2^651047-49687	195985	Enzo Doria	10/2015
1359	10^195968-700001	195968	Robert Price	08/2021
1360	(29*10^195875-197)/3	195876	Robert Price	08/2021
1361	(25*10^195808-97)/9	195809	Robert Price	01/2022
1362	2^650285-2785333	195756	Enzo Doria	10/2015
1363	(10^195732+7)/18089/49605893	195721	Alfred Reich	08/2021
1364	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
1365	2^649811+1877573	195613	Enzo Doria	08/2016
1366	2^649662-170531	195568	Hans Havermann	10/2018
1367	2^649586+182839	195545	Enzo Doria	11/2016
1368	2^649537-1867363	195531	Enzo Doria	04/2016
1369	2^649536-1861499	195530	Enzo Doria	12/2015
1370	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
1371	2^649102-59351	195400	Enzo Doria	10/2015
1372	(2*10^195399+529)/9	195399	Robert Price	01/2018
1373	(202*10^195383-13)/9	195385	Robert Price	01/2020
1374	2^648988+1178971	195365	Enzo Doria	06/2016
1375	2^648975-114319	195361	Enzo Doria	02/2015
1376	(11*10^195350-137)/9	195351	Robert Price	01/2018
1377	2^648619-24835	195254	Enzo Doria	09/2013
1378	5*10^195250-21	195251	Robert Price	12/2021
1379	(14*10^195234-83)/3	195235	Robert Price	12/2018
1380	5*10^195221+81	195222	Robert Price	03/2019
1381	10^195143-5001	195143	Robert Price	12/2021
1382	2^648190-24737	195125	Enzo Doria	09/2013
1383	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
1384	(29*10^195098-197)/3	195099	Robert Price	08/2021
1385	10^195060+89701	195061	Patrick De Geest	02/2021
1387	10^195060-40000000001	195060	Robert Price	09/2020
1386	10^195060-110337	195060	Patrick De Geest	02/2021
1388	56*10^195032-3	195034	Robert Price	03/2020
1389	11^187185-90	194934	Enzo Doria	09/2012
1390	(86*10^194818-437)/9	194819	Robert Price	03/2021
1391	2^647068+77281	194787	Enzo Doria	05/2016
1392	2*10^194716-93	194717	Robert Price	12/2021
1393	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
1394	F(931517)	194676	Henri Lifchitz	09/2008
1395	4*10^194668+49	194669	Robert Price	01/2019
1396	2^646589+1179407	194643	Enzo Doria	06/2016
1397	2^646289-114621	194553	Enzo Doria	05/2015
1398	2^646236-39659	194537	Enzo Doria	09/2015
1399	(16*10^194536+53)/3	194537	Robert Price	03/2019
1400	2^646161-59833	194514	Enzo Doria	11/2015
1401	(17*10^194502+31)/3	194503	Robert Price	01/2019
1402	(19*10^194428+287)/9	194429	Robert Price	10/2021
1403	2*10^194413+3	194414	Robert Price	07/2015
1404	2^645360-1848599	194273	Enzo Doria	08/2015
1405	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
1406	2*10^193981-43	193982	Robert Price	04/2018
1407	2^644382+75169	193979	Enzo Doria	04/2016
1408	2^644304-1861409	193955	Enzo Doria	11/2015
1409	(29*10^193950-23)/3	193951	Robert Price	03/2022
1410	5*10^193907-9	193908	Robert Price	05/2015
1411	2^644043+1876703	193877	Enzo Doria	07/2016
1412	2*10^193841-63	193842	Robert Price	01/2022
1413	2^643735+1879733	193784	Enzo Doria	09/2016
1414	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
1415	9*10^193712+71	193713	Robert Price	08/2020
1416	2^643216-286565	193628	Enzo Doria	07/2015
1417	10^193566+1126339	193567	Patrick De Geest	09/2022
1419	10^193566-10000000001	193566	Robert Price	04/2021
1418	10^193566-454041	193566	Patrick De Geest	08/2021
1420	2^642888-24965	193529	Enzo Doria	09/2013
1421	2^642448-114825	193397	Enzo Doria	05/2015
1422	2^642437-1856623	193393	Enzo Doria	10/2015
1423	2^642039-59797	193273	Enzo Doria	11/2015
1424	10^193230+513861	193231	Patrick De Geest	07/2018
1425	10^193230-8001	193230	Robert Price	03/2018
1426	(62*10^193225-233)/9	193226	Robert Price	02/2022
1427	2^641692-286349	193169	Enzo Doria	07/2015
1428	2^641690-24737	193168	Enzo Doria	09/2013
1429	2^641514+1876549	193115	Enzo Doria	07/2016
1430	2^640888-2785619	192927	Enzo Doria	10/2015
1431	2^640874-2783741	192923	Enzo Doria	09/2015
1432	10^192922+192207	192923	Patrick De Geest	08/2021
1433	10^192922-7001	192922	Robert Price	04/2021
1434	2^640854+25	192917	Stefano Morozzi	05/2021
1435	34*10^192868-9	192870	Robert Price	06/2020
1436	(46*10^192841+683)/9	192842	Robert Price	03/2019
1437	2^640181+467	192714	Lelio R Paula	08/2013
1438	2^639536-1850249	192520	Enzo Doria	08/2015
1439	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
1440	5*10^192422-43	192423	Robert Price	01/2019
1441	2^639110-2792441	192392	Enzo Doria	02/2016
1442	2^638955-29827	192345	Enzo Doria	08/2015
1443	2^638713-2784223	192272	Enzo Doria	10/2015
1444	(10^192216+7)/149	192214	Alfred Reich	07/2021
1445	2^638490-113507	192205	Enzo Doria	08/2014
1446	2^638189-39943	192115	Enzo Doria	09/2015
1447	2^638110+1877119	192091	Enzo Doria	07/2016
1448	2^638066-2785211	192078	Enzo Doria	10/2015
1449	(35*10^191973-341)/9	191974	Robert Price	08/2021
1450	(112*10^191900+17)/3	191902	Robert Price	03/2020
1451	2^637475-115309	191900	Enzo Doria	07/2015
1452	(68*10^191754-113)/9	191755	Robert Price	03/2021
1453	2^636930-11	191736	Stefano Morozzi	07/2022
1454	(47*10^191732+259)/9	191733	Robert Price	03/2022
1455	2^636661+1876577	191655	Enzo Doria	07/2016
1456	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
1457	2^636177-1855123	191509	Enzo Doria	09/2015
1458	2^636158-113627	191503	Enzo Doria	08/2014
1459	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
1460	2^636035+79823	191466	Enzo Doria	06/2016
1461	2^636011-1860847	191459	Enzo Doria	11/2015
1462	2^635926-1860611	191433	Enzo Doria	11/2015
1463	3*10^191152-7	191153	Robert Price	08/2015
1464	2^634883-1865677	191119	Enzo Doria	02/2016
1465	2^634801+1871957	191095	Enzo Doria	05/2016
1466	(77*10^191080+157)/9	191081	Robert Price	05/2022
1467	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
1468	9*10^191018-41	191019	Robert Price	08/2020
1469	2^634470-59861	190995	Enzo Doria	11/2015
1470	2^634368-29519	190964	Enzo Doria	08/2015
1471	2^634188-350609	190910	Enzo Doria	06/2015
1472	(65*10^190899+493)/9	190900	Robert Price	08/2021
1473	(62*10^190795-413)/9	190796	Robert Price	09/2021
1474	(26*10^190789-131)/3	190790	Robert Price	10/2019
1475	(13*10^190732-61)/3	190733	Robert Price	11/2018
1476	(7*10^190683+143)/3	190684	Robert Price	03/2018
1477	2^633088-113879	190579	Enzo Doria	10/2014
1478	2^633064+1874911	190572	Enzo Doria	06/2016
1479	(43*10^190547+83)/9	190548	Robert Price	11/2018
1480	99*10^190543+7	190545	Robert Price	05/2021
1481	(299*10^190533+1)/3	190535	Robert Price	04/2020
1482	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
1483	2^632815-15	190497	Stefano Morozzi	07/2022
1484	2^632795-351205	190491	Enzo Doria	06/2015
1485	(16*10^190420-19)/3	190421	Robert Price	02/2019
1486	(43*10^190351+101)/9	190352	Robert Price	11/2018
1487	2^632156+78391	190298	Enzo Doria	06/2016
1488	97*10^190295-3	190297	Robert Price	05/2020
1489	2^632082-1851971	190276	Enzo Doria	08/2015
1490	2^632020+1880311	190257	Enzo Doria	09/2016
1491	(5*10^190242-77)/9	190242	Robert Price	04/2021
1492	7*10^190210+13	190211	Robert Price	03/2021
1493	2^631637-462373	190142	Enzo Doria	08/2015
1494	2*10^190126-21	190127	Robert Price	09/2020
1495	(28*10^190105+191)/3	190106	Robert Price	02/2020
1496	2*10^190093+33	190094	Robert Price	11/2021
1497	(68*10^190053-113)/9	190054	Robert Price	03/2021
1498	2^631122-39251	189987	Enzo Doria	08/2015
1499	(26*10^189928-89)/9	189929	Robert Price	06/2018
1500	2^630839-97	189902	Yves Minet	07/2017

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Probable Primes Top 10000

(291910 PRPs in the top)