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	33^129128+129128^33	196083	Norbert Schneider	06/2022
1252	6*10^196070+73	196071	Robert Price	04/2019
1253	2^651218-1868201	196037	Enzo Doria	04/2016
1254	2^651047-49687	195985	Enzo Doria	10/2015
1255	10^195968-700001	195968	Robert Price	08/2021
1256	(29*10^195875-197)/3	195876	Robert Price	08/2021
1257	(25*10^195808-97)/9	195809	Robert Price	01/2022
1258	2^650285-2785333	195756	Enzo Doria	10/2015
1259	(10^195732+7)/18089/49605893	195721	Alfred Reich	08/2021
1260	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
1261	2^649811+1877573	195613	Enzo Doria	08/2016
1262	2^649662-170531	195568	Hans Havermann	10/2018
1263	2^649586+182839	195545	Enzo Doria	11/2016
1264	2^649537-1867363	195531	Enzo Doria	04/2016
1265	2^649536-1861499	195530	Enzo Doria	12/2015
1266	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
1267	2^649102-59351	195400	Enzo Doria	10/2015
1268	(2*10^195399+529)/9	195399	Robert Price	01/2018
1269	(202*10^195383-13)/9	195385	Robert Price	01/2020
1270	2^648988+1178971	195365	Enzo Doria	06/2016
1271	2^648975-114319	195361	Enzo Doria	02/2015
1272	(11*10^195350-137)/9	195351	Robert Price	01/2018
1273	2^648619-24835	195254	Enzo Doria	09/2013
1274	5*10^195250-21	195251	Robert Price	12/2021
1275	(14*10^195234-83)/3	195235	Robert Price	12/2018
1276	5*10^195221+81	195222	Robert Price	03/2019
1277	10^195143-5001	195143	Robert Price	12/2021
1278	2^648190-24737	195125	Enzo Doria	09/2013
1279	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
1280	(29*10^195098-197)/3	195099	Robert Price	08/2021
1281	10^195060+89701	195061	Patrick De Geest	02/2021
1283	10^195060-40000000001	195060	Robert Price	09/2020
1282	10^195060-110337	195060	Patrick De Geest	02/2021
1284	56*10^195032-3	195034	Robert Price	03/2020
1285	11^187185-90	194934	Enzo Doria	09/2012
1286	(86*10^194818-437)/9	194819	Robert Price	03/2021
1287	2^647068+77281	194787	Enzo Doria	05/2016
1288	2*10^194716-93	194717	Robert Price	12/2021
1289	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
1290	F(931517)	194676	Henri Lifchitz	09/2008
1291	4*10^194668+49	194669	Robert Price	01/2019
1292	2^646589+1179407	194643	Enzo Doria	06/2016
1293	2^646289-114621	194553	Enzo Doria	05/2015
1294	2^646236-39659	194537	Enzo Doria	09/2015
1295	(16*10^194536+53)/3	194537	Robert Price	03/2019
1296	2^646161-59833	194514	Enzo Doria	11/2015
1297	(17*10^194502+31)/3	194503	Robert Price	01/2019
1298	(19*10^194428+287)/9	194429	Robert Price	10/2021
1299	2*10^194413+3	194414	Robert Price	07/2015
1300	2^645360-1848599	194273	Enzo Doria	08/2015
1301	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
1302	2*10^193981-43	193982	Robert Price	04/2018
1303	2^644382+75169	193979	Enzo Doria	04/2016
1304	2^644304-1861409	193955	Enzo Doria	11/2015
1305	(29*10^193950-23)/3	193951	Robert Price	03/2022
1306	5*10^193907-9	193908	Robert Price	05/2015
1307	2^644043+1876703	193877	Enzo Doria	07/2016
1308	2*10^193841-63	193842	Robert Price	01/2022
1309	2^643735+1879733	193784	Enzo Doria	09/2016
1310	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
1311	9*10^193712+71	193713	Robert Price	08/2020
1312	2^643216-286565	193628	Enzo Doria	07/2015
1313	10^193566+1126339	193567	Patrick De Geest	09/2022
1315	10^193566-10000000001	193566	Robert Price	04/2021
1314	10^193566-454041	193566	Patrick De Geest	08/2021
1316	2^642888-24965	193529	Enzo Doria	09/2013
1317	2^642448-114825	193397	Enzo Doria	05/2015
1318	2^642437-1856623	193393	Enzo Doria	10/2015
1319	2^642039-59797	193273	Enzo Doria	11/2015
1320	10^193230+513861	193231	Patrick De Geest	07/2018
1321	10^193230-8001	193230	Robert Price	03/2018
1322	(62*10^193225-233)/9	193226	Robert Price	02/2022
1323	2^641692-286349	193169	Enzo Doria	07/2015
1324	2^641690-24737	193168	Enzo Doria	09/2013
1325	2^641514+1876549	193115	Enzo Doria	07/2016
1326	2^640888-2785619	192927	Enzo Doria	10/2015
1327	2^640874-2783741	192923	Enzo Doria	09/2015
1328	10^192922+192207	192923	Patrick De Geest	08/2021
1329	10^192922-7001	192922	Robert Price	04/2021
1330	2^640854+25	192917	Stefano Morozzi	05/2021
1331	34*10^192868-9	192870	Robert Price	06/2020
1332	(46*10^192841+683)/9	192842	Robert Price	03/2019
1333	2^640181+467	192714	Lelio R Paula	08/2013
1334	2^639536-1850249	192520	Enzo Doria	08/2015
1335	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
1336	5*10^192422-43	192423	Robert Price	01/2019
1337	2^639110-2792441	192392	Enzo Doria	02/2016
1338	2^638955-29827	192345	Enzo Doria	08/2015
1339	2^638713-2784223	192272	Enzo Doria	10/2015
1340	(10^192216+7)/149	192214	Alfred Reich	07/2021
1341	2^638490-113507	192205	Enzo Doria	08/2014
1342	2^638189-39943	192115	Enzo Doria	09/2015
1343	2^638110+1877119	192091	Enzo Doria	07/2016
1344	2^638066-2785211	192078	Enzo Doria	10/2015
1345	(35*10^191973-341)/9	191974	Robert Price	08/2021
1346	(112*10^191900+17)/3	191902	Robert Price	03/2020
1347	2^637475-115309	191900	Enzo Doria	07/2015
1348	(68*10^191754-113)/9	191755	Robert Price	03/2021
1349	2^636930-11	191736	Stefano Morozzi	07/2022
1350	(47*10^191732+259)/9	191733	Robert Price	03/2022
1351	2^636661+1876577	191655	Enzo Doria	07/2016
1352	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
1353	2^636177-1855123	191509	Enzo Doria	09/2015
1354	2^636158-113627	191503	Enzo Doria	08/2014
1355	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
1356	2^636035+79823	191466	Enzo Doria	06/2016
1357	2^636011-1860847	191459	Enzo Doria	11/2015
1358	2^635926-1860611	191433	Enzo Doria	11/2015
1359	3*10^191152-7	191153	Robert Price	08/2015
1360	2^634883-1865677	191119	Enzo Doria	02/2016
1361	2^634801+1871957	191095	Enzo Doria	05/2016
1362	(77*10^191080+157)/9	191081	Robert Price	05/2022
1363	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
1364	9*10^191018-41	191019	Robert Price	08/2020
1365	2^634470-59861	190995	Enzo Doria	11/2015
1366	2^634368-29519	190964	Enzo Doria	08/2015
1367	2^634188-350609	190910	Enzo Doria	06/2015
1368	(65*10^190899+493)/9	190900	Robert Price	08/2021
1369	(62*10^190795-413)/9	190796	Robert Price	09/2021
1370	(26*10^190789-131)/3	190790	Robert Price	10/2019
1371	(13*10^190732-61)/3	190733	Robert Price	11/2018
1372	(7*10^190683+143)/3	190684	Robert Price	03/2018
1373	2^633088-113879	190579	Enzo Doria	10/2014
1374	2^633064+1874911	190572	Enzo Doria	06/2016
1375	(43*10^190547+83)/9	190548	Robert Price	11/2018
1376	99*10^190543+7	190545	Robert Price	05/2021
1377	(299*10^190533+1)/3	190535	Robert Price	04/2020
1378	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
1379	2^632815-15	190497	Stefano Morozzi	07/2022
1380	2^632795-351205	190491	Enzo Doria	06/2015
1381	(16*10^190420-19)/3	190421	Robert Price	02/2019
1382	(43*10^190351+101)/9	190352	Robert Price	11/2018
1383	2^632156+78391	190298	Enzo Doria	06/2016
1384	97*10^190295-3	190297	Robert Price	05/2020
1385	2^632082-1851971	190276	Enzo Doria	08/2015
1386	2^632020+1880311	190257	Enzo Doria	09/2016
1387	(5*10^190242-77)/9	190242	Robert Price	04/2021
1388	7*10^190210+13	190211	Robert Price	03/2021
1389	2^631637-462373	190142	Enzo Doria	08/2015
1390	2*10^190126-21	190127	Robert Price	09/2020
1391	(28*10^190105+191)/3	190106	Robert Price	02/2020
1392	2*10^190093+33	190094	Robert Price	11/2021
1393	(68*10^190053-113)/9	190054	Robert Price	03/2021
1394	2^631122-39251	189987	Enzo Doria	08/2015
1395	(26*10^189928-89)/9	189929	Robert Price	06/2018
1396	2^630839-97	189902	Yves Minet	07/2017
1397	99*10^189876-7	189878	Robert Price	07/2020
1398	2^630359+1788953	189757	Enzo Doria	05/2016
1399	2^630228+1871971	189718	Enzo Doria	05/2016
1400	2^630108+781	189682	Lelio R Paula	08/2013
1401	2^629870-1867811	189610	Enzo Doria	04/2016
1402	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
1403	2^629326+2792929	189447	Enzo Doria	02/2016
1404	4*10^189401+13	189402	Robert Price	02/2021
1405	(10^189385-61)/3	189385	Serge Batalov	12/2014
1406	2^629036+1874011	189359	Enzo Doria	06/2016
1407	2^628930+80779	189327	Enzo Doria	07/2016
1408	(134*10^189309-11)/3	189311	Robert Price	01/2022
1409	2^628582+1179439	189223	Enzo Doria	06/2016
1410	(44*10^188999-503)/9	189000	Robert Price	12/2018
1411	(16*10^188823+167)/3	188824	Robert Price	06/2019
1412	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
1413	2^627037-2785843	188757	Enzo Doria	10/2015
1414	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
1415	(16*10^188457+161)/3	188458	Robert Price	02/2019
1416	L(901657)	188436	Renaud Lifchitz	11/2008
1417	(19*10^188375+137)/3	188376	Robert Price	03/2022
1418	2^625651+74213	188340	Enzo Doria	04/2016
1419	2^625584-460919	188320	Enzo Doria	06/2015
1420	(14*10^188218+139)/9	188219	Robert Price	11/2021
1421	(10^188164+359)/9	188164	Serge Batalov	12/2014
1422	2^624481-113611	187988	Enzo Doria	08/2014
1423	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
1424	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
1425	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
1426	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
1427	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
1428	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
1430	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
1429	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
1431	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
1432	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
1433	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
1434	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
1435	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
1437	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
1436	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
1438	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
1439	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
1440	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
1441	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
1442	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
1443	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
1444	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
1446	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
1445	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
1447	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
1448	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
1449	2^624077-112723	187866	Enzo Doria	07/2014
1450	2^624008+1874941	187846	Enzo Doria	06/2016
1451	2^623870+78679	187804	Enzo Doria	05/2016
1452	2^623714-114035	187757	Enzo Doria	11/2014
1453	2^623651-1834251	187738	Enzo Doria	07/2015
1454	(7*10^187645+53)/3	187646	Robert Price	05/2018
1455	2^623146+1879609	187586	Enzo Doria	09/2016
1456	(401*10^187512+13)/9	187514	Robert Price	09/2021
1457	(5*10^187471+91)/3	187472	Robert Price	04/2018
1458	2^622500+81931	187392	Enzo Doria	08/2016
1459	(13*10^187382-157)/9	187383	Robert Price	05/2021
1460	2^622300-1861739	187331	Enzo Doria	12/2015
1461	(22*10^187317-91)/3	187318	Robert Price	02/2022
1462	(38*10^187281+349)/9	187282	Robert Price	10/2018
1463	2^622052+76771	187257	Enzo Doria	05/2016
1464	2^622005-24091	187243	Enzo Doria	08/2013
1465	7*10^187205-57	187206	Robert Price	06/2020
1466	2^621879-351787	187205	Enzo Doria	07/2015
1467	(5*10^187168-53)/3	187169	Robert Price	09/2020
1468	(23*10^187164-143)/3	187165	Robert Price	12/2019
1469	2^621700+79411	187151	Enzo Doria	06/2016
1470	(7*10^187101+131)/3	187102	Robert Price	06/2020
1471	(2*10^187062-71)/3	187062	Robert Price	12/2017
1472	2^620929-113203	186919	Enzo Doria	07/2014
1473	10^186842+168223	186843	Patrick De Geest	07/2018
1474	10^186842-8001	186842	Robert Price	03/2018
1475	2^620347-1777	186744	Lelio R Paula	07/2013
1476	(11*10^186659+133)/9	186660	Robert Price	04/2022
1477	11^179143-4170	186559	Enzo Doria	12/2012
1478	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
1479	2*10^186517+33	186518	Robert Price	11/2021
1480	2^619297-2792353	186427	Enzo Doria	02/2016
1481	(49*10^186409+383)/9	186410	Robert Price	04/2019
1482	2^618940-460139	186320	Enzo Doria	06/2015
1483	2^618046+74179	186051	Enzo Doria	04/2016
1484	3*10^186019+11	186020	Robert Price	07/2018
1485	(16*10^185978-19)/3	185979	Robert Price	02/2019
1486	2*10^185930-3	185931	Robert Price	07/2015
1487	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
1488	4*10^185905+91	185906	Robert Price	08/2018
1489	(34*10^185902-601)/9	185903	Robert Price	07/2022
1490	(19*10^185873+131)/3	185874	Robert Price	06/2020
1491	(37*10^185811+377)/9	185812	Robert Price	11/2018
1492	2^617250+9385	185811	Lelio R Paula	07/2013
1493	2^617130+9	185775	Stefano Morozzi	05/2021
1494	39^116749+2	185756	Robert Price	04/2015
1495	2^616924-39719	185713	Enzo Doria	09/2015
1496	2^616712+1867621	185649	Enzo Doria	04/2016
1497	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
1498	8*10^185529-67	185530	Robert Price	08/2019
1499	4*10^185355+9	185356	Robert Price	05/2015
1500	(16*10^185347+89)/3	185348	Robert Price	03/2021

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Probable Primes Top 10000

(291192 PRPs in the top)