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	2^635926-1860611	191433	Enzo Doria	11/2015
1252	3*10^191152-7	191153	Robert Price	08/2015
1253	2^634883-1865677	191119	Enzo Doria	02/2016
1254	2^634801+1871957	191095	Enzo Doria	05/2016
1255	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
1256	9*10^191018-41	191019	Robert Price	08/2020
1257	2^634470-59861	190995	Enzo Doria	11/2015
1258	2^634368-29519	190964	Enzo Doria	08/2015
1259	2^634188-350609	190910	Enzo Doria	06/2015
1260	(65*10^190899+493)/9	190900	Robert Price	08/2021
1261	(62*10^190795-413)/9	190796	Robert Price	09/2021
1262	(26*10^190789-131)/3	190790	Robert Price	10/2019
1263	(13*10^190732-61)/3	190733	Robert Price	11/2018
1264	(7*10^190683+143)/3	190684	Robert Price	03/2018
1265	2^633088-113879	190579	Enzo Doria	10/2014
1266	2^633064+1874911	190572	Enzo Doria	06/2016
1267	(43*10^190547+83)/9	190548	Robert Price	11/2018
1268	99*10^190543+7	190545	Robert Price	05/2021
1269	(299*10^190533+1)/3	190535	Robert Price	04/2020
1270	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
1271	2^632795-351205	190491	Enzo Doria	06/2015
1272	(16*10^190420-19)/3	190421	Robert Price	02/2019
1273	(43*10^190351+101)/9	190352	Robert Price	11/2018
1274	2^632156+78391	190298	Enzo Doria	06/2016
1275	97*10^190295-3	190297	Robert Price	05/2020
1276	2^632082-1851971	190276	Enzo Doria	08/2015
1277	2^632020+1880311	190257	Enzo Doria	09/2016
1278	(5*10^190242-77)/9	190242	Robert Price	04/2021
1279	7*10^190210+13	190211	Robert Price	03/2021
1280	2^631637-462373	190142	Enzo Doria	08/2015
1281	2*10^190126-21	190127	Robert Price	09/2020
1282	(28*10^190105+191)/3	190106	Robert Price	02/2020
1283	2*10^190093+33	190094	Robert Price	11/2021
1284	(68*10^190053-113)/9	190054	Robert Price	03/2021
1285	2^631122-39251	189987	Enzo Doria	08/2015
1286	(26*10^189928-89)/9	189929	Robert Price	06/2018
1287	2^630839-97	189902	Yves Minet	07/2017
1288	99*10^189876-7	189878	Robert Price	07/2020
1289	2^630359+1788953	189757	Enzo Doria	05/2016
1290	2^630228+1871971	189718	Enzo Doria	05/2016
1291	2^630108+781	189682	Lelio R Paula	08/2013
1292	2^629870-1867811	189610	Enzo Doria	04/2016
1293	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
1294	2^629326+2792929	189447	Enzo Doria	02/2016
1295	4*10^189401+13	189402	Robert Price	02/2021
1296	(10^189385-61)/3	189385	Serge Batalov	12/2014
1297	2^629036+1874011	189359	Enzo Doria	06/2016
1298	2^628930+80779	189327	Enzo Doria	07/2016
1299	(134*10^189309-11)/3	189311	Robert Price	01/2022
1300	2^628582+1179439	189223	Enzo Doria	06/2016
1301	(44*10^188999-503)/9	189000	Robert Price	12/2018
1302	(16*10^188823+167)/3	188824	Robert Price	06/2019
1303	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
1304	2^627037-2785843	188757	Enzo Doria	10/2015
1305	(16*10^188457+161)/3	188458	Robert Price	02/2019
1306	L(901657)	188436	Renaud Lifchitz	11/2008
1307	2^625651+74213	188340	Enzo Doria	04/2016
1308	2^625584-460919	188320	Enzo Doria	06/2015
1309	(14*10^188218+139)/9	188219	Robert Price	11/2021
1310	(10^188164+359)/9	188164	Serge Batalov	12/2014
1311	2^624481-113611	187988	Enzo Doria	08/2014
1314	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
1312	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
1313	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
1315	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
1316	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
1317	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
1319	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
1318	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
1320	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
1321	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
1322	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
1323	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
1324	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
1326	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
1325	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
1327	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
1328	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
1329	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
1330	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
1331	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
1332	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
1333	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
1335	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
1334	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
1336	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
1337	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
1338	2^624077-112723	187866	Enzo Doria	07/2014
1339	2^624008+1874941	187846	Enzo Doria	06/2016
1340	2^623870+78679	187804	Enzo Doria	05/2016
1341	2^623714-114035	187757	Enzo Doria	11/2014
1342	2^623651-1834251	187738	Enzo Doria	07/2015
1343	(7*10^187645+53)/3	187646	Robert Price	05/2018
1344	2^623146+1879609	187586	Enzo Doria	09/2016
1345	(401*10^187512+13)/9	187514	Robert Price	09/2021
1346	(5*10^187471+91)/3	187472	Robert Price	04/2018
1347	2^622500+81931	187392	Enzo Doria	08/2016
1348	(13*10^187382-157)/9	187383	Robert Price	05/2021
1349	2^622300-1861739	187331	Enzo Doria	12/2015
1350	(38*10^187281+349)/9	187282	Robert Price	10/2018
1351	2^622052+76771	187257	Enzo Doria	05/2016
1352	2^622005-24091	187243	Enzo Doria	08/2013
1353	7*10^187205-57	187206	Robert Price	06/2020
1354	2^621879-351787	187205	Enzo Doria	07/2015
1355	(5*10^187168-53)/3	187169	Robert Price	09/2020
1356	(23*10^187164-143)/3	187165	Robert Price	12/2019
1357	2^621700+79411	187151	Enzo Doria	06/2016
1358	(7*10^187101+131)/3	187102	Robert Price	06/2020
1359	(2*10^187062-71)/3	187062	Robert Price	12/2017
1360	2^620929-113203	186919	Enzo Doria	07/2014
1361	10^186842+168223	186843	Patrick De Geest	07/2018
1362	10^186842-8001	186842	Robert Price	03/2018
1363	2^620347-1777	186744	Lelio R Paula	07/2013
1364	11^179143-4170	186559	Enzo Doria	12/2012
1365	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
1366	2*10^186517+33	186518	Robert Price	11/2021
1367	2^619297-2792353	186427	Enzo Doria	02/2016
1368	(49*10^186409+383)/9	186410	Robert Price	04/2019
1369	2^618940-460139	186320	Enzo Doria	06/2015
1370	2^618046+74179	186051	Enzo Doria	04/2016
1371	3*10^186019+11	186020	Robert Price	07/2018
1372	(16*10^185978-19)/3	185979	Robert Price	02/2019
1373	2*10^185930-3	185931	Robert Price	07/2015
1374	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
1375	4*10^185905+91	185906	Robert Price	08/2018
1376	(19*10^185873+131)/3	185874	Robert Price	06/2020
1377	(37*10^185811+377)/9	185812	Robert Price	11/2018
1378	2^617250+9385	185811	Lelio R Paula	07/2013
1379	2^617130+9	185775	Stefano Morozzi	05/2021
1380	39^116749+2	185756	Robert Price	04/2015
1381	2^616924-39719	185713	Enzo Doria	09/2015
1382	2^616712+1867621	185649	Enzo Doria	04/2016
1383	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
1384	8*10^185529-67	185530	Robert Price	08/2019
1385	4*10^185355+9	185356	Robert Price	05/2015
1386	(16*10^185347+89)/3	185348	Robert Price	03/2021
1387	2^615622+76639	185321	Enzo Doria	05/2016
1388	2^615591+1879223	185312	Enzo Doria	08/2016
1389	2^615503+1876643	185285	Enzo Doria	07/2016
1390	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
1391	(4*10^185221-91)/3	185222	Robert Price	03/2018
1392	(7*10^185221+131)/3	185222	Robert Price	06/2020
1393	(62*10^185216-413)/9	185217	Robert Price	09/2021
1394	(232*10^185180+17)/3	185182	Robert Price	04/2021
1395	56*10^185139-3	185141	Robert Price	03/2020
1396	(28*10^185105+47)/3	185106	Robert Price	02/2021
1397	2^614783-2790097	185069	Enzo Doria	12/2015
1398	2^614745-29323	185057	Enzo Doria	07/2015
1399	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
1400	(49*10^184993-67)/9	184994	Robert Price	03/2019
1401	(5*10^184954-191)/3	184955	Robert Price	05/2021
1402	(14*10^184950+211)/9	184951	Robert Price	04/2018
1403	2^614315+81353	184928	Enzo Doria	08/2016
1404	2^614294-1849961	184921	Enzo Doria	08/2015
1405	2^614266+1877809	184913	Enzo Doria	08/2016
1406	(185*10^184878-11)/3	184880	Robert Price	10/2020
1407	91*10^184867-9	184869	Robert Price	06/2021
1408	2^613715-1860727	184747	Enzo Doria	11/2015
1409	(4*10^184730+89)/3	184731	Robert Price	08/2021
1410	2*10^184723+41	184724	Robert Price	05/2018
1411	(49*10^184703+293)/9	184704	Robert Price	03/2021
1412	2^613487-349987	184678	Enzo Doria	07/2015
1413	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
1414	14^161089-161089^14	184629	Serge Batalov	05/2016
1415	2^613033-114621	184542	Enzo Doria	05/2015
1416	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
1417	2^612341-1604809	184334	Enzo Doria	05/2015
1418	(11*10^184308-161)/3	184309	Robert Price	11/2021
1419	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
1420	(14*10^184150+37)/3	184151	Robert Price	12/2018
1421	2^611731-4837	184150	Yves Minet	08/2018
1422	3*10^184124-7	184125	Robert Price	08/2015
1423	2^611628-24537	184119	Enzo Doria	08/2013
1424	3*10^184110+13	184111	Robert Price	07/2018
1425	(194*10^184093+1)/3	184095	Robert Price	01/2022
1426	2^611460+71881	184068	Enzo Doria	04/2016
1427	4*10^184004-63	184005	Robert Price	10/2018
1428	2^610982-1867301	183924	Enzo Doria	03/2016
1429	3*10^183872-49	183873	Robert Price	07/2018
1430	2^610597+1178897	183809	Enzo Doria	05/2016
1431	(8*10^183773-269)/9	183773	Robert Price	09/2021
1432	(65*10^183768-29)/9	183769	Robert Price	01/2021
1433	(17*10^183764+31)/3	183765	Robert Price	01/2019
1434	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1435	2^610401+1277	183750	Lelio R Paula	07/2013
1436	2^610356-1849019	183736	Enzo Doria	08/2015
1437	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1438	23*10^183710-7	183712	Robert Price	02/2020
1439	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1440	(4*10^183659+149)/9	183659	Robert Price	04/2018
1441	2^609846-1834251	183582	Enzo Doria	07/2015
1442	10^183546+1547323	183547	Patrick De Geest	02/2021
1444	10^183546-800000001	183546	Robert Price	09/2020
1443	10^183546-584297	183546	Patrick De Geest	02/2021
1445	(23*10^183477-71)/3	183478	Robert Price	07/2020
1446	11^176176-240	183469	Enzo Doria	11/2012
1447	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1448	6*10^183429+53	183430	Robert Price	05/2020
1449	(28*10^183403+191)/3	183404	Robert Price	02/2020
1450	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1451	2^608965-113989	183317	Enzo Doria	10/2014
1452	A005165(43592)	183312	Serge Batalov	07/2017
1453	(61*10^183294+119)/9	183295	Robert Price	05/2019
1454	2^608814-461261	183272	Enzo Doria	06/2015
1455	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1456	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1457	2^608293+143807	183115	Enzo Doria	10/2016
1458	2^608164-462419	183076	Enzo Doria	08/2015
1459	2^607950-1862303	183012	Enzo Doria	12/2015
1460	(46*10^182896+683)/9	182897	Robert Price	03/2019
1461	(2*10^182787+73)/3	182787	Robert Price	09/2020
1462	2^607101+1871987	182756	Enzo Doria	05/2016
1463	2^606869-69175	182686	Enzo Doria	11/2015
1464	(23*10^182666-71)/3	182667	Robert Price	07/2020
1465	3*10^182614-11	182615	Robert Price	07/2018
1466	2^606560-357	182593	Enzo Doria	05/2014
1467	66*10^182420+7	182422	Robert Price	07/2020
1468	2^605687+1866983	182330	Enzo Doria	03/2016
1469	2^605655-114445	182321	Enzo Doria	02/2015
1470	94*10^182291-3	182293	Robert Price	05/2020
1471	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1472	(14*10^182177-221)/9	182178	Robert Price	04/2018
1473	2^605174-112751	182176	Enzo Doria	06/2014
1474	2^604761+1874507	182052	Enzo Doria	06/2016
1475	2^604705+1871957	182035	Enzo Doria	05/2016
1476	(14*10^182000+229)/9	182001	Robert Price	03/2018
1477	(10^181996+41)/3	181996	Robert Price	12/2017
1478	(5*10^181950-101)/3	181951	Robert Price	04/2018
1479	2^603915+75233	181797	Enzo Doria	04/2016
1480	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
1481	7*10^181594-57	181595	Robert Price	06/2020
1482	8*10^181580+29	181581	Robert Price	11/2021
1483	(194*10^181369-11)/3	181371	Robert Price	09/2020
1484	11^174145-360	181354	Enzo Doria	10/2012
1485	2^602351-396765	181326	Enzo Doria	08/2013
1486	6*10^181306+17	181307	Robert Price	04/2019
1487	(286*10^181220-1)/3	181222	Robert Price	11/2020
1488	2^601957-113833	181208	Enzo Doria	09/2014
1489	66^99581-65^99581	181193	Robert Price	09/2013
1490	10^181182+383973	181183	Patrick De Geest	04/2016
1491	10^181182-21	181182	Serge Batalov	12/2014
1492	(5*10^181127-29)/3	181128	Robert Price	03/2018
1493	2^601521-29143	181076	Enzo Doria	07/2015
1494	2^601442-2797811	181053	Enzo Doria	04/2016
1495	44*10^181029+3	181031	Robert Price	04/2020
1496	5*10^180992-9	180993	Robert Price	05/2015
1497	10^180979+79477	180980	Patrick De Geest	04/2016
1498	10^180979+107739	180980	Patrick De Geest	04/2016
1499	10^180979-11	180979	Serge Batalov	12/2014
1500	2^601023-113851	180926	Enzo Doria	10/2014

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