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	7*10^190210+13	190211	Robert Price	03/2021
1252	2^631637-462373	190142	Enzo Doria	08/2015
1253	2*10^190126-21	190127	Robert Price	09/2020
1254	(28*10^190105+191)/3	190106	Robert Price	02/2020
1255	2*10^190093+33	190094	Robert Price	11/2021
1256	(68*10^190053-113)/9	190054	Robert Price	03/2021
1257	2^631122-39251	189987	Enzo Doria	08/2015
1258	(26*10^189928-89)/9	189929	Robert Price	06/2018
1259	2^630839-97	189902	Yves Minet	07/2017
1260	99*10^189876-7	189878	Robert Price	07/2020
1261	2^630359+1788953	189757	Enzo Doria	05/2016
1262	2^630228+1871971	189718	Enzo Doria	05/2016
1263	2^630108+781	189682	Lelio R Paula	08/2013
1264	2^629870-1867811	189610	Enzo Doria	04/2016
1265	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
1266	2^629326+2792929	189447	Enzo Doria	02/2016
1267	4*10^189401+13	189402	Robert Price	02/2021
1268	(10^189385-61)/3	189385	Serge Batalov	12/2014
1269	2^629036+1874011	189359	Enzo Doria	06/2016
1270	2^628930+80779	189327	Enzo Doria	07/2016
1271	2^628582+1179439	189223	Enzo Doria	06/2016
1272	(44*10^188999-503)/9	189000	Robert Price	12/2018
1273	(16*10^188823+167)/3	188824	Robert Price	06/2019
1274	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
1275	2^627037-2785843	188757	Enzo Doria	10/2015
1276	(16*10^188457+161)/3	188458	Robert Price	02/2019
1277	L(901657)	188436	Renaud Lifchitz	11/2008
1278	2^625651+74213	188340	Enzo Doria	04/2016
1279	2^625584-460919	188320	Enzo Doria	06/2015
1280	(14*10^188218+139)/9	188219	Robert Price	11/2021
1281	(10^188164+359)/9	188164	Serge Batalov	12/2014
1282	2^624481-113611	187988	Enzo Doria	08/2014
1283	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
1284	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
1285	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
1286	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
1287	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
1288	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
1290	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
1289	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
1291	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
1292	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
1293	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
1294	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
1295	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
1297	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
1296	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
1298	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
1299	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
1300	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
1301	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
1302	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
1303	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
1304	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
1306	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
1305	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
1307	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
1308	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
1309	2^624077-112723	187866	Enzo Doria	07/2014
1310	2^624008+1874941	187846	Enzo Doria	06/2016
1311	2^623870+78679	187804	Enzo Doria	05/2016
1312	2^623714-114035	187757	Enzo Doria	11/2014
1313	2^623651-1834251	187738	Enzo Doria	07/2015
1314	(7*10^187645+53)/3	187646	Robert Price	05/2018
1315	2^623146+1879609	187586	Enzo Doria	09/2016
1316	(401*10^187512+13)/9	187514	Robert Price	09/2021
1317	(5*10^187471+91)/3	187472	Robert Price	04/2018
1318	2^622500+81931	187392	Enzo Doria	08/2016
1319	(13*10^187382-157)/9	187383	Robert Price	05/2021
1320	2^622300-1861739	187331	Enzo Doria	12/2015
1321	(38*10^187281+349)/9	187282	Robert Price	10/2018
1322	2^622052+76771	187257	Enzo Doria	05/2016
1323	2^622005-24091	187243	Enzo Doria	08/2013
1324	7*10^187205-57	187206	Robert Price	06/2020
1325	2^621879-351787	187205	Enzo Doria	07/2015
1326	(5*10^187168-53)/3	187169	Robert Price	09/2020
1327	(23*10^187164-143)/3	187165	Robert Price	12/2019
1328	2^621700+79411	187151	Enzo Doria	06/2016
1329	(7*10^187101+131)/3	187102	Robert Price	06/2020
1330	(2*10^187062-71)/3	187062	Robert Price	12/2017
1331	2^620929-113203	186919	Enzo Doria	07/2014
1332	10^186842+168223	186843	Patrick De Geest	07/2018
1333	10^186842-8001	186842	Robert Price	03/2018
1334	2^620347-1777	186744	Lelio R Paula	07/2013
1335	11^179143-4170	186559	Enzo Doria	12/2012
1336	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
1337	2*10^186517+33	186518	Robert Price	11/2021
1338	2^619297-2792353	186427	Enzo Doria	02/2016
1339	(49*10^186409+383)/9	186410	Robert Price	04/2019
1340	2^618940-460139	186320	Enzo Doria	06/2015
1341	2^618046+74179	186051	Enzo Doria	04/2016
1342	3*10^186019+11	186020	Robert Price	07/2018
1343	(16*10^185978-19)/3	185979	Robert Price	02/2019
1344	2*10^185930-3	185931	Robert Price	07/2015
1345	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
1346	4*10^185905+91	185906	Robert Price	08/2018
1347	(19*10^185873+131)/3	185874	Robert Price	06/2020
1348	(37*10^185811+377)/9	185812	Robert Price	11/2018
1349	2^617250+9385	185811	Lelio R Paula	07/2013
1350	2^617130+9	185775	Stefano Morozzi	05/2021
1351	39^116749+2	185756	Robert Price	04/2015
1352	2^616924-39719	185713	Enzo Doria	09/2015
1353	2^616712+1867621	185649	Enzo Doria	04/2016
1354	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
1355	8*10^185529-67	185530	Robert Price	08/2019
1356	4*10^185355+9	185356	Robert Price	05/2015
1357	(16*10^185347+89)/3	185348	Robert Price	03/2021
1358	2^615622+76639	185321	Enzo Doria	05/2016
1359	2^615591+1879223	185312	Enzo Doria	08/2016
1360	2^615503+1876643	185285	Enzo Doria	07/2016
1361	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
1363	(4*10^185221-91)/3	185222	Robert Price	03/2018
1362	(7*10^185221+131)/3	185222	Robert Price	06/2020
1364	(62*10^185216-413)/9	185217	Robert Price	09/2021
1365	(232*10^185180+17)/3	185182	Robert Price	04/2021
1366	56*10^185139-3	185141	Robert Price	03/2020
1367	(28*10^185105+47)/3	185106	Robert Price	02/2021
1368	2^614783-2790097	185069	Enzo Doria	12/2015
1369	2^614745-29323	185057	Enzo Doria	07/2015
1370	(((((((((((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
1371	(49*10^184993-67)/9	184994	Robert Price	03/2019
1372	(5*10^184954-191)/3	184955	Robert Price	05/2021
1373	(14*10^184950+211)/9	184951	Robert Price	04/2018
1374	2^614315+81353	184928	Enzo Doria	08/2016
1375	2^614294-1849961	184921	Enzo Doria	08/2015
1376	2^614266+1877809	184913	Enzo Doria	08/2016
1377	(185*10^184878-11)/3	184880	Robert Price	10/2020
1378	91*10^184867-9	184869	Robert Price	06/2021
1379	2^613715-1860727	184747	Enzo Doria	11/2015
1380	(4*10^184730+89)/3	184731	Robert Price	08/2021
1381	2*10^184723+41	184724	Robert Price	05/2018
1382	(49*10^184703+293)/9	184704	Robert Price	03/2021
1383	2^613487-349987	184678	Enzo Doria	07/2015
1384	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
1385	14^161089-161089^14	184629	Serge Batalov	05/2016
1386	2^613033-114621	184542	Enzo Doria	05/2015
1387	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
1388	2^612341-1604809	184334	Enzo Doria	05/2015
1389	(11*10^184308-161)/3	184309	Robert Price	11/2021
1390	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
1391	(14*10^184150+37)/3	184151	Robert Price	12/2018
1392	2^611731-4837	184150	Yves Minet	08/2018
1393	3*10^184124-7	184125	Robert Price	08/2015
1394	2^611628-24537	184119	Enzo Doria	08/2013
1395	3*10^184110+13	184111	Robert Price	07/2018
1396	2^611460+71881	184068	Enzo Doria	04/2016
1397	4*10^184004-63	184005	Robert Price	10/2018
1398	2^610982-1867301	183924	Enzo Doria	03/2016
1399	3*10^183872-49	183873	Robert Price	07/2018
1400	2^610597+1178897	183809	Enzo Doria	05/2016
1401	(8*10^183773-269)/9	183773	Robert Price	09/2021
1402	(65*10^183768-29)/9	183769	Robert Price	01/2021
1403	(17*10^183764+31)/3	183765	Robert Price	01/2019
1404	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1405	2^610401+1277	183750	Lelio R Paula	07/2013
1406	2^610356-1849019	183736	Enzo Doria	08/2015
1407	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1408	23*10^183710-7	183712	Robert Price	02/2020
1409	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1410	(4*10^183659+149)/9	183659	Robert Price	04/2018
1411	2^609846-1834251	183582	Enzo Doria	07/2015
1412	10^183546+1547323	183547	Patrick De Geest	02/2021
1414	10^183546-800000001	183546	Robert Price	09/2020
1413	10^183546-584297	183546	Patrick De Geest	02/2021
1415	(23*10^183477-71)/3	183478	Robert Price	07/2020
1416	11^176176-240	183469	Enzo Doria	11/2012
1417	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1418	6*10^183429+53	183430	Robert Price	05/2020
1419	(28*10^183403+191)/3	183404	Robert Price	02/2020
1420	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1421	2^608965-113989	183317	Enzo Doria	10/2014
1422	A005165(43592)	183312	Serge Batalov	07/2017
1423	(61*10^183294+119)/9	183295	Robert Price	05/2019
1424	2^608814-461261	183272	Enzo Doria	06/2015
1425	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1426	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1427	2^608293+143807	183115	Enzo Doria	10/2016
1428	2^608164-462419	183076	Enzo Doria	08/2015
1429	2^607950-1862303	183012	Enzo Doria	12/2015
1430	(46*10^182896+683)/9	182897	Robert Price	03/2019
1431	(2*10^182787+73)/3	182787	Robert Price	09/2020
1432	2^607101+1871987	182756	Enzo Doria	05/2016
1433	2^606869-69175	182686	Enzo Doria	11/2015
1434	(23*10^182666-71)/3	182667	Robert Price	07/2020
1435	3*10^182614-11	182615	Robert Price	07/2018
1436	2^606560-357	182593	Enzo Doria	05/2014
1437	66*10^182420+7	182422	Robert Price	07/2020
1438	2^605687+1866983	182330	Enzo Doria	03/2016
1439	2^605655-114445	182321	Enzo Doria	02/2015
1440	94*10^182291-3	182293	Robert Price	05/2020
1441	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1442	(14*10^182177-221)/9	182178	Robert Price	04/2018
1443	2^605174-112751	182176	Enzo Doria	06/2014
1444	2^604761+1874507	182052	Enzo Doria	06/2016
1445	2^604705+1871957	182035	Enzo Doria	05/2016
1446	(14*10^182000+229)/9	182001	Robert Price	03/2018
1447	(10^181996+41)/3	181996	Robert Price	12/2017
1448	(5*10^181950-101)/3	181951	Robert Price	04/2018
1449	2^603915+75233	181797	Enzo Doria	04/2016
1450	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
1451	7*10^181594-57	181595	Robert Price	06/2020
1452	8*10^181580+29	181581	Robert Price	11/2021
1453	(194*10^181369-11)/3	181371	Robert Price	09/2020
1454	11^174145-360	181354	Enzo Doria	10/2012
1455	2^602351-396765	181326	Enzo Doria	08/2013
1456	6*10^181306+17	181307	Robert Price	04/2019
1457	(286*10^181220-1)/3	181222	Robert Price	11/2020
1458	2^601957-113833	181208	Enzo Doria	09/2014
1459	66^99581-65^99581	181193	Robert Price	09/2013
1460	10^181182+383973	181183	Patrick De Geest	04/2016
1461	10^181182-21	181182	Serge Batalov	12/2014
1462	(5*10^181127-29)/3	181128	Robert Price	03/2018
1463	2^601521-29143	181076	Enzo Doria	07/2015
1464	2^601442-2797811	181053	Enzo Doria	04/2016
1465	44*10^181029+3	181031	Robert Price	04/2020
1466	5*10^180992-9	180993	Robert Price	05/2015
1467	10^180979+79477	180980	Patrick De Geest	04/2016
1468	10^180979+107739	180980	Patrick De Geest	04/2016
1469	10^180979-11	180979	Serge Batalov	12/2014
1470	2^601023-113851	180926	Enzo Doria	10/2014
1471	(23*10^180862-143)/3	180863	Robert Price	12/2019
1472	3*10^180852+29	180853	Robert Price	05/2018
1473	(79*10^180710-1)/3	180712	Robert Price	02/2020
1474	2^600300-1852559	180709	Enzo Doria	08/2015
1475	(2*10^180706-77)/3	180706	Robert Price	02/2021
1476	(10^180689+71)/9	180689	Serge Batalov	07/2015
1477	2^600209+76487	180681	Enzo Doria	05/2016
1478	(8*10^180536-269)/9	180536	Robert Price	09/2021
1479	2^599702-369885	180529	Enzo Doria	11/2013
1480	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1481	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1482	(29*10^180432-17)/3	180433	Robert Price	09/2019
1483	4*10^180360+93	180361	Robert Price	08/2018
1484	2^598942+80779	180300	Enzo Doria	07/2016
1485	(38*10^180296+403)/9	180297	Robert Price	10/2018
1486	2^598591-1844797	180194	Enzo Doria	06/2015
1487	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1488	(29*10^180072+691)/9	180073	Robert Price	08/2021
1489	6*10^179970+91	179971	Robert Price	05/2019
1490	(4*10^179963-79)/3	179964	Robert Price	02/2018
1491	(403*10^179944-43)/9	179946	Robert Price	06/2021
1492	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1493	2^597424-1859729	179843	Enzo Doria	11/2015
1494	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1495	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1496	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1497	(29*10^179697+223)/9	179698	Robert Price	09/2018
1498	2^596884+73	179680	Stefano Morozzi	04/2021
1499	(68*10^179656+7)/3	179658	Robert Price	01/2020
1500	(10^179643+173)/3	179643	Robert Price	05/2021

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Probable Primes Top 10000

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